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DEVELOPMENT AND PRELIMINARY VALIDATION OF AN INSTRUMENT FOR THE IDENTIFICATION OF MATHEMATICALLY GIFTED PUPILS IN EBONYI

STATE.

BY

OKEREKE SILAS CHINYERE. PG/Ph.D/9 7/24329.

DEPARTMENT OF SCIENCE EDUCATION UNIVERSITY OF NIGERIA, NSUKKA.

AUGUST, 2008.

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TITLE PAGE

DEVELOPMENT AND PRELIMINARY VALIDATION OF AN INSTRUMENT FOR THE IDENTIFICATION OF MATHEMATTICALLY

GIFTED PUPILS IN EBONYI STATE

A THESIS REPORT PRSENTED TO THE DEPARTMENT OF SCIENCE EDUCATION, UNIVERSITY OF NIGERIA,NSUKKA, IN PARTIAL

FULFILMENT OF THE REQUIREMENT FOR THE AWARD OF Ph.D IN MEASUREMENT AND EVALUATION

BY

OKEREKE SILAS CHINYERE. PG/Ph.D/97/24329.

DEPARTMENT OF SCIENCE EDUCATION UNIVERSITY OF NIGERIA, NSUKKA.

AUGUST, 2008.

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CERTIFICATION

Mr. Silas Chinyere Okereke, a postgraduate student in the Department of Science Education, University of Nigeria , Nsukka with Registration Number: PG/Ph.D/97/24329 has satisfactorily completed the requirement for the award of the degree of PhD in Measurement and Evaluation. Thee work embodied in this dissertation is original and has not been submitted in part or in full for any other Diploma or Degree of this or any other University. ……………………….. ………………………… OKEREKE SILAS C. PROF. B.G. NWORGU SUPERVISOR

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APPROVAL PAGE

This Thesis Has Been Approved For Department of Science Education, University of Nigeria, and Nsukka. ……………………… ………………………….. Prof. B.G. Nworgu Dr. B.C Madu SUPERVISOR INTERNAL EXAMINER ………………………. …………………………….. Prof., Chinedu Mordi D.E.K.N Nwagu EXTERNAL EXAMINER HEAD OF DEPARTMENT

………………………... Prof. B.G. Nworgu

DEAN OF FACULTY

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DEDICATION

This work is dedicated to God, the giver of life, knowledge and wisdom; it also dedicated to my wife, Anthonia Okereke and my in-law Miss Cordelia Okoye.

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ACKNOWLEGEMENTS The first authority to acknowledge is God, the giver of wisdom and true knowledge for the successful completion of this work. The next authority is Prof. B. G. Nworgu whose guidance and wealth of knowledge contributed immensely to the successful completion of this work. There are other colleagues whose contributions fastened the realization of this mission. They include: Prof.S.E.Omebe, a bosom friend and colleague whose constant warnings over the delay in getting Ph.D. kept forging the researchers on against all odds, Dr O.S.Abonyi , a friend and colleague who took the pain to embark on the factor analysis despite the pressure of work on him then. Dr.I.O.Igwe, whose inputs at the design aspects helped in the successful completion of the work. Ugama , J.O,whose advice on the problems associated with postgraduate programme helped in the successful completion of the work ,Sr.Dr.Elizeliora , whose wonderful words of encouragement aided in the successful completion of the study. This acknowledgment would be incomplete if it fails to recognize Dr. S.N Agwu for his invaluable inputs, criticisms and regular accessibility, all of which were instrumental to the completion of this study. Also recognize are the good roles of my colleagues during the course of the study especially Mrs. Omebe C.A, Mrs. Anugwo, M. and Mrs. Irene Nweke for providing adequate coverage for me when away from place of work.. The acknowledgement goes to the management of Ebonyi State University, Abakaliki, for the co-operation, the cordial and friendly relationship that has existed between them and the workers which aided the completion of this work. The academic and non-academic staffs of the Department of Science are also recognized for the wonderful cooperation given during the study. The acknowledgement is extended to all my friends especially Mr. Ajaero, D.O., Mr. Onwumere, Sunday, Mr.Oleh Eze Paul, Eluu, Patrick and Mr. Omiko Anni. Although words only may not be sufficient to acknowledge your invaluable roles, accept thank very much for the wonderful contribution. The acknowledgement is extended to Isaac and Bros Business Centre, Abakaliki especially the managing Director, Brother Isaac Kanu, for their wonderful roles in typing the work. The Annan World Business Centre is also acknowledged for providing internet services, which made it possible for me to have access to the works of the scholars outside the Nigeria shore. The acknowledgement will be incomplete if it fails to recognize the invaluable roles of the Work And Study Students of Ebonyi State University, Abakaliki especially the various course leaders’ in aiding the data collection processes. The acknowledgement is extended to all the headmasters and headmistresses of the schools used for the usage of their pupils even when schools are in not session. The acknowledgement is extended to the teachers of the primary schools used for their wonderful assistance and the pupils themselves for accepting willingly to participate.

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Finally,Mrs. Okereke Onyidia is acknowledged for her cooperation, encouragement, financial and moral support and those that assisted in one way or the other in the course of this study.

TABLE OF CONTENTS TITLE PAGE ……………………………………………………………………i CERTIFICATION………………………………………………………………ii APPROVAL PAGE……………………………………………………………iii DEDICATION…………………………………………………………………iv ACKNOWLEDGEMENTS……………………………………………………..v

TABLE OF CONTENTS…………………………………...………………….vi LIST OF TABLES…………………………………………..…………………ix

ABSTRACT……………………………………………………………………xi CHAPTER ONE: INTRODUCTION

Background to the study……………………………………………..…………1 Statement of the problem………………………………..……………..………13 Purpose of study……………………………………………………………….14 Significance of the study………………………………………………………13 Scope of the study……………………………………………………………..14 Research Question…………………………………………………………….15

CHAPTER TWO: LITERATURE REVIEW The meaning of Giftedness-Historical Perceptive………………………………20

Characteristic of Giftedness-Perceptive……………...………………………24 Characteristic of Mathematical Giftedness………… ………………………….30 Giftedness Concerns in Nigeria………………………………………………31 Incidence Rate of Gifted Children…………………………………………….33 Mathematical Giftedness and Socio-Economic Status {SES} Of Parents……..33 Parental Background as a factor in Mathematics achievement……………….35 Attitude of Gifted Pupils toward Mathematics………………………………38

Gender and Giftedness…………………………………………………….……39 Tests and Identification Models………………………………………………42 Rationale for use of Inventories for Identification of the Gifted………………46

Importance of Validity and Reliability of Measurement Instrument……….48 Reliability………………………………………………………………...….50 Procedure for validating instrument…………………………………….…53

Theory of Multiple Intelligence………………………………………...……59 (C) Empirical Studies on Giftedness:………………………………………...69

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(D) Summary of Literature Review…………………………………….73 CHAPTER THREE: RESEARCH METHODOLOGY

Design of the Study………………………………………………………….75 Area the Study………………………………………………………..………75

Population of the Study……………………………………………………76 Sample and Sampling Techniques……………………………………………..76 Instrumentation………………………………………………………………77 Numeric Ability Measure…………………………………………………….77 Summary of the Findings…………………………………………………118

CHAPTER FIVE: DISCUSSION OF FINDINGS, RECOMMENDATION, CONCLUSION AND SUGGESTION FOR FURTHER STUDIES

Educational implication of the Study………….……………………………129 Recommendation……………………………………………………………131 Conclusion ………………………………………………………………….131 Limitations of the Study……………………………………………………...132 Suggestions for Further Study…………………..……………………………132 Summary of the Study………………………………………………………133

References ……………………………………………………………………139 Appendix……………………………………………………………………157

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LIST OF TABLES Table 1.0: School Population and the number sample in Ebonyi State…..……76 Table 2.0: Number of items that survived after validation ……………………80 Table 3.0: The four factors and their corresponding items factor loadings and Communality…………………………………………………………………86 Table 4.0: Proportion of the pupils failing/passing each item of the Numeric, Spatial, Quantitative and Creativity Subscales and the whole test……………87 Table 5.0: Proportion of Pupils passing/failing each item of the creativity Subscale..............................................................................................................89 Table 6.0: The Mean and Standard deviation on the Influence of Gender on the pupils’ Performance on the Instrument……………………………………..…90 Table 7.0: Mean And standard deviation on the Gender influence on the Characteristics of the Distribution of the Pupils’ score on the subscales on the Entire Test…………….……………………………………………………..…91 Table 8.0: Mean and standard Deviation on the Influence of Parental Educational Level on performance of Pupils’ on the Instrument……………93 Table 9.0: Mean and standard Deviation on the Influence of Parental Educational Level (Status) on the characteristics of the Distribution of The Pupils’ Scores On The Subscales And On The Entire Test (MAGII)…………96 Table 10.0: Mean and standard deviation on the interactive Effect Effects of Gender and Parental Education status on Pupils’ Performances On The Instrument……………………………………………………………………97 Table 11.0: Pairwise correlation matrix of the subscales and the entire Instrument……………………………………………………………...………99 Table 12.0: Pairwise correlation matrix between the teacher nominating scores and the pupils’ scores on the instrument……………………………..………100 Table 13.0: Z-test Statistics on gender influence on the functioning of the individual items of the instrument………………………..…………….……101 Tables 14.0: Z-test Statistics on gender influence on the performance of the pupils’ on each subscale and on the whole scales………………………....105 Tables 15.0: T-test statistics on the characteristics of the distribution of the pupil’s scores on the whole and on the subscales as a result of parental educational

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status……………………………………………….…………107 Tables 116.0: A One – way analysis of Variance on the external the individual items of the instrument functioned as a result of parental education status…108 Table 17.0: Z-test Statistics on the Influence of parental educational status on the functioning of the individual subscales of the…………………………..133 Table 18.0: A-one –way ANOVA Statistics on the characteristics of the distribution of the pupils’ scores on the subscales and on the entire instrument………………………………………………………………114 Table 19.0: source table for two-way ANOVA on the interactive effects of gender and parental educational level………………………………………..……………………….166 Table 20.0: Source table for the t-test statistics on the different between the mean scores of the pupils on the subscales and on the entire instrument and teacher nomination scores……………………………………………………177

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ABSTRACT The main purpose of the study is to develop and validate in instrument for the Identification of candidates who are gifted mathematically in Ebonyi State of Nigeria. The present study developed and validated an instrument that could be used to identify mathematically precious pupils’ within the Ebonyi State Primary school systems. The instrument was based on constructs, namely: numeric, spatial, quantitative and creativity ability measures, which were considered essential for the description of mathematical precocity of a child. The influences of gender and parental educational status, which were considered serious factors that could affect the pupils’ performances on the instrument, were investigated. Also, the influences of the psychological constructs: numeric ability, spatial ability, quantitative ability and creative ability, which are important constructs of mathematical giftedness, were investigated. Eight research questions were formulated to guide the study. In addition, eight hypotheses were formulated and tested at the 0.05 significance levels. Data for the study were collected from a total of five hundred and one pupils who participated in the study. The summary of the results of data analyses showed that: the instrument is valid and reliable to permit its use as a giftedness identification instrument in Ebonyi Primary school system. Gender significantly influenced the pupils’ performances on the subscales and on the entire instrument. There were very low relationships between the pupils’ performances on thee subscales, although a moderate positive relationship was found between the pupils’ performances on the spatial and Numeric subscales. However, an above-average relationship between pupils’ performances on the spatial and numeric and entire subscales was found. The interactive effects of gender and parental education status are not significant to pupils’ performances on the instrument. Based on these findings of the study, the following recommendations were made: government should be involved in education and training teachers about the behavioural characteristics of pupils; who are gifted intellectually, review the current Teacher Education curriculum to incorporate more courses in test and evaluation, and sponsor more independent researches on giftedness identification and services delivery options for mathematically gifted pupils’ in particular and intellectual precociousness in general at the school levels. Independent researchers should develop and validate giftedness-monitoring instrument, which should b based on rating scale to enable the teachers rate the degree of the gifted characteristics and variables as they are displayed at the classrooms level in Ebonyi State.

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CHAPTER ONE INTRODUCTION

Background to the Study

Experience as well as research findings have shown that education plays invaluable

roles to the lives of the citizens of any nation. Education constitutes a worthy social

index for measuring any country’s level of development and attainment. Ezewu

(1986) corroborated this view when he averred that the tone of a nation depends on

the character of the citizenry. Indeed efficiency in the production of goods and

services in any nation depends more on the available human factor rather than on

equipment and materials rather than on capital. This may be the reason many

advanced countries of the world invest reasonable proportion of their gross national

product in education sector. In order to equip education with more devices that

would enable it achieve the proximate and distant society aims, goals and objectives;

education is usually provided with enough and adequate theories. Education systems

of many nations are normally subjected to constant reforms and reviews. In Nigeria,

the Federal Republic of Nigeria (2004:8) conveyed the intentions of the Nigerian

government to use education as an instrument for national development thus:

The desire that Nigeria should be free, just and democratic society, a land full of opportunities for all citizens, able to generate a great and dynamic economy, and growing into a united and self reliant nation cannot be over emphasized. In order to realise fully potentials of the contributions of education to the achievement of the objectives, all agencies will operate in concert with education to that end. Furthermore, to foster the much-needed unity of Nigeria, imbalance in inter—state and intra state have to be corrected. Not only is education the greatest force to bring about redress, it is also the greatest investment that the nation can make for quick development of its economic, political, sociological and human resources.

In order to achieve these lofty intentions, the Federal Government of Nigeria, as

expected, in the last few years, embarked on a series of reforms of her educational

programmes. The introduction of the adult and non-formal education, and recently the

Universal Basic Education programme are few of the reforms that were made to correct some

of the observed deficiencies in Nigerian Education. The Gifted and Talented Children

Education was another reform introduced in order to enable the Nigerian government benefit

from the contributions of as well as encourage equal access to education and equal

development among and within the ethnic groups and among the various segments of the

population (Federal Republic of Nigeria, 2004).

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The 2004 State of Texas Department of Education defined Gifted Education as the

identification and provision of services for children, youth or student who perform at or show

the potential for performing at a remarkably high level of accomplishment when compared to

others of the same age, experience, or environment and who: (I) exhibits high performance

capability in an intellectual, creative or artistic area; (ii) possesses an unusual capacity for

leadership; or (iii) excels in a specific academic field. .In Nigeria, the need to develop all

segment of the Nigerian population may have been the compelling force behind the

introduction of the Gifted and Talented Children Education Programme popularly known as

“operation catch the geniuses young” which was launched in 1982.A planning Committee for

Gifted and Talented Children Education was formed. The Federal Republic of Nigeria (2004)

adopted a working definition, which merely recognised the gifted children as special children

who are intellectually precocious and find themselves insufficiently challenged by the

programme of the normal school and who may take to stubbornness and apathy, in resistance

to it.

The Gifted Education programme has the potential of helping the Nigerian

government achieve her objective of being self-reliant in the long run. Baum, Reis and Max

(1998) indicated the same idea when they observed that the purpose of the education of the

gifted and talented children remains to:

provide young people with equal and maximum opportunities for self-fulfilment through

the development and expression of one or combination of performance areas where

superior potential may be present; and

raise persons who will contribute in solving the problem of contemporary civilizations by

becoming producers of knowledge and arts instead of being mere consumers of

information.

However, as demonstrated by Delmo cited in Jackson (1996:11): Many of the plans for gifted and talented today are designed to repeat the same mistake made in the 1930’s and in the post-sputnik era. We appear, in many states, compelled to use new or additional funds for the gifted to do the wrong thing even harder than before.

The Gifted and Talented Children Education Programme which has major interest on general precocity, was launched based on some depleted proposals that did not consider the mathematical component of the nation’s curriculum and many important policy statements in the identification. As a way of concretising her campaign for general precocity, the Federal government of Nigeria (2004) merely stated that government had already directed that

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children, including the gifted as well as those with physical, mental and learning difficulties, must be provided for under the education system. Consequent upon this, the Nigerian government went into the Programme implementation proper. Nonetheless, as rightly pointed out by Igboke (2002) that implementation of policies in Nigeria is more problematic than planning it, the hasty way and manner Gifted and Talented Children Education Programme was launched made the stakeholders in the programme lose sight of the specific virtues that should have been considered very important in its continuity and implementation. Less important issues were given important considerations. All these faulty elements that were hastily introduced and / or omitted, one of which is the central thrust of the present study, need to be readdressed. The presence or absence of these elements has created a number of implementation problems, a feature that is least expected at this stage of the programme implementation. The first oversight was the failure to set the modalities for the identification of children

with the specific academic abilities. This aspect of giftedness is equally if not more important

than the general precocity that was being emphasised. Children with specific academic field

giftedness are children who are gifted or talented as identified by professionally qualified

persons, who by virtue of outstanding abilities are capable of high performance in specific

content areas such as Mathematics, physics, and English e.t.c. but may not demonstrate equal

or comparable abilities in other subject areas. These children require differentiated

educational programme and / or services beyond those normally provided by the regular

programme in order to realise their contributions to self and the society.

Giftedness in mathematics, physics, sciences normally belong to the specific academic

field giftedness. Available and documented literature (Okafor, 1988) on the space exploits of

the United States of America demonstrated the importance of the specific subject content area

ability. As relayed by Okafor (1988) when the American ingenuity was being challenged by

the Russian’s space exploits, America was forced to change her school curricula in favour of

mathematics and rocketry and few years latter American did not only conquer the space but

overtook Russia in the space exploit. The cited example provides much evidence to attest for

the need to include this aspect of giftedness if the stakeholders had wanted to reap fully the

advantages accruing from Gifted Education Programme. However of interest in the present

study is giftedness in mathematics. Miller (1990:2) defined Mathematics Giftedness as “an

unusually high ability to understand mathematical ideas and to reason mathematically, rather

than just a high ability to do arithmetic computations or get top grades in Mathematics”.

Work in this aspect of giftedness has given birth to terms such as mathematically talented,

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mathematically gifted, and highly able in Mathematics being generally used to refer to

students and pupils whose mathematical abilities place them in the top 2% or 3% of the

population from all cultural, racial, ethnic and socio-economic backgrounds.

The Nigerian Gifted children education programme also failed to take of the policies and

objectives. The failure of the stakeholders to accommodate the Federal Republic of Nigeria

(2004) intention to use mathematics education as bases for scientific and technological

advancement as well as to achieve self- reliance is a case in point. The much emphasis on

general precocity makes the programme apparently weak in addressing the nation’s intentions

and philosophy. Bajah (2000) observed that no nation can make any meaningful progress in

this information technology age, particularly in economic development without technology

whose foundations are science and Mathematics. The state of art in the Nigerian Gifted and

Talented Children Education makes one believe that the stakeholders in the Nigerian

education industry are not even unanimous on the particular developmental trajectory

envisaged for the country.

Further, the inability to develop a working definition of giftedness to aid service delivery within the Nigerian context is another omission. Pamberton (2006) identified disagreement over the definition of giftedness and creativity as one of the problems of implementation of the Gifted Education programme the world over. The same problem of disagreement over the definition of the gifted had hitherto hampered the location of gifted and creative children in Nigeria. Experts in the area of giftedness, the federal government, and state education agencies are expected to have by now developed both working and operational definitions of giftedness. The importance of developing a working definition is conveyed in Pamberton’s (2006) observation that the many ways in which pupils can be construed gifted and creative are theoretical framework from which they are reflected in the development of measurement devices. Disagreement over the definition of giftedness has created many misconceptions of giftedness the world over, which undermine the understanding and catering for the needs of the gifted children. However, in the more advanced countries of the world, there are a lot of operational and working definitions being advocated for and adopted. The advantage of this multiplicity of definitions put up by the stakeholders in Gifted Children Education the world over namely; parents, teachers and other professionals is that they create more awareness and understanding of giftedness as well as generate variety of tags or labels often used in association with giftedness (Department of Education, 1997).They also aid in the designing measurement devices for the gifted.

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Today in these advanced countries, researchers, educators and organizations have

fashioned definitions commonly used to identify the characteristics within their educational

systems. The most popular of these definitions and of course the only one that has remained

steady with few changes is proffered by Marland in a report to US congress cited in Eric

(1990:2), which states thus:

Gifted and talented children are those identified by professionally qualified persons who by virtue of outstanding abilities are capable of high performance These are children who require differentiated educational programmes and/or services beyond those normally provided by the regular school programme in order to realize their contributions to self and society.

The same report continued: children capable of high performance include those with demonstrated achievement and or potential ability in any of the following area singly or in combination: General intellectual ability; Specific academic aptitude Creative or productive thinking; Leadership ability Visual or performing arts; psychomotor ability. The effective education of these calibres of children is inextricably linked with the efficiency

of the identification procedure. The identification process must be such that will carter for all

these variables earlier mentioned. Salvia and Yesseldyke (1981) and Department for Gifted

Children (2006) stated that identification is a two- stage process – screening and actual

identification. To them screening is an initial sorting of all the students into two groups-those

who are likely to be candidates for the gifted education programme and those who will not be

served by the programme. Department for education of the gifted (2006) observes that the

second step in all identification programme is the actual identification. The actual

identification consists of close examination of all the successful candidates from the first

stage. The aim at this stage is to establish a group of pupils suspected to have high ability to

be suitable candidates for the Gifted and Talented Children Education Programme. This may

be the reason Gowan cited in Jackson (1980) termed this stage the “reservoir of talents.

Identification here means to test the pool of the “potentially gifted” on different tests of

aptitude and achievement in order to identify those who need immediate attention. Johnsen

(2004) observes that variety of measures of pupils’ capability and potential can be used when

identifying gifted children. These may include portfolios of pupils’ work, classroom

observation, achievement measures and intelligence scores. Most education professionals

(Department of education for the gifted, 2003) accept that no single measure can be used in

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isolation to actually fulfil the entire two part- process of identification of the gifted pupil.

Varieties of instruments are employed depending on the level of identification and suitability

of the device. Miller (1990) corroborated the same view when he enumerated intelligence

tests, creative test, achievement tests, aptitude tests, and out-of-grade-level aptitude tests etc.

as tests that could be used for the identification. Whatever the nature of a child’s giftedness

may be, early identification is necessary to enable the government plan and provide suitable

specilialised programme for the gifted children. This is also necessary in order to enable the

government obtain and keep a statistical record of the gifted children. Reiterating and

emphasising the need to have an accurate statistics (i. e. identification) of the gifted and

talented persons, Oladokun cited in Makinde (1993:105) opined that:

It cannot be said that Nigeria does not have our own fair share of the gifted and talented. No, it is simply that, to paraphrase a famous poet, they are like roses that blossom in the desert destined to grow, boom and die unnoticed and unappreciated. Adding that even though we have no census on them nor do we have scientific means of identifying them, they do come to our attention once a while.

Besides the need to keep an accurate statistical record of the gifted, the need to provide an enabling environment for them to develop themselves and the Nigerian society at large seam more demanding. Incidentally, for want of instrument for the effective identification of the gifted children in Nigeria the planning committee adopted, contrary to expectation, the observational- related technique instead of formal testing technique as an identification strategy for the Nigerian Gifted and talented Children Education Programme. Specifically, nomination procedure was recommended. The planning committee on gifted and talented children education programme put up an identification mode which read thus: Two pupils are to be nominated from each primary school of a local Government Area for the Local Government area screening based on the results of their continuous assessment. Two pupils again will be nominated from each Local Government Council level for the state level based on the results of their continuous assessment. Ten pupils from each state will be nominated for the gifted and talented education programme. The adoption of the nomination procedure generated new sets of problems that are hampering the effectiveness of the specialised programme. There is, therefore, a need to refocus and redirect the Nigerian Gifted and Talented

Children Education Programme. One way of redirecting the implementation of the

programme is to retool the identification of the gifted pupils to include children endowed

with specific academic field exceptionalities with mathematics and other mathematical

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sciences as areas of interests. The rational for these proposals are that: Mathematics is of

immense benefit to the development of science and technology in any nation. Its utilitarian

values are gradually being felt in virtually all spheres of human endeavours namely:

engineering, social sciences, physical sciences and business etc. Even fields of specialization

like law; Christian religious studies and other arts courses hitherto known to have alienated

themselves from Mathematics now demand a sound knowledge of Mathematics from

candidates or students who wish to major in them.

This increasing importance and attention to Mathematics is summarized by Ukeje

(1997: 5) thus: “the fact that modern society depends so much on Mathematics stem from the

fact that without Mathematics there is no science, without science there is no modern

technology and without modern technology there is no modern society”. In other words

Mathematics remains the precursor and the Queen of science and technology. The scientific

and technological capability of a nation is the only social index and determinant for assessing

the economic progress, prosperity and power of such a nation. To Spiegel (1956)

Mathematics is the language of modern science and technology and learning Mathematics is

learning the language of modern civilisation. All these reasons may have compelled Ale

(1979) to believe that Mathematics and mathematical principles could apply to virtually

everything, adding that if our society is to develop along modern trend then mathematical

knowledge must be considered seriously. Aminu (1989) corroborated this view when he

observed that Mathematics does not only liberate the mind and give an individual an

assessment of intellectual ability, but points to direction of improvement. Probably, all these

benefits may have accounted for the reasons the advanced countries of the world spend

reasonable proportion of their Gross National Product in the development of the

mathematical component of their education curriculum and why the Mathematics content of

any Nation’s School curriculum is normally slated for review whenever malfunctioning

within the education system is suspected and new developmental or alternative programmes

are being anticipated.

However, the absence of instrument for the identification of exceptional abilities in

mathematics is another serious impediment to the proposal. Interestingly, the present study is,

principally, an organised search for an instrument, which could be used, for the identification

of mathematically gifted pupils in Ebonyi State Primary Education System.Thorndike and

Haggen cited in Okereke (2002) appeared to be confronted by the same problem when they

provided a list of possible steps to adopt in securing such needed instrument whenever a

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research worker is in need of one. They observed that whenever a research worker is

confronted with the scarcity of instrument for his work; he has the option to adopt, or adapt

an existing instrument or develop the needed instrument.

The first possibility open to the researcher is to adapt an instrument for his work. Adaption demands that an existing instrument(s) for the same, similar, or different purpose be modified to meet his present research requirement (Encarta Premium, 2007). In Ebonyi state there are no achievement tests or aptitude tests already in existence for the identification of mathematical giftedness, or for similar or other purposes that could be instantly modified to help in the identification of gifted pupils in Ebonyi State. There is incidentally the National Examination of Nigeria, which has been in use for the purpose that could be adapted to serve the he purpose of identification at the local government level of Ebonyi state. The problem with the proposal to adapt is that the instrument is scarce at the school and local government levels of identification. This makes adaption a highly unsuitable proposal in this circumstance. Another possible procedure that could be used is adoption. Adoption demands that an

existing instrument be accepted as it were for use without any modifications (Encarta

Premium( 2007). Again there are no achievement tests or aptitude tests to adopt in Ebonyi

State School System. There is, however, the National Examination of Nigeria (NECO), which

could be adopted for this purpose. The problem with the recent proposal is that it is scarce

especially at the local government and state levels of identification. Besides, it contains very

few constructs, which address mathematical giftedness. Further, the National Examination

Council of Nigeria (NECO) instrument currently in use consists of two sections, namely:

Mathematics and English. According to Henkin (1972) mathematics relate to English in that

mathematics uses a special English language or uses English languages in a special way, and

learning Mathematics involves learning new linguistic patterns. Thus, a child who is good in

English language will usually record good performances on the instrument not necessarily

that such a child is gifted but because of his/her ability in English language. In addition, the

same strong English language influence on the instrument as a result of the predominance of

the Numeric subscale makes the instrument quite unfair and disadvantageous to a child who

does not speak English as a first language or a child who has very poor background in

English language (Mcguinness, 2003). This makes socio- economic status, ethnicity, culture

and parental background of a child serious treats to the use of the instrument to accomplish

the purpose of identification of giftedness.

The only option left for the present work is to develop and validate an instrument for the

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identification of mathematical giftedness in the Ebonyi State Primary School System. In

developing and validating an instrument, there are three possibilities, namely; developing and

validating a teacher- made achievement test, an aptitude or an instrument based on distinct

mathematical constructs. A teacher – made achievement test could be developed and

validated for the identification of gifted and talented children in Ebonyi State. The problem

with this idea is that over-achievers, that is, those children who are keen at obtaining very

high scores for the sake of it may be unduly advantaged. The associated problem is that such

children may find it difficult to cope when faced with high-level intellectual tasks such as

reasoning. Secondly, in teacher- made test, the class teacher does the sampling of the contents

on which test items are based. The teacher’s test and the items will vary as the teachers. The

test may be hurriedly and haphazardly constructed. There may be no item blueprint, no try-

outs, item analysis or revision. Because of these the quality of the item might be quite low

and only local classroom norms for interclass comparison can be provided with this test

(Menhrens and Lehman, 1978:463). All these would affect the efficacy of the identification

mode.

Apart from these shortcomings of the teacher- made tests, if it becomes necessary to

compare the standard of pupils’ performance in relation to those of their counterparts in other

schools, the result of the teacher- made test cannot facilitate such comparisons. In addition,

teacher- made tests are achievement tests and according to Nworgu (2003) are designed to

measure what an individual has learned. Achievement tests are tied to a particular academic

curriculum. It therefore tends to tap recent learning and it is more or less used to evaluate an

executed curriculum and not to tap what one can do in future. Finally, there would be ceiling

problem. So, developing and validating a teacher- made test was not suitable in this study.

To develop and validate an aptitude test based on specific construct(s) should have been

a more possible option. However, there is yet a problem associated with the proposal. In the

opinion of Enyi (2006), an aptitude test is a test design to tap what a child would be able to do

in future not necessarily to ascertain the learner’s progress after undergoing a unit of

instruction or to identify a learner’s condition. Identification of giftedness is synonymous

with identification of human condition, which is an endowment in specific areas of endevour.

So, developing and validating an aptitude test based on specific construct(s) may not be an

ideal approach in the study otherwise some essential constructs of mathematical giftedness

would be missed. Indeed an approach that appears relatively more suitable is to develop and

validate an instrument based on some selected psychological constructs of mathematical

10

giftedness. The present approach demands that an instrument equipped with construct(s)

sufficient enough to define the mathematical giftedness of a child be developed using

instrument development steps as contained in (Thorndike and Haggen; 1969). Necessary

psychometric properties principally among those enumerated by Enyi (2006) would further

be built into the instrument.

One of the important validation procedures missing in Enyi’s (2006) list is construct

validation. Construct validity is the degree to which inference can legitimately be made from

the operationalisations in a study to the theoretical constructs on which those

operationalisations were based (Trochim, 2007). Constructs are themselves mere labels and

the need to ascertain the accuracy of the labels is important in this work. They relate more to

generalisation from the study to concepts of the study. Such accuracy would be determined

through construct validation. Construct validity is usually assessed using the multitrait-

multimethod matrix method. The method entails demonstrating that the measure or

instrument has both convergent and discriminant validity. In other words, there is the need to

show that measures that are theoretically supposed to be interrelated are actually, in practice,

highly interrelated as well as demonstrate that measures that should not relate are actually

not.

The employment of well-developed and validated instrument which has both

psychological and psychometric qualities comparable to NECO G.I.F.T. instrument presently

used at the federal level of identification would control for the noted flaws or abuses in the

identification of children with general precocity from penetrating into the current exercise.

Employment of such instrument in the identification of mathematical giftedness would ensure

that:

(i) Teacher’s opinion and bias of a child has virtually no effect on the result since the gifted student produces the scores with which the comparisons are made by themselves, and

(ii) It would serve as an accurate predictor of the pupils’ giftedness in a wide range of

areas. Further employment of such instrument equipped with adequate psychological and

psychometric attributes would ensure that the suspected pupils’ interest; aptitude, creative

and abilities are taken care of in the identification. These are important qualities missing in

the NECO instrument and which would serve, as a demerit should it be utilised for the

identification of mathematical giftedness. The new instrument must be equipped by

Gardner’s (1983) psychological construct as contained in Marland’s (1972) report and which

are included in Nwana’s (1993) list of constructs for developing gifted children instruments.

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In the opinion of Dave (1979) cognitive psychologists, through factor analysis, have

identified mathematical abilities, verbal fluency abilities, spatial perception abilities,

analogical reasoning, series and sequence manipulation abilities and spatial social skill as

different components of human intelligence. Mathematical ability, an aspect of general

intelligence, has two important elements, namely; reasoning and computational abilities.

Thus such constructs as numeric ability, Quantitative reasoning ability, spatial ability and

creativity Numeric ability measures the pupils’ numerical reasoning ability. According to

Price water house coopers’ (2007) the numeric ability provides us with consistent and

effective measures of candidates’ numerical problem solving abilities and Moonmaden

(2007) added that they provide for both basic and advanced skills in handling mathematical

calculations . Cooijmans (1999) viewed numeric ability as synonymous with the verbal

ability, but exposure to numerical ability varies more per individuals than in the case of

language, which explains why numerical ability correlates slightly low with G than with

verbal ability. This scale thus contains items developed to assess the numerical ability of the

participants. In the opinion of Wolfe (1990) numerical ability or mathematical computations

is assumed rightly or wrongly before entering college and there is no direct instruction on

mathematical computation in college. Numeric ability or mathematical computation is

different from quantitative ability, which is neither the ability to solve simple arithmetic nor

advanced calculus. Quantitative ability is required for some discipline especially for the

description of mathematical giftedness. According to wolfe and Haynes (2002) quantitative

ability provides pupils with the ability to use quantitative information for the description,

discovery, analysis and problem solving. It plays critical roles just as the spatial ability in

describing mathematical giftedness especially in computation aspects such as in computing

compound interest. Wikipedia, the free encyclopaedia (2007) defines spatial ability as the

ability to mentally manipulate 2- and 3- dimensional figures in space. The specific cognitive

test used to measure the spatial ability is the mental rotation tasks. Lohnmans (1993) shows

that spatial abilities are good measures of G. Spatial ability is an application of pattern of

reasoning, which is older than verbal and numerical abilities. Spatial ability correlates lowly

with G than do verbal and numerical because in human beings the verbal ands numerical

abilities have overtaken spatial ability. According to Alonso (1998) men achieve one

standard deviation higher than their female counterpart. Tests of spatial ability are good

measures of practical and mechanical skills, which are useful in predicting success in

technical occupations. They show substantial practice and training effects. Spatial ability

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relates moderately with the creative ability. There are, however, over sixty different

definitions of creativity. According to Wikipedia, the free Encyclopaedia (2008) creativity is

a mental process involving the generation of new ideas or conceptions, or new associations

between existing ideas or conceptions. This is why Wikipedia, the free Encyclopaedia (2008)

observes that creativity consists largely of re-arranging what we know in order to find out

what we do not know. Thus the product of creativity usually shows some degree of

originality and appropriateness. Evidence of studies by Guilford and Barron cited in

Wikipedia, the free Encyclopaedia (2007) suggested that correlations between creativity and

intelligence were low enough to warrant treating them as separate concepts. Hately (2003)

observed that all these separate factors correlate very closely with a concept called ‘G’ (i.e.

general intelligence factor) and G correlates closely with I.Q and I.Q is a fair predictor of all

types of intelligence.

The next issue to consider along side the psychological constructs is gender. This is so

because the exact position of gender on the achievement of the gifted child is not yet known

although studies (Science Blog, 2004) have indicated that there is gender inequality in favour

of boys. However, Blog (2004) observes that mathematical giftedness seems to favour more

boys than girls, appearing an estimated six to 13 times more often in boys than in girls. There

is no explanation to this but prenatal exposure to testosterone is believed to be the cause. One

influence of this exposure is its selective benefit to the right half of the brain, which induces

hemispheric differences in girls but not in boys. Davis and Rimm (1985) attributed the under

achievement of the females to both internal and external factors. The external causes include

sexism and the lack of resources. Women receive fewer graduate fellowships and lower

salaries. In addition, they remain primarily responsible for childcare and are thus forced to

achieve at less than their potential due to their culturally relegated role as primary parent and

home managers. Shea and Bauer (1994) enumerated personality causes of under achievement

in females to include two unique socialization patterns:

(a) The gifted impostor phenomenon (i.e. a personal belief that one is not truly as successful as others believe) and (b) Cinderella complex (wait to be rescued from personal responsibilities by a male partner). Silverman (1986), however, observes that females who achieve with highly degree in mathematics share the beliefs, values, behaviours and expectation of both males and females. Another factor that merit necessary consideration is the family socio economic status

of the gifted children. This is so because family socio- economic status indicates many

13

influences beyond the issue of financial and informational resources for supporting the gifted

and talented in fulfilling further potential. Hovt and Hebelor (1973) suggested that the

aspirations and expectations the family holds and transmits become critical to the limits and

opportunities which children receive. According to Marine and Green Berger (1978) socio

economic factors are more powerful determinants of the educational aspirations and

expectations of the boys than they are for girls. Specifically, more prominent among the

socio-economic variables that may affect a child’s giftedness is the parental educational level.

Parental involvement has been identified as one of the several factors that promote students’

success (Coleman, 1987, Epstein, 1990 and Uzoezie, 2004). As indicated by Uzoezie (2006)

the factors that may influence parents’ desire to participate in their children’s schooling can

be divided into three areas, namely: personal factors/ psychological factors, contextual factors

and socio-cultural factors referred to as demographic factors. The socio- cultural factors are

important in understanding parents’ level of participation in their children education. Few

studies have reported that parents from the middle and high socio- economic background are

more likely to participate in their children’s education than parents from low socio-economic

background (Epstein, 1990).

Statement of Problem In Nigeria, a series of educational reforms have been made. All these reforms are

made in a bid to address educational challenges, which had hitherto hampered the quick

realisation of the national objectives. The Gifted and Talented Children Educational

programme which aims at helping Nigeria to achieve an aspect of her national objective of

being self - reliant at the long run could as well be a useful reform towards stimulating

scientific and technological developments. The documented literature on the experience and

developmental trajectory of the advanced countries such as United States of America and

Japan, along whose philosophies our educational policies are patterned along indicate that

there is a need to emphasise the identification of children who are gifted in specific academic

content areas as well. This calibre of persons stimulates developments more than those with

general precocity.

These calibres of gifted and talented individuals are needed in virtually every field of human endeavours. However, since the Federal Republic of Nigeria {(2004) specifically believes in using mathematics as a base for the anticipated Scientific and technological development, there is the need to start the campaign with Mathematics. Unfortunately, there is no instrument to this effect in Ebonyi state Education system and Nigeria in general. In

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order to address and possibly arrest the situation if the anticipated identification of mathematical giftedness would not suffer the same problems as observed with the identification of general precocity, there is a need to make available, ahead of time, an instrument that could be used to fulfil this purpose. How to develop, validate and recommend an instrument that could be used for this purpose is the major preoccupation of the present study. It is also an educational gap, which the researcher would be attempting to close. The instrument being sought after cannot be teacher-made or standardised achievement.

Otherwise, the identification will only provide information on the interest and computational

abilities of the pupils. Standardised aptitude or intelligence or creative cannot be singly used

otherwise some of the essential constructs and traits of mathematical giftedness would be

sacrificed. The needed instrument must contain sufficient number of constructs or traits of

mathematical giftedness as contained in Marland’s (1972) report. The instrument being

proposed must thus contains the following four sections, namely: Numeric ability measure to

take care of the students’ interest and ensure subject matter placement, Quantitative ability

measure to test the pupils’ ability to handle number relationship, Spatial ability measure to

measure the pupils’ ability in observing spatial relationship and Creativity ability measure to

tap the pupils’ creative reasoning which is an essential attribute of mathematical giftedness.

The present study aims at developing; validating and recommending an instrument

equipped with these necessary and adequate mathematically construct that could be used to

identify mathematically precocious pupils at the local government area levels of Ebonyi State

of Nigeria. The problem of study posed as a question is: What instrument could be developed

and validated to aid in the identification of pupils gifted in mathematics in Ebonyi State?

Purpose of the study The primary purpose of the study was to develop and validate an instrument that

would be used to identify more efficiently Mathematics giftedness within the Ebonyi state

school system. Specifically, this study determined:

1) The validity of the items of the instrument for the identification of mathematical giftedness within the Ebonyi State Primary School System (MAGII) 2) The reliability of the instrument for the identification of mathematical giftedness within the Ebonyi state primary school system (MAGII). 3) Whether the items of the instruments function differently as a result of the pupils’ gender. 4) The extent the items of the instrument function differently as a result of parental educational status. 5) The characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument as a result of gender.

15

6) The characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument as a result of parental educational status. 7) Whether the interactive effects of gender and parental educational level on the pupils’

achievement on the instrument is significant.

8) The Intercorrelation coefficients among the subscales as a measure of the giftedness

predicting ability of the subscales.

9) The intercorrelation coefficient between the teacher’s nomination score and the pupils’

scores on the instrument.

Significance of the Study

The present study is important in that the result of the findings made both theoretical

and practical contributions to the development of the identification modes for the Gifted and

Talented Children Education Programme in general and the Nigerian case in particular. The

examining bodies, researchers and stakeholders in the Gifted and Talented Children

Education Programme and the Nigerian society at large would benefit enormously from some

of the theoretical and practical contributions.

Practically, over the year the identification of the general precocious pupils from the

classrooms has experienced a little problem due to the absence of identification instrument(s).

The present study was deemed fit in that its result would make available an instrument that

could be used to improve the efficiency in the nomination of the gifted and talented at the

school levels. Furthermore, the greatest problem that confronted the identification of pupils

with general precocity is the near lack of identification instrument at the local government

and school levels. The present study developed and validated an instrument that would be

used as an alternative either to monitor the giftedness and talented ness of the pupils from

time to time or as an alternative to the present National Examination Council of Nigeria

(NECO) GIFT identification instrument. Other colleagues, stakeholders in the Gifted

Education Programme would be informed of this during conferences, workshops and

seminars.

In any programme implementation there is always the need to identify new areas that

may need further works either for the purposes of expansion or as way of injecting efficiency

in the existing programmes. The present work would be beneficial to the policy makers,

researchers and other stakeholders in the Gifted and Talented Children Programme because it

provided information on areas that need further woks to augment the few achievements so far

recorded with Gifted and Talented Children Education programme in Nigeria. Other

16

Colleagues, other researchers and the Nigerian society would be informed of these identified

areas of need during conferences, workshops and seminars.

The work so far done in establishing reliability and validity in this study have provided

some insights into the methods and procedures for development and validation of aptitude

tests and other inventories. Thus future researchers, curriculum planners and examination

bodies would find this work a useful working tool. The result of this work would be made

available to the serving teachers, other colleagues, educationists and other stakeholders in the

Gifted Education through workshops, seminar and conferences. Further, the method of

securing an alternative instrument that would function in exactly the same as way as another

of merit is of uttermost importance to educational researchers. The present work provided

some useful information and insights on the methods and available approaches for achieving

such economy. Other researchers, educationists and stakeholders in the Gifted and Talented

children education Programme would be availed of this useful information during

conferences, workshops and seminars.

Besides, there are few theoretical contributions of the present work, which might be highly

beneficial to other researchers, stakeholders, teachers and the Nigerian society at large.

Existing theories of giftedness have indicated that mathematical giftedness favour the male

more than their female counterparts as a result of differential biological endowment of both

sexes. The Nigerian society and even the wider world would benefit from the findings of the

present study because it would provide information on the veracity of the theory; particularly

the way and manner it concerns a disadvantaged culture such as Ebonyi state of Nigeria. The

finding of the present study with respect to theory and how it concerns a deprived and

disadvantaged culture would such as Ebonyi state be relayed to other colleagues, researchers

and stakeholders in the gifted Children Education Programme and other identical

programmes in Nigeria.

Scope of the study This study was delimited to the development and preliminary validation of an instrument for the identification of pupils who are mathematically gifted from the Ebonyi state Primary Education System (MAGII) in particular and Nigeria education system in general. The study addressed only the following psychological constructs or factors of mathematical giftedness: numeric ability (na), quantitative ability (qa), spatial ability (sa) and creative ability (ca), which are constructs that relate mathematical giftedness. The study involved only pupils nominated as being mathematically gifted in the Ebonyi State Primary school system in 2005/ 2006 academic year. Besides, the influences of the gifted

17

pupil’s gender and parental educational status on the functioning of the items of the instruments for identifying mathematical giftedness were investigated. Research Questions The following questions were posed to guide the researcher accomplish the purpose of the study: 1) What is the validity of the instrument for the subscales and the entire instrument for

the identification of mathematical giftedness within the Ebonyi State Primary School system?

2) What is the reliability index for the subscales and the entire instrument for the identification of mathematical giftedness within the Ebonyi State Primary School system?

3) To what extent do the items of the Instruments for the identification of mathematical giftedness among pupils within the Ebonyi state primary school system function differently as a result of gender?

4) What are the characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument for the identification of mathematical giftedness among pupils within the Ebonyi State Primary School system as a result of gender?

5) To what extent do the items of the instrument for the identification of mathematical giftedness within the Ebonyi state primary school function differently as a result of the parental Educational status?

6) What are the characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument for the identification of mathematical giftedness within Ebonyi State Primary School System (MAGII) as a result of parental educational status?

7) What are the interactive effects of gender and parental Education Levels on the pupils’ achievement on the instrument for the identification of pupils mathematically gifted in Ebonyi State Primary School system?

8) What are the magnitude and direction of the pairwise correlation coefficients between the pupils’ performances on the subscales and on the entire instrument for the identification of giftedness with the Ebonyi state primary school system?

9) What are the magnitude and direction between teacher nomination scores and the scores of the gifted pupils on the instrument?

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HYPOTHESES In addition to the above research questions, the following null hypothesise were tested at the 0.05 alpha level of significance (i.e. p< 0.05): H01: There is no significant difference between the proportion of items that function differently and those that do not function differently due to gender. H02: The characteristics of the distribution of the pupils’ scores as a result of gender are significant. H03: There is no significant difference between the proportions of items of the instrument that function differently and those that do not function differently due to gender. H04: There is no significant difference in the extent the individual items of the instrument function as a result of parental educational Status. H05: There is no significant difference between the proportions of items of the instrument that function differently and those that do not function differently due to the parental educational status. H06: The characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument as a result of parental educational status are significant. H07: The interactive effects between proportion of items that function differently and those that do not function differently due to gender and parental educational status are not significant. H08: The difference between the mean score of the gifted pupils on the instrument and mean teachers nomination score is not significant.

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CHAPTER TWO REVIEW OF LITERATURE

The researcher discussed giftedness in general and mathematical precocity in particular. He also discussed gender influence on giftedness, the rationale for use of inventories for the identification purposes, Procedure for validating instrument in general, a review of empirical related studies to the present. Finally, attempts were made to summarize the literature reviewed. For clarity of purpose and presentation the chapter was organised under the following heading: Theoretical framework, Conceptual framework, empirical Studies and Summary of Reviews. The specific topic (s) discussed under each of the headings Include: (A) Conceptual Framework, Discussed under: (1) a) Meaning of Giftedness- Historical Perspective. b) Characteristics of the gifted- General Perspective. c) Characteristics of mathematical giftedness. d) Gifted concerns in Nigeria. e) Incidence rate of gifted children (2) Factors affecting giftedness: a) Attitude of the gifted pupils towards Mathematics, b) Gender and Giftedness c) Mathematical giftedness and Socio-economic status d) Parental Background. (3) Measurement of Giftedness: a) Tests and Identification model b) Rationale for the use of inventories for identification of gifted children. c) Importance of validity and reliability of measuring instrument, d) Procedure for validating instruments. (B) Theoretical framework: Theory of Multiple Intelligence (C) Empirical Studies (D) Summary of review of literature Conceptual Framework discussed under the following :

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The meaning of giftedness – historical perceptive Historically, giftedness has been closely linked with the concept of genius. This

association began around the turn of the century when psychologists developed tests that

were designed to measure intelligence (Terman, 1925); people who score on the low end of

the scale were labelled retarded and those who scored on the high end were considered

geniuses. The use of intelligence tests as the only measure of giftedness has suffered greatly

from criticism in recent years, primarily because the tests are often biased in favour of the

white middle class and because they penalize children in the differing linguistic styles.

Also, many researchers and educators have come to believe that giftedness is more

than high intellectual ability; it also include creativity memory, motivation, physical

dexterity, social adeptness, and aesthetic sensitivity (Lima, 2001). Another step toward

defining giftedness was by Hollingsworth (1975) and although she defined giftedness in

terms of I.Qs above 170, Hollingsworth believed that children could have other types of gifts,

such as mechanical aptitude or artistic ability (Pritechard 1957).

During the 1840s, the concept of giftedness was expanded further when the American

Federal government began to take interest in the education of the gifted and talented children.

This Federal interest was sparked off during and after World War II when policy makers

perceived a need for technological advancement in order to maintain the nation’s military and

political superiority.

By 1950, congress had passed the National Science Foundation Act, which marked

the first time the Federal Government provided funds specifically for the gifted and talented

(Zettel, 1982). By providing funds for encouraging students to develop their abilities in

Mathematics and physical sciences, the Act led, in essence, to the designation of specific

academic aptitude as a type of giftedness.

Another significant development was the publication of Guilford’s (1959) studies of

the structure of the intellect. Guilford had urged psychologists to explore the area of creativity

or divergent thinking. It was his structural model of the 120 theoretical components of

intelligence that led to the development of tests to measure intellectual abilities other than

those measured by conventional I.Q tests.

The development of creativity tests and results of many studies of the relationships

between intelligence and creativity (Getzels and Jackson 1962) have led many educators to

include creativity in their definitions. Renzulti (1976) considers giftedness to be a

combination of above average ability, creativity and task commitment.

21

Traffinger (1988) in an attempt to answer the question, who are the gifted and

talented?, defined the gifted and talented as those who display exceptional ability or

outstanding performance in one or more of the following areas: general intellectual ability,

specific academic aptitude, creative and productive thinking, visual and performing arts and

leadership ability. In Traffinger’s (1988) opinion, the concept of giftedness is closely related

to the fulfilment of a person’s creative potential through demonstrated record of

accomplishment over a substantial period of time. Marland’s (1972) report contains a

definition of giftedness that has been and continues to be one of the most widely adopted. She

defines gifted and talented children as those identified by professionally qualified persons

who, by virtue of outstanding abilities are capable of high performance. These are children

who require differential educational programmes and/or services beyond those provided by

the regular school programme in order to realize their contribution to self and society.

Children capable of high performance include those with demonstrated achievement and/or

potential abilities in any of the following areas, singly or in combination: General intellectual

ability, specific academic aptitude, creative or productive thinking, leadership ability, visual

and performing arts and psychomotor ability.

Although the definition has been criticized as being limiting (Reis and Renzulli

(1982) and of promoting elitism (Feldman 1979) over 80% of the 204 experts were in favour

of the selection of the categories of high intellectual ability, creative or productive thinking,

specific academic aptitude arts. Close to half of the experts agreed on the inclusion of social

adeptness and psychomotor ability in the definition (Martinson 1975). Mathematical talent

refers to an unusually high ability to understand mathematical ideas and to reason

mathematically, rather than just a high ability to arithmetic computation or get high grades in

Mathematics. This may be why the regulations for educational security act of 1984, which

provides grants for strengthening the skills of teachers and instruction in Mathematics,

science, foreign languages and computer learning have defined the term “gifted student” as “a

student identified by various measures who demonstrates actual or potential high

performance capability in the field of Mathematics, science, foreign language or computer

learning”. Gifted students may come from “historically under represented and underserved

groups, including females, minorities, handicapped persons, persons of limited English –

speaking proficiency and migrants (Mceledlan 1985).

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Students with specific ability in Mathematics may or may not also have high general

intellectual ability. The relationship between these two groups is best considered as

intersecting sets.

The concept of giftedness originated from the field of psychology, specifically as a

part of the study of individual differences. Over the years, its psychological focus was lost

and it became embedded in the field of education - special education. Curriculum and

instruction planners adopted it and the search began for an elusive differentiated curriculum

for the gifted. Gifted children are fast learners and this singular fact distinguishes them from

other children.

For the Columbus group (1991), students with specific academic aptitude are students with specific academic aptitude test in one area such as Mathematics or language arts. Other definitions so far have one element in common - a gifted person is someone who

shows, or has the potential for sharing in exceptional level of performance in one or more

area of expression. Some of these abilities are very general and can affect a broad spectrum of

a person’s life, while others are specific and only evident in particular circumstances, such as

a special aptitude in Mathematics, science or music. The term giftedness provides a general

reference to this spectrum of abilities without being specific or dependent on a single measure

or index.

The Columbus group then advocates that the schools must provide educational experiences appropriate to the needs of all children, including those who are high-ability gifted learners. The group also adopted Marland’s (1972) definition of giftedness stated thus: Gifted and talented children are those identified by professionally qualified persons who by

virtue of understanding abilities are capable of high performances. These are children who

require differentiated educational programmes and / or services beyond those normally

provided by the regular school programme in other to realize their contribution to self and

society. The gifted educations itself is not the study isolated aspect of the giftedness but

interactions of a variety of elements that combine into gifted and gifted education. As a step

towards the development of policies and programmes for the gifted, the concept of giftedness

need to be defined and differentiated from talentedness and high achievement both of which

are two major related characteristics of superior performance. Research studies (Torrance,

1974; and Renzulli, 1989) clarify this issue. The high achieving child is the studious

intellectual who is keen in obtaining higher grades in school; appreciate precise institutions to

execute academic assignment (Kalu –1993) His ultimate goal is to satisfy the requirement to

23

excel and meet his or her need for high achievement. He/She often cannot manage low grades

and consider mistakes a failure. He is a model to both teachers and parents. On the other

hand, a child is regarded as talented if he is highly skilled in the performances of a task,

whether academic or non-academic orientations. This can be in music, fine art, drama,

oratory, leadership, electrical, mechanical and carpentry etc.

Gagne (1977) observed that performance of prescribed movements in a highly

organized way for smoothness and precision in action reflect a high degree of internal

organization. Thus a child can be talented but may not necessarily be gifted or scholarly

oriented. Many mentally retarded and artistic children have been known to be talented in

painting or music.Gifted, as a combination of intellectual and cognitive characteristics means

superior ability in most areas of academic endeavours with a major feature being creativity, a

unique product of exercise. It therefore involves a high intellectual functioning characterized

by divergent and convergent thinking, elaboration, transformation, evaluation (Guilford,

1967) and creativity, product oriented behaviour from high motivation, task commitments,

skill and self-initiated, independent study, project oriented style of learning (Whitmore,

1990). There are general characteristics of fluency in generation of ideas, synthesis of

materials and resources from divergent sources, determination and love for details and

precision. The energy in the gifted brain leads to proliferation in ideas, projects, zeal and

enthusiasm and the demand for knowledge. There is general dislike for routine, superficial

simplicity, inconsistency in logic (Clark, 1979).

Torrance (1970) found that the identification of giftedness from 20% of a given population on an intelligence test alone misses 60% of those who could be identified as gifted by test of creativity. Treffinger and Rennzulli (1986) found that the obstacle to identification and education of gifted children are the use of intelligence – based tests, such as adopting cut- off like the Nigerian Federal or State Common Entrance Examinations. These definitions and identification procedures are harmful to those labelled and unlabeled under them (Traffinger and Renzulli, 1986). Intelligence is dynamic and misleading in its estimate of individual’s potential over a long period of time and for creativity. Intelligence Quotient score alone represents a limited unrepresentative sample of whole sphere of what is called “intelligent behaviours” (Stenberg, 1981; Gardener, 1983). The I.Q. score emphasises the schoolhouse sense of the concept of giftedness, rather than creative productiveness. I.Q. score does not tell us how potential and traits like independent learning skills, interact in the individual. Gifted children are known to possess the following traits independent enquiry, self-initiation and learning discussion-oriented individuals. The general population of students on the other hand is known to prefer

24

structured instructional method, lectures or assignment (Torrance, 1997). It is worthwhile to note that children with specialized ability or talent to a specific subject(s) or performance area(s), like Mathematics, language arts, crafts, electronic equipment, athletics, gymnastic, drama, poetry, fine arts are considered talented and not necessarily gifted. It is not, however, expected that we should place scholarly, high expectations on them. The problem is that the concept of talented and gifted has been used interchangeably or as an adjective which qualifies a noun such as talented musician, gifted poet, talented sculptor (Steward, 1981; Davis and Rimm, 1985). The clarification in the use of the terms in the Nigeria context is necessary so as to minimize or avoid completely some policy muddle about them.

Educational programmes required for each group are costly and unnecessarily escalate

cost. Rise and Renzulli (1982) after an extensive review of literature identified three major

elements in the various attempt to conceptualise giftedness. The three elements tried to

conceptualise giftedness as the following three clusters of interacting traits: above average

intellectual ability, creativity and task commitment. This results in the three-ring conception

of giftedness. Runzulli and associate have argued that the main contribution of the Marland’s

definition quoted profusely is that it has widened the scopes of the conceptualization of

giftedness.Literature on gifted adult (Terman and Oden, 1947; Terman, 1954; Roe 1952)

strongly suggested that the achievement of the gifted in adult is a function of a combination

of the three factors rather than simply a function of high intelligence quotient. In addition to

genetic factors at least two other factors, activation and predisposing factors, are necessary

for developing high ability in Mathematics and science. According to him, activating factors

are those associated with inspirational teachers; predisposing factors are further classified into

two-persistence and question, adding that while persistence is characterized by a “Marked

willingness to spend time beyond the ordinary schedule on a given task, a willingness to

withstand discomfort, Question is that trait which compel an individual to seek more precise

and accurate explanation of phenomena (Brandwein, 1958). According to Brandwein, all

these factors are necessary for developing high ability in science; no one factor is sufficient in

itself although La Salle (1977) agues that the persistence factors should weigh most heavily

in the combination. In a study of the personality of the intellect of successful scientist, Roe

(1952) found the most striking characteristic to be high I. Q.; but she also identified

personality characteristics that coincide with Brandwien, (1958) observation among which

are:

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A general need for independence, autonomy and personal mastering of the environment

Attraction to fact such as might appear mutually contradictory and delight in finding a way to reconcile them.

A precious self-confidence about solving intellectual problems.

Renzulli (1986) then examined these literatures along with extensive study on

giftedness across many disciplines, and concluded that gifted is characterized by interaction

among three traits: above average ability, creativity, and task commitment. In using the term

“above-average ability” to describe the first component of his definition, Renzulli noted that

in effectiveness of intelligence test score above intermediate score in predicting individuals’

success in creative/productive thinking endeavours creates a problem for identification of

giftedness. He rather decided to opt for a definition that recognize that individuals who scores

slightly lower on standardized tests of general mathematical ability, specific aptitude, or

achievement may be the more likely to be recognized as gifted adults. In identifying the

gifted child, look for the student who has above average ability in Mathematics, but not

necessarily the highest scores, on test of general intellectual ability, specific aptitude or

achievement. Success in any field of endeavour depends also on the presence of the other two

factors. The second factor, creativity, is very difficult to define (Renzulli, 1986). Creativity,

in Renzzulli’s opinion, is the ability to meet the criteria for creative performances with

specific performance areas as established by the persons accomplished in that area. Persons

qualified to judge those areas on the basis of the performances or product should make

judgment of creativity.

Finally, an individual must also exhibit task commitment, a refined or focused form of

motivation in energy brought to bear on a particular problem or task on specific performance

area. The interaction of these three clusters of traits is crucial to the definition of specific

academic aptitude (i.e. mathematical precociousness). This is so because each cluster is

equally important in the constitution of the “gifted persons”; that is, a person with high

aptitude in Mathematics but little creativity or commitment in that area is unlikely to develop

into a “gifted” mathematician or scientist. The three must be brought to bear on some

potentially available area of human performance for giftedness to manifest itself and be

recognized.

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Renzulli and associates (1981) attributed this to the lack of reference to the critical non-intellectual factor of motivation – task commitment as one of the problems with Marland’s (1972) definition of giftedness. They argue that these categories do not belong to the same realm of human endeavour and hence create confusion in conceptualising giftedness (Awanbor, 1986). Subscribing to their view, they argue that six categories – i.e. specific academic aptitude and visual and performing arts are in the realm of human endeavours where talent and abilities are required; the remaining four categories belong to performance areas.In Substantiating Renzulli and Smith (1981) posit that a person can bring the process of creativity to bear on a specific aptitude (e.g. Physics, or Chemistry) or visual art (e.g. photography) just as the process leadership and intelligence might be applied to a performance area such as dancing.

A third criticism of the definition is that it is susceptible to abuse and misinterpretation because of conceptual overlap and because test experts would always develop instrument to determine giftedness. The investigator here is faced with the problem of conceptual overlap of these subsections and has decided not to use the THREE- RING conception of gifted model. The instrument will not adopt the Renzulli’s THREE-RING MODEL. The breakdown of the THREE-RING conception of giftedness is as follows:

Early 1920 psychologists; Terman and Thorndike of the United States and Burt and Thomason of Britain had constructed objective group tests of intelligence of achievement in different school subjects. This made it possible to assess the pupils on age scales. Literature has revealed as Terman (1959) posited that intelligence does not necessarily mean the same as giftedness. Intelligence does not subsume giftedness. Also evidence abounds in literature that the most of the world’s inventions are not product of individual who perform in the upper ranges of intelligence test score mainly (Hoyt and McClelland, 1973 and Wallach, 1976).

Above Average ability

Creative task commitment

Creativity Locus of interaction

Fig. 1.0 Cluster that make up giftedness (The Three – Ring Conception).

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Renzulli et al (1981) warned that in defining giftedness efforts should be made to distinguish between proficient learners and adept test takers. For the purpose of determining giftedness, above average ability is seen as that performance high enough to require additional resources and services more than provided in the normal classroom situation. Vernon (1977) argues that giftedness is a matter of degree; one cannot fix any precise point above, which children are adjudged gifted and below which they are adjudged otherwise. He advised that although intelligence test score alone cannot determine giftedness, things like parlova’s dancing and Namtjira paintings could. Creativity is a general concept embracing three behavioural types namely: creative thinking, problem solving and creative expression (Roothby, 1980). Thus it may be stated that a child who is above average and creative may or may not be regarded as gifted or talented. Such a decision has to await a third variable, which is a major element of giftedness – the task commitment.

Task commitment has greater motivational impetus and directed energy in the pursuit

of determined goals than urge or drive (Awambor, 1986). It is not simply a matter of where

there is a will there is a way but a will that is service- assisted. For Galton (1959), it is a will

urged by an inherent stimulus. In Renzulli view, it is the “Psychological yeast”.

Today both logical and operational perceptive are combined in defining giftedness as reflected in the Marland’s (1977) Report. Characteristics of Giftedness-General Perspective Who are the gifted? Are they social isolates? Are they well adjusted and well liked? Are

some of the pertinent questions for the teachers, parents and anybody who is interested in the

gifted education? The exceptional child places more demands on the teachers and parents

because of their uniqueness and susceptibilities. Some will be energetic, verbal and popular;

other will be less social and energetic. Some will be taller than average, others will be shorter

than average. There will be wide differences in social, academic, and personal skills, growth

patterns and motor abilities and socio-economic class, creed and race. The common

denominator that emerges is an outstanding ability in more than one area of human

endeavours. Many gifted children advance through development stages earlier than others.

They may walk before the age of one or start to speak in sentences while their peers are just

struggling to pick simple words.

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Silverman (1988) opines that many gifted children say their first word at six month or

earlier than that. Others do not talk until at the age of three probably, but when they do speak,

they do so well ahead of their peers”.

Gifted and talented children may differ greatly from the list of characteristics we expect

to find. Boston (1978) presents the following list of characteristics, which according to him

are mere generalizations of the characteristics of the gifted and talented children:

Typically learn to read earlier with better comprehension of the nuances of language. Half

of the gifted and talented population have learned to read before entering school.

They read widely, quicklyand intensely, and have a wide range of vocabularies.

Commonly learn basic skills better, more quickly, and with less practice.

Are better able to handle abstractions than their age mates.

Are frequently able to pick up and interpret non-verbal signs and draw inferences than

other children.

Talkless for granted, seeking the “how” and “why”.

Display a better ability to work independently at an earlier age and for longer

periods of time than other children.

Can sustain longer periods of concentration and attention than other children.

Have interests that are often both widely eclectic and intensely focused.

Frequently have seemingly boundless energy, sometimes leading to misdiagnosis of

“hyperactive”.

Are usually able to respond and relate well to parents teachers and adults. They may

prefer the company of older children and adults to that of their peers. According to

Swassing (1984) some like to learn, explore and seek more information than other

children. Gallagher (1981) points out that three skills the gifted have in abundance are:

The ability to relate one idea to another.

The ability to make sound judgment.

The ability to see the operation of larger system of knowledge than is seen by ordinary

citizen (P. 137).

Experts stress the importance of early identification and simulation. This tends to agree

with the federal government intention to catch them young. Identifying children for special

experience i.e. among millions of school age children has a long and difficult history.

Compounding the enormity of the job is the need to avoid “false positives” those who are

gifted but later proved not to be and “false negatives’ – that is those who are gifted but do not

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appear to be. Literature has revealed that even parents of gifted children often find too late,

that exceptional ability is not enough to guarantee that a child will do well in school. Other

characteristics such as motivation and good study habits are equally necessary.

Without help and encouragement gifted children can grow bored and frustrated and many

perform very poorly and often drop out of school.

According to Busse, Dahme, Wagner (1986), given the widespread variation in

defining who the gifted are, it is not surprising that there are substantial differences of

opinion about what characteristics gifted children posses. For instance, Swassing (1984)

provided a list that contains a lot of characteristics that are missing in Boston’s (1978) list.

Swassing (1984) considers both the positive and negative behaviours/characteristics of the

gifted children. Creative and high drive which; Seagoe (1975) deemed important was omitted

in Laycook’s (1979) and Swassing’s (1984) lists.

On the contrary, Laycook (1979) included “co-operation” and sense of humour and “self-critical” traits, which Seagoe omitted. Because of this confusion, Busse et al (1986) used the classroom teachers to obtain a baseline data about characteristics of gifted children. Renzulli and Smith (1980) in their three-ring conception of giftedness identified three

interacting clusters of traits that make up giftedness as: above average intellectual ability,

creativity and task commitment. Hence a child with an above average ability and also creative

may not be adjudged gifted until a third factor – that is task commitment is added.

Creativity is a general concept, which encompasses behavioural types: creative thinking, creative problem solving and creative expression (Roothby 1980).

Literature on creativity identifies ability to deter judgment, above average I. Q.

adaptability, aesthetic appreciation, attraction to the complex and mysterious curiosity,

delight in invention for its own sake, extensive knowledge background, good memory and

attention to details; others are high energy level, enthusiasm, internal locus of control, sense

of mission etc. From these behavioural traits, there are four other traits which have emerged,

namely: self –expressions, specialized productive design/innovative and revelatory (Roothby,

1980). This behavioural trait may be helpful for purposes of easy and accurate identification

of giftedness. These clusters are operational in that they are observable and measurable in and

outside the classroom settings and at an early stage of development. Guilford’s structure of

intelligence (s) Model (1956) has substantial impact on the entire education and

psychological field (Wolf, 1981). Guilford classified human intellect into the following

components: operations, contents and products, which the intellect performs. The operations

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or abilities he further classified into: cognitive, memory, divergent thinking, convergent

production and evaluative abilities. The contents or information he classified into four broad

classes: figural, symbolic, semantic and behavioural. He further identified content as concrete

materials as perceived through the senses. Visual materials have properties such as size, form,

colour, location or texture. Symbolic content is composed of letters, digits and other

conventional signs usually organized in general systems, such as the alphabet, and semantic

content is the form of verbal meanings of ideas for which no example is necessary.

The Mathematics G.I.F.T identification instrument for Nigerian primary schools has used a lot of figural content, visual (spatial) materials and their properties, symbolic and semantic. Characteristics of mathematical giftedness

Mathematically gifted students have needs that differ in nature from those of other

students. They require some differentiated instruction, defined by Tomlinson (1995) as

consistently using a variety of instructional approaches to modify content, process, and / or

product in response to learning readiness and interest of academically diverse students. Gifted

and talented students differ from their classmates in three key areas that are especially

important in Mathematics. These are summarized as:

Pace at which they learn Dept of their understanding Interest that they hold (Maker, 1982). Mathematically gifted students differ from the

general group of students studying Mathematics in the following areas: spontaneous

formation of problems, flexibility in handling data, mental agility of influence of ideas,

data organization ability, originality of interpretation, ability to transfer ideal, and to

generalize (Greene’s, 1981)

Blake (1981) lists the intellectual characteristic of mathematically gifted and talented student

to include: ability to acquire complex discrimination, memorize, and form some concepts

faster and to a higher level than the normal student can do;they also solve problem better” (P-

326).

Further, Reisman (1981) proposed generic factor as a an alternative assessment procedure to cognitive stages, pointing out that implications for applying Piagetian theory to teaching have been strongly supported by Furth and Wails (1974), questioned by Smedslumed (1977), and strongly opposed by Engelman (1971). Reisman proposes these generic factors to describe mathematically gifted students’ characteristics: Learning at rapid rate Attending to salient aspects of situations

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Conserving (e.g. relates transformation and accompanying invariants Retaining information with minimal repetition Understanding complex materials Constructing relationships, concepts and generalization (P.5).

Clear from the above is that no list of characteristics of the mathematically gifted student

includes “computational proficiency” and yet this is commonly used as the criterion that

determines who gets to move to more interesting materials.

Further, research by Carter (1954) using Piagetian stages of development found that learners who are gifted and talented demonstrate all operations earlier than did children with normal ability as one of the cognitive characteristics. Davis and Rimm (1985) included good comprehension, good problem solving skills and ease in recognizing cause- and- effect relationships.

These learners participate at an early age in reading, writing, Mathematics, music, and

artistic endeavour. They are capable of retaining and manipulating extraordinary quantities of

information. They are analytic thinker, capable of manipulating abstract concepts and acting

intuitively. There is even a myth that gifted students do not need special attention since it is

easy for them to learn what they need to know.

Consequently, their needs dictate curriculum that is deeper, broader, and faster than

what is delivered to other students. Mathematics can be the gatekeeper for many areas of

advanced study. In particular, few gifted girls recognize that most college majors leading to

high level careers and professions require four years of high school Mathematics and science

(Kerr, 1997) students may drop out Mathematics courses or turn toward other fields of

interest if they experience too much repetition, not enough depth, or boredom due to slow

pacing. A review of the characteristics of students gifted in the Mathematics is important in

this study since the researcher is involved in the preliminary identification of students

suspected to be mathematically gifted.

Giftedness Concerns in Nigeria

Efforts to recognize the gifted child and his educational need in Nigeria could be

traced to the Federal Republic of Nigeria (F.R.N, 1998) policy statement on special

education. In it, different types of handicaps and the gifted and talented were mentioned and

considered. One objective of the policy is to make educational opportunity available for the

gifted to enable them develop at their own pace for themselves and the Nigerian economic

and technological development. By 1986, government budget for the first time revealed

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provision for gifted education. The policy is then articulated and a blue print developed.

Unfortunately, neither the National policy nor the gifted education blue print contained the

actual definition of giftedness. There was neither a theoretical or operational definition of the

gifted either. The blue prints dwelt much on the description of a whole range of curriculum

types and content that will facilitate learning experience for the gifted. It was not clear what

theoretical positions were represented. No specific programme models were articulated and

recommended, a crucial feature, which negated personal development and training for

teaching the gifted. Gifted teachers, that is, teachers that appreciate originality, or teachers

with similar teaching styles to their learning styles are best teachers for the gifted children

(Bishop, 1968; Shiner, 1980; Davis and Rimm, 1985; Torrence 1984; and Beaudry and

Klavas, 1989) the omission of an operational definition crystallized the first confusion in the

gifted education programme. Assumptions were that the general population and school

personnel (Teachers and principals) already know who the gifted children are. Too, that both

the government and the schools share the same operational definition. The first attempt to

search for the gifted children in 304 local government areas in the Nation yielded a test score

of 24.45% for the brightest pupil. The previous year selection for common entrance

examination yielded a highest score of 85%.

The local government areas did their own screening and many officials and school

principals added their own candidates. Selected pupils were required to score a minimum of

95%. A reaction to the results of the examination to the gifted education brought this

confusion to the limelight. The gifted education programme was then seen as favouritism

“restricted to only few lucky children regarded as gifted”. It was seen as a waste of time,

money and efforts in a futile selective endeavour to pick specially talented and gifted children

when there is so much needed to improve the lot of all school children.

This supported the fact that genius is ninety percent perspiration and ten percent inspirational. The concept of giftedness has been confused with the high achieving studious child who flourishes under the influence of a good nurturing environment. The conceptual muddle, the non-development of specifically trained teachers in gifted education up to masters level in education, and lack of more government funds for wholistic, beyond intellectual performance level gifted identification has slowed down the development in the field of gifted education. We need at least ten years to assess the impact of the products from present School.

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Incidence Rate of Gifted Children There is no dividing line and agreed upon rate of occurrence of giftedness among

children. The Blue print on gifted and talented children suggests 5% of total school

population. The five percent will be selected using a multi stage sampling technique starting

from the local government area – that is the top 5% of the school population will be selected

at the local government level at first stage. These will be screened statewide and 5% of local

government selected. At the national level, 5% of the statewide screened and 5% will be

selected. In practice, the screening procedures recommend that two pupils will be selected

from each school. Ten pupils from each local government area will be selected for the federal

level. Ten students from each state will be selected as state representatives. Awanbor (1986)

presents a conservative view of the incidence at top 2 to 3 percent or the 96th percentile on

standardized tests. Further, Awanbor asserts that a more liberal rate of incidence being

advocated for is to include between 10 and 15 percent of the school age population. Terman

(1959) published his last volume of longitudinal study of 1000 gifted children desired to

include as many as possible much of the brightest percent and using an I. Q of 135 – 140 as a

borderline. However, Vernon (1977) disagrees with the use of this criterion arguing that in

some schools the highest I. Q may be 130, it means that children with I. Q. range of 120 –

130, will be left out. These suggestions appear to provide the needed guideline for deciding

what cut- of to apply in selecting any desired percentage of gifted children for the gifted

programme.

Mathematical giftedness and socio-economic status (SES) of parents

Family socio-economic status indicates many influences beyond the issues of financial and informational resources for supporting the gifted and talented clusters. Majority of families with children who are gifted and talented experience moderate

levels of adaptation and cohesion, suggesting that having a child who is gifted in the home is

not necessarily associated with extreme patterns of family functioning (West, Hosie and

Matthews, 1989). Family relationship may be affected in the areas of the tempo of family

interactions, family system make up, sibling self-perceptions and collective attitude towards

the gifted (Mcmann and liver, 1998). Children who were creatively gifted have been shown

to have family environments that stress independence, have fewer children and exhibit tense

family relationships and more negative affect, resulting in motivation to attain power.

Academic achievers come from cohesive, child centered families in the strong parent

34

–child identification (Olszewski, Kulieke and Byescher, 1987). Families with children who

are gifted and talented have been shown to demonstrate higher levels of adjustment in

problem solving, communication roles and effective responsiveness (Matthews, West and

Hosie, 1986).

Recent research has convincingly established the hereditary contributions to the

mental ability (Bouchard and MCGue, 1981). While it is difficult to separate hereditary and

environmental contributions to extra ordinary talent, we study the family first by setting the

generic heritage and then by creating the environment in which talents and abilities develop

or fail to develop or exercises multiplicative influence (Bloom, 1981).

The literature contains numerous references to the way families contribute to

decisions about types and levels of occupational choice, including psychoanalytic

interpretation of choice based on early inferential relationships and other more eclectic views

of the ways early experience in the family shape personality, attitude and interests

(Fredrickson and Rothney, 1972). Family socio-economic status indicates many influences

for supporting the gifted and talented child fulfil his/her potential. The aspirations and

expectations the family holds and transmits become critical to the limits and opportunities

that children perceive (Hoyt and Hebeler, 1973; Wantanable, 1979, and Samborn, 1979).

Some studies suggest that socio-economic factors may be more powerful determinants

of the educational aspirations and expectations of boys than they are for girls (Marini and

Greenberger, 1978), although such influences may be extended to females and minority

members where the family reinforces cultural stereotypes to the gifted child’s detriment. One

talented young woman who wished to explore the legal profession as a possible field of study

was told by her lawyer father to think about becoming a legal secretary, a more suitable

occupation for a woman. As late as 1979, attorneys in Sears Roebuck and company sex

discrimination suit argued that women do not want better paying jobs and cannot handle

stress, competition or risk. The historical and accepted perception remain that women are not

really suitable candidates for leadership (Tell, 1987). Historically, women are perceived as a

powerful group, as is reflected in discrepancies in salaries and number of females in

executive positions or with doctorates (Curcio, Morsink and Bridges, 1989).

A recent longitudinal study of gifted young women identifies socio-economic status

as a critical factor in predicting career choice and describes how parental education and

higher status occupations interact to determine non-traditional job entry. Surprisingly,

daughter of better-educated parents choose finial careers in medicine while those with parents

35

with college training chose Mathematics and engineering. Young women aspiring to become

nurses and teachers came from families with little education, who were engaged in low status

occupations, and resided in rural areas, small towns, or very large cities (Vidulich, Sachs, and

Christman, 1978).

On the differential effects parents have on same sex and different sex children, Viernstein and Hogan (1975) report after studying highly gifted seventh and eighth participants in the John Hopkins verbal test search that: achievement motivation in boys may be explained in terms of dynamic, ambitious, achievement – oriented mothers, to an acceptable paternal model, and to parents with similar values. In contrast, achievement motivation in girls may be aroused through exposure to parental conflict, and from modelling after the parents of opposite sex. In both cases, achievement motivation may be a function of modelling rather than experience with a particular set of child-rearing practices designed to foster independence and self-esteem. It follows that parents who are not ambitious or disaffected may have considerable difficulty producing upwardly mobile children.

In addition, the presence and absence of role models is another determinant. Biographies of creative individuals document the importance of these influences in shaping their lives. For many gifted and talented children, no such role models exist; they have no adult with whom to share ideas in stimulating exchanges (Herr and Watanable, 1979). The review is important because the influence of socio-economic status of parents was be investigated by the researcher.

Parental Background as a factor in Mathematics achievement

In the opinion of (Ocho 2005) education, as a concept, is the process through which individuals are made participating members of their society. It is the system through which man becomes a moral agent capable of living in society and contributing towards the growth and development of the society. It is believed that through education the youths acquire desirable ability that would make them useful to himself and others. On the relationship between parental education factor and intelligence, Bee (1978) observed that father’s level of education or his measured intelligence is somewhat predictive of his child’s school success on I. Q. (Intelligence Quotient) test. Part of this is clearly as the result of genetic influences but there also may be specific environment influences from the father. A number of recent studies by Norman Radin and her associates are relevant to this

point. Radin initially found in several studies that there was a correlation between parental

nurturance and intellectual performance in sons. More nurturance fathers have sons who

performed better on a variety of tests, although this relationship was in stronger middle class

pairs.

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However, in another study, Oyebode (1980) found out that the level of education of

parents do not influence their children choice of vocations rather parental education

background tend to determine their taste in choice -making. Furthermore, Douglas (1994)

asserts that a child from a poor home whose memories are associated with the feelings of

personal satisfaction or sense of achievement give evidences to show that the academic

performance of understanding parents in the early years give the background and meaning to

their children academic achievement.

Kennedy (1991) corroborated this when he observed that socio-economic status of the

parents is probably the most critical variable that determines academic achievement of the

secondary school students because there is an opportunity of special help at home by parents

and availability of related textbooks, which reflect mainly on academic achievement.

Essin (2002) found that students from low and socio-economic backgrounds, more often

preferred mathematics, whereas those from high socio-economic backgrounds preferred other

subject like English Language and English Literature etc.

The amount of interaction that exists in a family can also affect the academic

achievement of mathematics students in senior secondary school. Educated sponsors know

the value of interaction needed. Banks (1993: 69-70) provided the view that “Children

internalised parental expectations as a means of retaining parental warmth and protection

consequently, the internalisation process tends to be most successful in a family environment

where there is frequent and warm interaction between parents and students”

However, any careful observer of the world’s current events can see that some men,

women or parents do not give a din to remain with their children for a mere thirty minutes in

a day as to find out something about their educational welfare and growth. When they are not

looking for money, they are looking for other materialistic things thereby creating a gap in

the family. Children from a home where they are abandoned hardly gain anything from his

sponsors and hence have no person to encourage him in terms of education. Such children

may not complete their secondary education of as a result of lack of nature on the part of the

parents. Clark and Starr (1996: 54-55) probably was referring to this when he said that,

“Students are often handicapped by poor health, fatigue, physical and mental limitation,

emotional difficulties, environmental factors family attitudes or peer pressures”.

Miner (1988: 31) emphasized that children of middle-class families have more

stimulating homes than children of working class families in United States and perform better

in class work and stay longer in schools than children of the working class families”. One

37

would not be surprised by the above assertion because the children would be provided with

all their needs as far as school or academic is concerned. One who is not provided with the

facilities to read has no other alternative than to stop schooling. Hence, the reason why so

many school drop-outs or those who are unable to complete their secondary school studies

may come from illiterate or uneducated parents. Musgrove and Taylor (1986: 171)

strengthened this by rightly stressing on parental encouragement thus: The educated parents

take interest in their children’s progress”. Silver (1993: 124) emphasized that “children’ from

urban areas in Grammar schools have increased considerably.

They constitute both Grammar and modern school population. By contrast children

from rural areas despite their numerical superiority in the population as a whole continue to

be seriously under represented. They constitute only fifteen percent of the grammar school as

against forth two percent of the modern school sample”. What is more probable is that the

performance of the children at the selection examination at the age of eleven-plus was such

that only very few come within the fifth of the age group which would qualify them for entry

into the Grammar school. It might be argued, in turn, that this occur because in the rural

areas, the number of children or students of the requisite ability is small.

Educated sponsors, however, value scholastic achievement because it is the concern

of all members of the family. Since educated parents is valued as the necessary means not

only to getting on, but also of maintaining existing social status. Difference in parental

attitude towards education may well influence a child’s attitude to school work and so affects

his performance in the examination. Educated parents provide greater opportunities for extra-

curricula learning.

Farrant (1984: 57) argues that, “The chances that intelligent parents will have

intelligent children are the same that tall parents will produce tall children”. Georgiou (1996)

in an analysis of educational mobility drew attention to the fact that even among the selected

grammar school population, the odds were heavily weighted against children from the urban

areas, compared with the children from the rural areas Disproportionately; small number of

working class children obtained the school certificate. The first formal qualification and an

even smaller number proceeded to further education leading to professional qualification.

Havighurst and Vengarten (1995: 144) emphasized, “The child rearing practices of a

given social class favour a more rapid cognitive development than those of another social

class”.

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Attitudes of Gifted Pupils toward Mathematics

According Kersh and Reisman (1981), many-gifted students, like their regular peers,

initially like Mathematics in the primary grades, but acquire more negative feelings as they

progress through school. This often results in Mathematics avoidance by the very learners

who can most benefit from further mathematical experiences. The dexterous effects of

negative attitudes toward Mathematics and subsequent Mathematics avoidance are especially

evident with gifted women and most minorities.

In a study of mathematically precocious youth, Fox (1975) found far more males than

females who are exceptionally gifted in Mathematics. After reviewing research on sex

differences in Mathematics, Fox ascribed it to the following three factors that may contribute

to this difference in numbers;

1. Differential career interests and expectations

2. Encouragement from significant others, and

3. Early identification of education opportunities for the gifted female.

Bright girls tend to self – select themselves out of advanced high school Mathematics

courses (Haven, 1971). Yet, Fennena and Sherman (1971, 1978) found that when females

choose to take to Mathematics courses, they do so as well as the males. In relation to

attitudes, the perception of the usefulness of Mathematics seems to relate to the participation

of the gifted female in Mathematics. If gifted females see Mathematics as useful in their

career choice, the more likely they are to continue its study (Haven, 1971). Programme that

have attempted to provide spatial Mathematics classes for the gifted females have focused on

one or more of these factors; awareness of the usefulness of Mathematics, cooperative rather

than competitive learning increased confidence in doing Mathematics, female role models

and spatial ability (Work and Kersh, 1980, fox 1975).

Easterly in a study of 20 public schools where males and females consistently school

equally well in Mathematics assessments, found that though the schools are diverse, they

share these features.

Teachers have a strong service and Mathematics background Teachers openly express love and appreciation of Mathematics Bright learners are grouped together in Mathematics classes Teachers emphasize reasoning and course students.

The overview of Mathematics achievement and attitudes of minorities (excepting oriental

males) is much the same as that of females. A low Mathematics achievement profile, negative

Mathematics attitudes, and subsequent Mathematics avoidance after Mathematics

39

participation becomes optional is the pattern, with even more dramatic score differences from

white males than in the case of females. Research on gifted minorities in relation to

Mathematics makes the following recommendations:

Early exposure to experiential science and Mathematics

Use of instructional strategies that accommodate the variety of cognitive style seemingly

associated with minority groups.

Career awareness courses to expand professional aspirations among minorities.

Provision of academic role models in Mathematics and science.

Kersh and Reisman (1981) are of the opinion that further efforts are needed to identify gifted

women and minorities early enough to influence aspirations, and expectations, and to develop

appropriate curricula to accommodate various learning modes.

Gender and giftedness

Giftedness whether specific academic or general is not known to be restricted to any sex;

male and female controversy abounds as to whether or not sex and race directly account for

individual differences in ability.

The debate spurred by Beribow and Stanley’s (1980) came to the conclusion that deficiencies

in mathematical abilities of females are a function of biological factors.

According Callahan (1979), the only areas where boys in the general populations seem

clearly and consistently superior to girls are visual spatial ability and achievement in

Mathematics and science and that these differences are only apparent after the onset of

adolescence. FOX (1975) investigated sex differences in Mathematics and found that there

are far more males than females who are exceptionally gifted in Mathematics.

He attributed this difference to three distinct factors:

A. Differential career interests expectations;

B. Encouragement from significant others; and

C. Early identification and educational opportunity for the female.

Callahan (1979) further attributed the differences between sexes in the intellectual

processes of perception, learning and memory to the differences in their weight.

Haven (1971) observed that bright girls tend to self-select themselves out of advanced high

school Mathematics courses. Furthermore, on the participation of women in Mathematics,

Haven (1971) opines that if gifted female see Mathematics as useful in their career choice the

more likely they continue its study. There were thus attempts at providing special

40

Mathematics classes for the gifted females. Haven focused on one or more of the following

factors; awareness of the importance of Mathematics, Cooperative rather than competitive

learning increased confidence in doing Mathematics, female role.

On creativity, Macaby and Jackin cited in Gowan (1979) stated that men are more

represented than women in the ranks of outstanding creative artists, writers and scientists but

believe that women may get “stuck” in one developmental stage thus delaying progress into

the next stage because of some fear. This suggests that studies should be carried to help some

women overcome those fear, which Ronny (1970) describes as “stuck”, “retreat” and

“escape” tendencies (Gowan, 1979), adding that these tendencies are believed to result in lack

of creativity and productivity. Another convincing reason proffered for the failure of women

to achieve is that creativity requires training to some extent and women in the past were

denied equal opportunities with men. Addressing these issues raised, Cook and Kersh (1989)

opined that attempt at providing special Mathematics classes for the female have focused on

one or more of the following factors: awareness of the usefulness of Mathematics, females

role model, cooperative rather than competitive learning, increased confidence in doing

Mathematics and spatial ability.

On possible reasons for the failure of women in Mathematics and creativity,

Rodeinstein, Pffeger, and Colangelo (1977) described the mixed message that confront and

confuse the gifted females thus:

They are socialized to behave in one way as women, but their giftedness demands diametrically opposed behaviours: Selfishness versus energetic development of talent, passive versus activity: Marriage ahead or instead of career is career success: Femininity versus non-traditional career aspiration in science Mathematics, and business.

Li (1988) opined that girls who are gifted and talented are confronted with a series of challenges in order to meet their potential. During elementary school, the interests of girls are more similar to the interest of boys who are gifted or talented than to the interest of their normal ability peers. However, by the time they reach adolescence, young women who are gifted and talented develop lower career aspirations than those of young men who are gifted and talented (Kerr, 1985). These changes in career aspiration occur at approximately 14 years of age. At this stage, young women are confronted with socialization patterns towards passivity and dependence.

Kerr highlighted some of the external and internal reasons for the under achievement of females who are gifted and talented as Sexism and lack of resources. He added that women receive fewer graduate fellowships and receive lower salaries. Beside, they remain primarily

41

responsible for childcare, frequently performing what has been termed a second shift because they frequently must balance professional interest and higher education with traditional sex roles. Women who are gifted and talented are described as being “Cultural under achievers” (Davis and Rimm, 1985), that is, they are forced to achieve at less than their potential due to their cultural relegated roles as primary parents and home managers. When developing a gifted identification programme, it is important to take into account the context of the nominated group. It is also important to decide upon a definition of giftedness from which to expand. Both areas have a profound affect on the validity of the designed agenda (Gibson 1997). Social and cultural differences within the classroom insist on culturally unbiased detection processes. Therefore the cultural context of the nominated class gains importance. Such issues as cultural norms, as well as individual values, language differences and economic backgrounds all relate directly to how an individual may appear and relate to others (Gibson 1997). When assessing the behaviour of individuals it is important to consider these factors.

The influence the accepted definition of giftedness has on the identification process is significant. If a definition that supports a static interpretation of giftedness were used, the identification process would be relatively simple and almost entirely objective. On the other hand, if a developmental concept of giftedness were supported, the procedure would become more complex and subjective (Braggett 1997). The notion of subjectivity should not be considered negatively; rigorously collected qualitative data are just as valid as easily manipulated quantitative research. The manner with which the class is to be divided in order for a valid examination to

be conducted is also open to discussion. While some consider individuals assessment to be

more acceptable (Clark 2002), others uphold the value of small group work (Rogers 1998).

Considering the fact that many of the identifiable traits the gifted may display are more

visible within an interactive environment, small group work should in theory be better suited

to initial investigations. Once suspected candidates for further scrutiny have been identified,

individual attention may prove more useful. Emotional intelligence – considered by some to

be more important than academic intelligence (Goleman 1995) – is an area that appears better

suited to group work assessment, Whereas abstract reasoning abilities is an area that appears

better suited to group work assessment, whereas abstract reasoning abilities seem to be easier

to identify through individual consultation (Keating 1976).

Deciding upon a coherent definition of intelligence, or intelligences, is a further

important aspect. Whether intelligence is considered a general ability (Bartholomew 1995) or

a collection of specific field intelligences (Krechevsky & Gardner 1990), dictates the focus of

an intelligence, and therefore giftedness assessment. A test for general ability is going to be a

42

lot easier to construct than one that needs to take into account many different areas of

application. A more inclusive curriculum may be implemented if the initial identification

process produces a more comprehensive overview of abilities (Frasier 1997). With this in

mind identification process that dissects to a greater extent, and therefore enables a more

detailed account, should be favoured. This aspect of the review is important because the

researcher developed and validated an identification instrument and critically examined the

influence of some essential factors on the performances of the gifted pupils on the instrument.

Tests and Identification Models

We discussed the variety of definitions of giftedness; however, there is a substantial difference between the conceptual definitions and an operational definition. To identify a human attribute accurately, one must have a precise operational definition. Unfortunately, there is no universally accepted operational definition of giftedness (Davis and Rimm, 1980). Besides, giftedness is not a unitary trait like tallness, where we can agree on what tallness

means and an appropriate procedure for measuring it. It is rather a human condition, which

follows some developmental trajectory. Part of the problems of identifying the gifted is that

giftedness cannot be observed directly, but must be inferred by observing the behaviour of

individuals either in the naturally occurring situations or in situations constructed specifically

to elicit the type of behaviour (Davis and Rimm, 1980). Thus the identification of the gifted is

purely a measurement issue and as such relies on a set of specific measurement variables.

There are a lot of identification procedures based on either one of the following: using an I.

Q. – or multiple alternative criteria. The use of tests of achievement and intelligence are tied

to measurement of some statistical concepts, particularly validity, reliability and often

usability. In most cases, the uses of objective and subjective multi dimensional criteria are

recommended. Teacher, parents and peer nominations are commonly made use of including

some type of form or checklist. Checklists may at best possess face validity – items on

checklist appear to be appropriate for locating gifted and talented children. Often teachers’

biases may ruin the purpose for which the checklists are designed.

The two notable exceptions to the lack of statistical information of checklist are the

scale for rating the behavioural characteristics of superior students (SRBCSS, Renzulli et al,

1976) and the G.I.F.T. identification instrument (Male and Perron, 1979; 1980).

The Stanford- Binet and Wisc-R individual intelligence tests are recommended

because the Binet has a very high ceiling; the wise-R produces both verbal and full scale I. Q.

scores. Group intelligence tests are equally useful but they suffer low reliability and validity,

43

low ceiling and high verbal content (Davis and Rimm, 1980). Individual intelligence test

remains good predictors of general academic ability.

Achievement tests are good indicators of specific academic talent but usually have

low ceiling and may discriminate well among gifted children because they contain items of

differing difficult levels. Stanley (1976) in the study of mathematically precocious youth

(SMPY) makes a strong case. In both cases, achievement motivation may be a function of

modelling rather than experience with a particular set of childbearing practices designed to

foster independence and self-esteem. It follows that parents that are not ambitious, disaffected

and may have considerable difficulty producing upwards-mobile children.

Ikpaya (1986) notes that “poor socio-economic conditions in conjunction with

pedagogical neglect” is a factor that can prevent the child from attaining his/her “full mental

ability”. He referred to Suffer and Bruch who defined disadvantaged gifted youths as:

… Those who have experienced economic, social and/or emotional deprivation

as dominant factor (s) in their lives.

Gowan (1979) described them as those “reared by poor, low native parents”. According to

Dubey (1973), the word “background” itself may mean two things; it may refer to:

The nature or hereditary factor – the genetic characteristics within an individual which

limits the potentials of individual or

The social background of an individual – the people around him. The researcher will be

investigating the impact of socio-economic status on the (MAGII Since the identification

is not 100% accurate, it is better to over identify them. The identification processes in

Nigeria have received as much criticism as testing and decision- making based on test

scores. It is, however, the intention of the researcher to highlight some of these available

tests for the identification of the gifted.

Our purpose here is to examine the tests available for the identification of the gifted

and talented children in Nigeria. School psychologists may opt for I. Q. tests. The scales for

rating behavioural characteristics of superior students (SRBCSS; Renzulli et al, 1976), which

was developed to provide an objective and systematic instrument to aid in guiding teacher’s

judgment in the identification processes which has ten scales is also available. The 10 scales

currently available have been analysed for internal consistency. Factor analytic studies have

been performed to identify which factor are identified by the scale items and the total scales.

Children nominated for the gifted programme were assessed to determine the relationship

44

among certain behavioural and intellectual characteristics. Records were kept comprising 132

children’s race, sex, age, grade level, Slossan intelligence test (SiI) I. Q. scores, scale W. Sc-

RI. QS; only children who achieved an I. Q. score of 130 or above were included. A

regression equation for predicting a wise –R full scale I. Q. score for a given S. I. score was

computed and to that developed for predicting WISC-R I.Q in another study. All existing

variables but ST I Q. were poor predictors of WISC-R I.Q scores.

The Torrence tests of creative thinking (Torrence, 1974) are the most frequently used

tests for identification. Clark (1979) presents an integrated model of creativity and describes

creativity as a rational thinking function. Thus, creativity can be defined as a high I. Q. score

on creativity test. Most instruments for identification of the gifted originate from this point of

view.

Other Tests include:

The G.I.F.T.S identification instrument (Male & Perrone; 1979; 1980) which consists of

six categories: convergent thinking and behaviour, divergent/creative thinking and

behaviour, goal- related thinking and behaviour social skills and behaviour, physical skills

and behaviour and affective thinking and behaviour. Instruments are administered to

student, teachers and parents alike. The six categories are different but related and if used

as the authors suggest, may augment the identification process.

Divergent thinking tests (e.g Torrence Tests of creative thinking (Torrence, 1974).

The group inventory for finding interest I, II, (GIFFI, II).

The group inventory for finding talent (GIFT) elementary grades 3 –4 upper elementary

grades 5 – 6.

Pre-school and kindergarten interest descriptor (PRIDE) age 3 – 5.

Creative aptitude survey grades 4 – 6.

Renzulli Hartman scale for rating characteristics of creative students.

Adjective checklist

Remote Association Test.

Identification involves both standardized or/and norm-reference testing. Individualized

intelligence tests remain good predictors of general academic ability. Stanley (1976) in a

study of mathematically precocious children makes a case for the use of achievement test for

specific academic abilities thus:

Tests are prime ways – probably the prime way for the preliminary identification of high

level developed aptitude or achievement.

45

Tests have enough “ceiling’ and “floor” too for each individual tested.

The higher an examinee’s score are, the greater his/her potential tends to be. According to

Keating (1976), if we wish to determine the extent of a youngster’s knowledge in a

certain subject area, testing the youngster’s limits can be achieved only through advanced

instrumentation.

Mcginn (1976), in his study of verbally gifted children, modelled it after the study of

mathematically precocious children and then used the Scholastic Aptitude Test (SAT) as the

initial selection device. The SAT is commonly administered to both high school juniors and

seniors for college entry. The study aims at locating and developing verbal precocity at the

seventh and eighth grade levels. The children selected had scores at or above the 98th

percentile on grade appropriate tests.

Other tests for identifying gifted children in music include:

IOWA test of music literacy (7-12)

Gordon, E. E. University of IOWA.

Colwel, R. New York Follert.

Music aptitude profile (4 –12)

Music achievement tests (3-12)

Gordon E. E., Boston, Houghton-Mifflin

Seashore test of music talent

Seashore C. et al. New York: Psychological Corporation.

Identification of children gifted and talented in the arts presents serious problems. Kretner

and Engin (1981) report that music talent … must be measured not by its products but by its

symptoms and there seem to be precocious little agreement as to what symptoms really are”

(P.193). They break musical talent into five categories:

Perception – the ability to distinguish differences in physical quantities (frequency,

aptitudes, wave form, duration etc).

Memory – the ability to remember these discriminations over time.

Reproduction – the ability to recreate (by singing, playing an instrument or whatever) is

remembered.

Taste – the ability to distinguish good sounds from bad ones, either by culture’s definition

or one’s own.

Artistry – the ability (including creativity) to put emotions into music (Kreitner & Engin

1981:193 – 194).

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As a result of these very few tests have been developed to identify gifted students in the

arts. Standardized tests in arts tend to aid the selection of students for history theory.

However, the few available ones include:

Baron Welsh Art Scale.

Welsh G. S., Palo Alto: consulting, Psychologists press

Grave Design judgment scale.

Graves, M. New York Psychological Corporation.

Meire art test

Meir N IOWA city: Bureau of ED resource and services.

Ellison (1981) suggested using biographical information to identify artistic talents. He

further identified three major biographical keys that would offer predictive validity across

artistic areas and groups of individuals, performance, academic achievement and leadership

(P.167). The identification of the artistic talent is further complicated by the interactions of

definitions, “symptoms”, measurement strategies and the predictive validity of the

instrument.

Rationale for use of Inventories for Identification of the Gifted

The giftedness identification inventory is an attempt to develop and validate

instruments, which can be used for identification of gifted children. To date many inventories

are used to assess different behaviours in school, at home and play. Strong (1960) developed

interest inventories on the assumptions that interest is a complex interaction of traits.

Giftedness, like interest, is an assortment of unitary traits as reflected in the sub-sections.

Inventories are scaled instrument, which may be in the form of checklist, rating scales,

questionnaire and interview schedules used to obtain useful information for solving

educational problems.

In Iwuji’ (2000) views an inventory as the “description of trait, which describes

behaviour characteristics in which an individual is asked to indicate whether or not the

statements describe his/her feeling on the particular trait. Ipaye (1982) views an inventory as

a multi-item format that covers a broad area and to some extent serves as standardized

interview sheet since all the respondents answer the same type of question. The Federal

Ministry of Education handbook on Continuous Assessment (FME, 1982) defines inventory

as a type of questionnaire, like checklist, and an individual is expected to rank the items or

statements, as he/she considers appropriate. The definition emphasizes the importance of

47

inventories as an assessment mode for obtaining feedback about the individual behaviour or

attitude under certain conditions.Inventories, which may be of different types, generally cover

a variety of interests. A respondent is then expected to indicate the extent to which a

particular statement characterizes him /her.

Information concerning individuals on particular traits, attributes, emotions, and

attitudes provide vital data for decision-making. Inventories aid test experts and guidance

counsellors to interpret certain behaviour characteristics of the individual.

Cartell (1967: 31) discussing the important of inventories assert that:

Whichever kind of inventory that is used, reflect the individual’s reaction to an occurrence in the presence of something, which he feels, not why he feels this way. In this sense, the scores from the inventory serve as indication of the directions further investigation must take in order to achieve a clearer statement of probabilities in helping predict further behaviour. They may also indicate the process or instruments to use in order to clarify further the student decision about how the future analysis of results may be carried out effectively a technique that would be somewhat better in taking short essay from categorizing the responses.

On the use of multiple choice categories, the author further advised and advocated for the use of closed –ended questions and then use their answers to developed the categories for the multiple choice item that will be included in the final form of the instrument. These have motivated the investigator on the choice of inventory items. In addition, some of the identified traits of the sub-section cannot be responded to ordinarily by use of multiple-choice answers. Some activities are required for the psychomotor ability skill.

Further, Thorndike and Haggen (1969) assert that when the inventory is used in counselling clients, the respondents, there is probably little reason to anticipate intentional faking. This gives backing to the use of inventories for attitude scales, interest scales, aptitude etc. In Nigeria, there are two widely used inventories: the Bakare’s vocational interest inventory and the Nsukka interest profile, a vocational interest inventory for post- primary school students developed by Asuman (1986).

These suggest the importance of inventories for various research purposes and justify the use of an inventory by the research to identify children in Nigerian primary schools who are mathematically precocious. The investigator has equally developed the multiple-choice categories and the short-answer categories- the open form in which the subject marks whether he/she wishes to in his/her own words. This is so because Borg and Gall (1973: 49) opines that:

Generally, though, it is desired to design the questions in closed form so that quantification and analysis of the results may be carried out efficiently. Perhaps the best method to use in determining multiple categories is to ask the questions in easy form to a small number of respondents and then use

48

their answers to develop the categories for the multiple choice items that will be included in the final form of the questionnaire.

Further, students tend to conceal most of their feelings particularly in the normal

school setting. Frustration may force the gifted to take to any option open to them. Remmere

and Gagne (1955) and Iwuji, (2000) opine that the use of interest invention is better than the

organized introspection than conversation because invention are systematically organized and

makes possible the comparison of interest of students with those of people of known status.

Although the inventory here is a Mathematics giftedness identification instrument, the researcher hopes that there will be no faking of any sort since the teachers will rate the pupil. Borg and Liall (1973) recorded many general inventories: 1. Minnesota Mmultiphase Personally Inventory (MMPI): determines which items out of 550-item pool differentiated empirically before particular psychiatric good -normal groups that developed this inventory. 1. The California Psychological Inventory (CPl): Its aim is to measure trait thought to be

relevant to interpersonal behaviour and intellectual functioning

2. The Sixteen – Personality Factor Questionnaire (16P.F. Q). This inventory is different

from others because the scales were developed by the method of analysis. Some of the

personality dimension measured by the scale is reserved versus outgoing, affected by feeling

versus emotionally stable etc.

Importance of Validity and Reliability of Measurement Instrument According to Ibanga (1989) measuring instrument are devices used to measure the

cognitive, affective and psychomotor aspects of the instructional process. To Nwana (1981)

measuring instruments are appliances, which enable us to obtain sets of numbers for our

observations.Measuring instruments are the same as evaluation instruments to some

reasonable extent in that both use predominantly quantitative as well as qualitative

instruments. Ali (1996) sees a measuring instrument as any device that can yield quantitative

and qualitative results. Measuring instrument thus enable us identify desirable change in

behaviour of learners.

A worthwhile measuring instrument should at least require a conscientious effort on

the part of it designer (Okpala, Onocha and Oyedeye (1993). Such an effort should ensure

that the instrument measures only relevant attributes. These authors outlined the important

qualities of a measuring instrument as validity, reliability and usability. These are known as

psychometric qualities of a measuring instrument.

49

Thus, the research worker or instrument designer must establish evidence of validity of the

instrument constructed. Nworgu (2003) identified four type of validity, namely, content

validity, criterion related validity, construct validity and face validity. The items so developed

in the test must be framed to reflect the objectives for which they are set.

Abonyi (2003) sees reliability of an instrument as measure of internal consistency and

the confidence we repose on the result obtained from the measuring instrument when

administered on some testee. An instrument is reliable if it indicates the same result or similar

results are obtained consistently under the same or slightly different condition of

administration of the same instrument (Okpala et al, 1993). A reliable instrument is usually a

valid instrument but a valid instrument may not be reliable because it is relative to time, space

and circumstances.

Many measurement experts and some authors have stressed the importance of the

psychometric qualities of measuring instruments. The importance of these qualities in

instrument construction as well as in the usage of these instruments could be understood and

realized from the various definitions and explanations given to them by these experts.

Gronlund (1981) says that the essence of validity instrument construction is to answer the

question, to what extent will the results serve the particular uses for which they are designed.

Test and measurement experts refer to validity as the single most important aspect of a test.

Gronlund (1981) then defines validity as the extent to which results of an evaluation

procedure serve the particular use for which they are intended. For Mehrens and Lehmann

(1978) validity is the degree to which a test is capable of achieving certain aims. Two general

aims have to be considered while discussing validity for making predictions about the student

and for describing or representing him. Ibegbunam (1982) recognizes the importance of

validity thus: it should be clear from educational principles that the relationship between

teaching and testing is typically intimate. Test content is drawn from what has been taught.

This implies that the instructional programme is the primary source of test

materials. In the opinion of Thorndike and Hagen (1977) a single test may be used for much

different purpose; thus there is no single validity index for a test. Each use of test requires a

different interpretation and each interpretation has its own degree of validity. Ibanga (1989)

in discussing validity of tests observes that content validity is the type of validity

achievement tests are supposed to have. This is so because they sample representatively and

ideally the content of a course of instruction.

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Okpala et al (1993) believe that content or curriculum of any course can be

defined to reflect both subject matter content and instructional objective. While the former is

concerned with topics or subject areas to be covered while teaching, the latter concerns the

behavioural outcome sought in the learners. Both of them, according them, are of primary

importance in determining content validity of test items. For them procedure involved should

be those of logical analyses and comparisons. The subject matter covered is considered; the

test questions are examined to reflect this content coverage, and the responses expected from

the pupils on the content covered. This is compared with the domain of objective to be

measured. Such an analysis from using the test grid reveals the apparent relevance of the test

items to the subject content and the behavioural outcomes to be measured. All these views

point out the importance of the item sample, being representative to elicit responses from

subject matter areas covered and the behavioural objectives. Inherent from the explanation so

far is that content validity procedures as inferred by Okpala et al (1993) depends on

subjective judgment, which mostly likely vary from teacher to teacher. Mehrens and

Lehmann (1978) recognizes the importance of adequate weighting of content and process

objectives by suggesting variation of proportions in the allocation of questions by sampling

different cognitive levels. To them “nothing in the logic of content validation requires that the

universe or the test be homogenous in content”.

Hassan (undated) buttressing the importance of adequate weighting of the content and

objective suggests that: It is necessary to explore at the class room setting, whether the

teacher who actually do implement the goal of education in the class room do in fact

emphasize or teach for understanding at the different “ cognitive levels in their classroom

teaching, and if so do they structure their questions to reflect these level of critical thinking?

This implies that teachers should in the course of teaching emphasize the content at the

various cognitive levels relating these areas of emphasis to the objective, and setting their

questions to reflect these levels, taking cognisance of the content coverage and objective. In

this study, the Mathematics aptitude instrument (MAGII) does not require any content

validations because it is aptitude test, which is not based on any content.

Reliability

Okpala et al (1993) define reliability as the trustworthiness and consistency of a

measuring device. For Ali (1996) when the researcher is interested in answering the question,

would repeated measurement of the same person, on the same attribute, under the same

condition, yield the same results? The concept of reliability of a measuring instrument makes

51

it possible to obtain similar results upon repetition. It indicates the degree to which

measurement is free from random influences (Mehrens and Lehmann(1978). Thus reliable

instrument is usually valid but a valid instrument may not be always reliable because validity

is relative to time, place and circumstances.

A test is reliable if it yields the same score for an individual or group of individuals on

two or more different occasions. Reliability is thus of great importance in testing. It is used

for predication studies, that is, studies of improvement resulting from training and analytical

studies of the relationships among group of tests. The degree of reliability of a set of

measurement is a very important consideration in educational evaluation in practical daily use

of tests or instruments in empirical research (Ibegbunam, 1993). Decisions are based on

scores obtained, so the test expert in selecting his test items first consider his instruments to

find out if they are both valid and reliable for the decisions to be made.

Gronlund (1981) sees reliability as the consistency of measuring instrument; for him

test scores merely provide a limited measure of behaviour obtained at a particular time.

Unless the measurement can be shown to be reasonably consistent over different occasions or

over different sample of the same behaviour, we cannot expect test results to be perfectly

consistent because there are many factors other than the traits being measured which can

influence test scores.

Reliability seeks to find out how accurate a test measures what it purports to measure.

Iwuji (2000) views reliability as the degree to which a test measures consistently whatever it

intends to measure. Agreeing with this conceptual view of reliability, Mehrens and Lehmann

(1978) believe that it is the degree of consistency between the measures of the same thing.

According to Thorndike and Hagen (1977) reliability has to do with the accuracy and

precision of a measurement procedure. This means that such reliability gives an indication of

the extent to which a given measurement is consistent and reproducible. The instrument for

the identification of mathematically gifted in the Ebonyi State Primary school system

(MAGIIPSS) and within Nigeria when constructed and used is intended to produce such

measurement that would be consistent and reproducible

Reliability concerns the extent to which measurement of particular traits is repeated under same conditions. Mehrens and Lehmann (1978) considers reliability from a more technical perspective, reliability refers to the consistency of the results obtained by the use of particular instrument, the stability of scores, the proportion of a variance that is true variance’’ (free from error variance) and the accuracy or precisions with which a test measures whatever it intends to measure.

52

Abonyi (2003) also speaks of reliability of a test as the consistency of scores obtained

by the same individuals on different occasions or with different sets of equivalent items. This

concept of reliability underlines the error of measurement of a single score, where the range

of fluctuations could be predicted as a result of influence of irrelevant chance factors. Iwuji

(2000) conceives reliability as a statistical concept, which denotes the accuracy or

consistency of measurement. For her, reliability refers to the extent to which repeated

measurement of the traits of an individual yield similar results. The central idea in all this

definition of reliability is that it refers to the degree of accuracy; consistency, stability and

Abonyi, Okereke, Omebe and Anuguo (2006) include dependability of a measuring

instrument. It is important to note that no measuring instrument is perfectly reliable all the

time because scores are invariable.

The variation in individual scores is known as error of variance and sources of

variations as source of error. High reliability indicates minimum error variance; errors of

measurement affect scores in a random fashion. Any systematic or consistent error does not

affect reliability but the validity of a measuring instrument (Mehrens and Lehmann, 1978).

Reliability, according to Lehmann (1963) and Stanley in Thorndike and Hagen (1977) can be

assessed from an absolute or relative point of view. Absolute consistency is the variability in

score that would be expressed in any individual performance if he were tested repeatedly with

the same test. This is to say consideration of the variability of a series of repeated

measurements of single characteristics of the individual. Also the average differential in test

scores on a test among student will help in giving one the consistency or trend in patterns of

students’ achievement in the test. This way of viewing reliability in test scores units is

expressed through a standard error of measurements of the attributes expressed as standard

deviation of the distribution.

Relative reliability refers to the ability of a test to yield scores, which place

testee in the same relative to each other. This approval views reliability as an individual’s

ability to maintain his relative position in the total group on repeating a measurement of the

same attribute. Relative reliability provides an index of the overall dependability of scores in

the form of a correlation coefficient. This approach is more common and yields a measure of

reliability referred to a coefficient of reliability.

In computing reliability coefficient an appropriate correlation technique such as the

Pearson Moment’s Correlation Coefficient, Spearmen Rank Correlation Coefficient, and

Kendal Coefficient of Concordance etc could be used. In this study the Person Product

53

Moment Correlation Coefficient will be used to compute the relationship between two sets of

data. Many procedures exist for establishing the reliability of measurement. Each method has

a different source of reliability, which affects the values obtained. An estimate of reliability

always refers to a particular type of consistency. The most common among them are measure

of stability (test-retest), measure of equivalence (parallel form), measure of equivalence and

stability, measures of internal consistency, which include the split- half method, Kuder-

Richadson estimates, coefficient alpha and Hoyt’s analysis of variance marker’s (judge)

reliability.

Procedure for validating instrument

In test construction, instruments are to be validated using the following methods.

1. Face validity procedure

2. Content validity procedure

3. Construct validity methods

4. Concurrent validation procedure and

5. Predictive validation procedure

However, in using any instrument for investigation, the researcher has three distinct

ways of getting the needed instrument: he can select from the existing pool of tests the one

that suits his purpose or he may decide to develop the needed instrument or choose from the

existing pool of instruments and modify the test to suit his purpose. In attesting for the first

option, Thorndika and Hagen (1977:72) wrote that.” whenever a research worker in

psychology or education deserves to measure some quality in a group of persons or in an

individual he faces the problem of choosing the best instrument for his purposes”.

The problem of choice with the present study is that there is no existing instrument

already constructed for the identification of mathematically precocious pupils in the country.

Many of the available instruments reviewed in the literature are for purposes of identifying

those pupils found to be generally gifted. Others are foreign, and thus culturally biased and

unfit for use in Nigerian socio-cultural setting. Thus the idea of selecting from the existing

pool of instruments is not feasible in this case. The researcher must, therefore, develop his

own instrument for this particular purpose and which, must in addition; reflect the Nigeria

social-cultural setting that can be used to identify pupils who are gifted mathematically in the

Nigerian educational system without bias. Is it then possible to develop an instrument with

Nigerian cultural background that will aid the identification of pupils who are gifted

mathematically in Nigerian primary Schools? Or is there a way of modifying the existing

54

foreign tests and possibly adapting them to suit the Nigerian socio-cultural setting?

These are possible options open to the researcher but whichever he considers best

makes available only one instrument for his purpose. There is still the need for the researcher

to worry about how the instrument so made available satisfies his immediate objective – the

identification of pupils found to be mathematically precocious within the Nigerian school

system. The researcher may not be interested in determining the best procedure but also how

well it satisfies his needs by some absolute standard” (Thorndike and Hagen, 1977). The

researcher is interested in carrying out the above stated procedures in this case since he is

quite aware of the fact that every score so obtained is inevitably influenced by chance and

systematic errors (Lewis, 1967). Any score obtained is either an over estimate or under-

estimate of the true score of trait under study.

The researcher will be striving to use instrument that will give score that are

minimally influenced by chance and systematic errors. It is important therefore that the

researcher should determine well ahead of its use the extent to which scores obtained from

the instruments are free from chance errors (reliability) and the extent to which it is free from

all error (validity). Okpala et al (1993) define reliability as the degree of consistency between

two sets of scores or observation obtained with the same instrument or equivalent form of the

instrument. Gronlund (1981) uses reliability to mean the consistency of evaluation results.

Kerlinger (1973) opines that for it to be interpretable a test must be reliable as well.

Furthermore, he advised that for reliability to be improved the researcher should maximize

the variances of the individual difference and minimize the error variance (Kerlinger, 1973).

In order to achieve this, he advised that:

1. Items should not be ambiguous 2. More items of equal kind and quality should be included; and 3. Clear and standard instruction should be given to reduce errors of measurement.

Ray (1973) observes that there are a number of different types of reliability each of

which is determined in a different manner and each deals with a different kind of consistency:

test retest, equivalent form, and split – half reliability are determined through correlation.

Rational equivalence reliability is established by determining how each item on a test relates

to all other items in the test and to the total test. The question of which of these listed

measures of stability is most appropriate for the instrument for the identification of

mathematically precocious pupils and the basic procedures for determining each of these

types of consistency is yet unanswered by the researcher. In order words, he will be deciding

on whether to use:

55

1. The test – retest method – administering the instrument so developed on given

individuals at two different occasions and then correlating the scores so obtained using an

appropriate statistical tool. Although, this is known to have it’s own short falls, the testee’

decline growth in ability may affect their performances at subsequent administration. Besides,

the testee’ interaction no matter how small must have changed over the times. This approach

is often used in predictive studies. In this current study, the researcher may not be interested

in this since the MAGII will be pre-tested.

2. The equivalent form approach. The researcher will be expected to administer two

equivalent forms of the instrument (tests) in terms of content and at the same or at different

times (Gronlund, 1981). The correlation coefficient between the two sets of scores so

obtained on the two equivalent instruments (test) is computed to obtain the reliability index

for the instrument. A suitable version of this approach is the test-retest with equivalent forms

approach, which is a measure of stability and equivalence. This may require the researcher to

administer two equivalent forms of the MAGII on two different occasions to a given group of

suggested pupils. The correlation coefficient is the computed as in the equivalent form

approach. The shortfalls the researcher will be facing in adopting this approach may include

the difference between the equivalent instruments, the testee interaction and testers’

differences if time lag is allowed in the administration of the instruments. In the present

study, the researcher may not be expected to go thus far since the two equivalent forms are

not necessary in developing the MAGII.

The third possible approach is the split-half or the Kuder-Richardson, which is a

measure of internal consistency, which involves splitting the items the MAGII into two

equivalent halves both administered at the same time to the same group of persons. The two

halves may have the same difficulty index and may also cover the same content. The two sets

of scores obtained from the two halves on the same group of persons are then correlated to

give the reliability coefficient from the half-test. The reliability coefficient of the whole test is

determined from the reliability of the half –test. The limitation of this method is that any

instrument (e.g. MAGII) can be split into many halves thus each pair of halves may probably

indicate different values of reliability indices and so the reliability of the instrument will

depend on the method of obtaining and the type of halves so used. This problem is simply

overcome by using the Kuder-Richardson approach. This method involves administering the

final instrument (i.e.MAGII) to the suspected gifted person once scoring the total and

applying Kuder-Richardson formula. However, since MAGII has just four distinct sub-tests

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or subscales, each comprising a different set of items and for the fact that items in each

subscale are few the split half procedure may not be applicable in the study. Instead the

researcher would use the Kuder-Richardson formula 21, which is the same as the Cronbach

alpha will be resorted to; since a subject will be considered as having either passed or failed

an item of MAGII. In this work the researcher is involved in a predictive study so the

measure of stability would be preferred to the cronbach alpha approach.

Having estimated the extent to which an instrument is free from chance errors (reliability), the next pertinent step is to ascertain the extent to which the instrument is free from systematic errors (validity). This is so because reliability is necessary but not a sufficient condition for validity (Gronlund, 1981). For an instrument to be valid, it must be reliable as well as relevant.

Gronlund (1981) defines validity as the extent to which the result of evaluation

procedure serves the particular uses for which they are intended. The relevance of an

instrument is, therefore, considered in terms of: content of courses or spectrum/scope of

behaviour patterns, facets of an attribute or construct and the nature of criterion, which the

instrument purports to measure.

Various authors have identified three to five types of validity.

Okpala et al (1993) classified validity into the following: content validity, construct

validity, criterion-related validity, predictive validity, concurrent validity. Gay (1976)

classified validity into the following four distinct types: content validity, construct validity,

concurrent validity and predictive validity. Gronlund (1981) describes four types as well:

content validity, Criterion – related validity, construct validity and face validity. Horrocks

and Schoonover (1908) identify four types of validity: content validity, construct validity,

predictive validity, concurrent validity while Kerlinger (1973) classified validity into the

following: content validity, construct validity, criterion-related validity. Kerlinger’s (1973)

explanation of criterion –related validity tallies with that of predictive and concurrent

validities concerned with psychological tests. The constructs in this study are:

1. Numeric ability

2. Specific academic ability 3. General quantitative ability 4. Creative or productive thinking.

Gronlund (1981) sees construct validity as the extent to which a test can be interpreted

in terms of certain psychological constructs.

However, to be able to determine the construct validity of the MAGII, the researcher must

adopt the following stages:

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a. Identifying the traits, skills or attributes presumed to account for performance on the

test or scale that measures the construct.

b. Constructing hypothesis regarding performance or standing on the test instrument;

and

c. Testing the hypothesis by logical and empirical means.

The construct of the MAGII has already been determined and the hypothesis

formulated. Determining the construct validity of the MAGII entails testing the hypotheses. It

is pertinent to determine the construct validity of MAGII because according to Piaget

intellectual development increases with age. Moreover, studies carried out by Pinillos

revealed that intelligence can be improved (Pinillos, 1983). This is also in line with Horrock

and Schoonover’s (1968) classification. Few authors included a quasi-type of validity – the

face validity.

Gronlund (1981) opines that a test is said to have face validity if it appears to be a

relevant measure based on superficial assessment. Thus, Face validation is dependent on the

appearance of the measuring device. The MAGII will be face validated although such a face

validation may not substitute its construct validation.

Content validation as it pertains to a measuring instrument means the extent to which

the items of a measuring device cover the topics of course content or facets of a construct,

which the instrument intends to measure. The coverage of the course content or construct

should not be only nominal but also horizontal, lateral and vertical. To ensure that the items

are valid contentwise, a list of the topics of the course contents or components of the

construct is made. The list is subjected to experts’ scrutiny and vetting. Based on the

scrutinized list, items are then constructed within the frame of blue print (i.e. table of

specification). The items are then subjected to the scrutiny of experts in measurement and

evaluation, psychologists and special education experts for another scrutiny. Content

validation is not necessary in this study and may not be carried out since MAGII is an

aptitude instrument, which is not based on any content.

Criterion – related validity and construct validity: Criterion – related validity of a

measuring instrument consists of predictive validity and concurrent validity. A measuring

instrument is said to have a predictive validity if the scores of individuals on the instrument

are used to predict future performance of the same individuals on some other task. In

predictive validity, the pertinent question is: “Do test scores predict a certain future

performance?” (Cronbach, 1970).

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Such an instrument is constructed, administered and scored. Sometime later, a

measure of success is obtained. Compare the prediction scores with the measure of success to

get the predictive validity of the instrument. For example, the screening scores of prospective

class one junior secondary schools students of the gifted school at Suleja is compared with

the marks obtained by the same set of student in the junior secondary school examination in

the school for the prediction of performance in the gifted and talented school at Suleja.

On the contrary, we are concerned with concurrent validity of an instrument if we use

scores of individuals on some aspects of a task to estimate the same individual’s performance

on the entire task or other closely related task being concurrently undertaken. Crobach (1970)

raised the question: Do test scores permit an estimate of a certain present performance when

an instrument is administered and scored? In a circumstance where an instrument is

administered and scored, a direct measure of the other permanence is obtained and a

comparison of the two scores yields the concurrent validity of the instrument, for instance,

score of foreign general verbal ability test of a group compared with locally developed verbal

ability test.

However, the experiment aims at developing and standardising an instrument (i.e the

MAGII) that would be used to identify children gifted mathematically. Thus, there is the need

to go into estimating or computing numerically the concurrent validity since there are as of

now locally standardized instruments for identifying giftedness in children who are in Nigeria

at the primary school level. The foreign ones may not be used for the purpose; they may not

be suitable for this exercise because they are culturally biased. Also, in the opinion of

Gronlund (1981), in determining criterion – related validity, a major problem is that of

obtaining a satisfactory criterion of success.

Another aspect of validity is construct validity. According to Kerlinger (1973), a

construct is a concept which has “added meaning” however, of having been deliberately and

consciously invented or adopted for a special scientific purpose. Lyman (1963) describes

construct validity as being concerned with psychological meaningfulness of the test. Put

differently, Gronlund (1981) describes construct validity as the extent to which tests can be

interpreted in terms of certain psychological constructs.

Process of determining construct validity include:

i. Identifying the traits, skills or attributes presumed to account for performance on the

test or scale that measures the construct.

ii. Constructing a hypothesis regarding performance or standing on the test/instrument

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and

iii. Testing the hypothesis by logical and empirical means the researcher will estimate the

construct validity of the MAGII. The constructs are grouped under four sub-sections

depending on the definition of mathematical precociousness as contained in

Columbus group (1991) definition of mathematical giftedness.

These are numeric ability measure, quantitative ability measure, spatial ability measure and

creative/productive thinking ability measure.

(B) The Theoretical Framework

The theoretical framework includes:

Theory of Multiple Intelligence

After years of research, Howard Gardner proposed a new theory and definition of intelligence

in his 1983 book entitled Frames of Mind: the Theory of Multiple Intelligences. The basic

question he sought to answer was: Is intelligence a single thing or various independent

intellectual faculties? Gardner a Professor of Cognition and Education at the Harvard

Graduate School of Education who holds an adjunct faculty post in psychology at Harvard

University in neurology at the Boston University School of Medicine. He is best known for

his work in the area of Multiple Intelligences, which has been a career-long pursuit to

understand and describe the construct of intelligence (Gardner, 1999a; Project Zero Website,

2000).

Gardner describes his work with two distinct populations as the inspiration for his

theory of multiple intelligences. Early in his career, he began studying stroke victims

suffering from asphyxia at the Boston University asphyxia Research Center and working with

children at Harvard’s Project Zero, a laboratory designed to study the cognitive development

of children and its associated educational implications (Gardner, 1999a: 32), in Intelligence

Reframed, Gardner states,

Both of the populations I was working with were clueing me into the same message:

that the human mind is better thought of as a series of relatively separate faculties, with only

loose and non-predictable relations with one another, than as a single, all-purpose machine

that performs steadily at a certain horsepower, independent of content and context.

Gardner concluded from his work with these two populations that strength in one area of

performance did not reliably predict comparable strength in another area. With this intuitive

conclusion in mind, Gardner set about studying intelligence in a systematic, multi-

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disciplinary, and scientific manner, drawing from psychology, biology, neurology, sociology,

anthropology, and the arts and humanities. This resulted in the emergence of his Theory of

Multiple Intelligences (MI Theory) as presented in Frames of Mind (1983). Since the

publication of that work, Gardner and others have continued to research the theory and its

implications for education in general, curriculum development, teaching and assessment. For

the purposes of this Hot Topic, the focus will be on a description of the theory, major

criticisms, and the implications for assessment.

According to Gardner (1999a: 34), intelligence is much more than 1Q because a high

1Q in the absence of productivity does not equate to intelligence. In his definition,

“Intelligence is a bio psychological potential to process information that can be activated in a

cultural setting to solve problems or create products that are of value in a culture”.

Consequently, instead of intelligence being a single entity described psychometrically with an

1Q score, Gardner’s definition views it as many things. He endeavoured to define intelligence

in a much broader way than psychometricians. To achieve this goal, Gardner (1983; 1999a)

established several criteria for defining intelligence. In identifying capabilities to be

considered for one of the “multiple intelligences” the construct under consideration had to

meet several criteria rather than resting on the results of a narrow psychometric approach.

To qualify as” intelligence” the particular capacity under study was considered from

multiple perspectives consisting of eight specific criteria drawn from the biological sciences,

logical analysis, developmental psychology, experimental psychology, and psychometrics.

The criteria to consider “candidate intelligences” (Gardner, 1999a: 36) are:

1. The potential for brain isolation by brain damage,

2. Its place in evolutionary history,

3. The presence of core operations,

4. Susceptibility to encoding,

5. A distinct developmental progression,

6. The existence of idiot-savants, prodigies and other exceptional people,

7. Support from experimental psychology, and

8. Support from psychometric findings (Gardner, 1999a).

To illustrate the specific of these criteria, a brief description and example of each is provided.

The potential for brain isolation by brain damage means that one’s “candidate intelligence”

(Gardner; 1999a: 36) can be dissociated from others. This criterion came from Gardner’s

work in neuropsychology. For example, stroke patients who are left with some forms of

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“intelligence” are intact despite damage to other cognitive abilities such as speech. From an

evolutionary perspective, the candidate intelligence has to have played a role in the

development of our species and its ability to cope with the environment. In this case, Gardner

(1999a) uses inference to conclude that spatial abilities were critical to the survival of our

species. Early hominids had to be able to navigate diverse terrains using spatial abilities. The

pressure of the environment then resulted in selection for this ability. Both of these criteria

emerged from the biological sciences.

From the perspective of logical analysis, intelligence must have an identifiable core set

of operations. Acknowledging the fact that specific intelligences operate in the context of the

environment, Gardner (1999a) argues that it is crucial to specify the capacities that are central

to the intelligence under consideration. For example, linguistic intelligence consists of core

operations such as recognition and discrimination of phonemes, command of syntax and

acquisition of word meanings. In the area of musical intelligence, the core operations are

pitch, rhythm, timbre, and harmony. Another criterion related to logical analysis states that

intelligence must be susceptible to encoding in a symbol system. According to Gardner,

(1999a) symbol systems are developed versus occurring naturally, and their purpose is to

accurately and systematically convey information that is culturally meaningful. Some

examples of encoding include written and spoken language, mathematical systems, logical

equations, maps charts and drawings.

Gardner (1999a) established two criteria from developmental psychology. The first is

the presence of a developmental trajectory for the particular ability toward an expert end-

state. In other words, individuals do not necessarily exhibit their “intelligence” in its raw

state. Rather, they prepare to use their intelligence by passing through a developmental

process. Thus, people who want to be mathematicians or physicists, spend years studying and

honing their logical/mathematical abilities in a distinctive and socially relevant way. The

second criterion borrowed from the discipline of developmental psychology, is the existence

of idiot -savants, prodigies and exceptional people. Gardner (1999a) refers to these as

accidents of nature that allow researches to observe the nature of a particular intelligence in

great contrast to other average or impaired abilities. One example of this type of highlighted

intelligence is the autistic person who excels at numerical calculations of musical

performance.

Finally, Gardner (1999a) draws his last two criteria from traditional psychology and

psychometrics to determine if a candidate’s intelligence may be included the list of specific

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abilities he calls Multiple Intelligences. There must be support from experimental psychology

that indicates the extent to which two operations are related or different, Observing subjects

who are asked to carry out two activities or different ones. For example, a person engaged in

working a crossword puzzle is unlikely to be able to carry on a conversation effectively,

because both tasks demand the attention of linguistic intelligence, which creates interference.

Whereas, the absence of this sort of competition allows a person to be able to work and

converse which, at the same time suggests that two different intelligences are engaged. In

spite of the fact that Gardner proposed his theory in opposition to psychometrics, he

recognizes the importance of acknowledging psychometric data.

From the preceding eight criteria, Gardner (1983:1999a) proposed and defined seven

intelligences. Logical-mathematical intelligence is the ability to detect patterns, think

logically, reason deductively and carry out mathematical operations. Linguistic intelligence

involves the mastery of spoken and written language to express oneself or remember things.

These first two forms of intelligence are typically the abilities that contribute to strong

performance in traditional school environments and to producing high scores on most 1Q

measures or tests of achievement. Spatial intelligence involves the potential for recognizing

and manipulating the patterns of both wide spaces such as those negotiated by pilots or

navigators, and confirmed spaces such as those encountered by sculptors, architects or

championship chess players. Musical intelligence consists of the capacity to recognize and

compose musical pitches, tones, rhythms and patterns and to use them for performance or

composition. Bodily-Kinesthetic Intelligence involves the use of parts of the body or the

whole body to solve problems or create products. Athletes, dancers, surgeons and

craftspeople are likely to have highly developed capacity in this area. The last two

intelligences are the personal intelligences: interpersonal and intra-personal. Interpersonal

intelligence indicates a person’s ability to recognize the intentions, feelings and motivations

of others. People who possess and develop this quality are likely to work well with others and

may choose fields like sales, teaching, counselling or politics in order to use them. Intra-

personal intelligence is described as the ability to understand oneself and use that information

to regulate one’s own life. According to Gardner each of these seven “intelligences” has a

specific set of abilities that can be observed and measured (Gardner, 1999a, 1983). More

recently, Gardner (1998) has nominated three additional candidate intelligences: Naturalist,

Spiritual and Existential intelligence and evaluated them in the context of the eight criteria he

established in his research as outlined earlier in this paper. He defines a naturalist as a person

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“who demonstrates expertise in recognition and classification of the numerous species- the

flora and fauna- of her or his environment.” (Gardner, 1998:115). Gardner is comfortable

with declaring that a Nationalist intelligence meets the criteria he set forth, however he is less

sure about how to define and incorporate Spiritual and Existential intelligences.

The two most widely used standardized tests of intelligence are the Wechsler scales

and the Stanford-Binet. Both instruments are psychometrically sound, but Gardner believes

that these tests measure only linguistic and logical/mathematical intelligences, with a narrow

focus within content in those domains. According to Gardner, the current psychometric

approach for measuring intelligence is not sufficient. In his view, assessment must cast a

wider net to measure human cognitive abilities more accurately. Gardner (1993) proposed

several improvements for the development of intelligence measures. Before enumerating

those improvements, it is important to understand how Gardner defines assessment. In his

view, the purpose of assessment should be to obtain information about the skills and

potentials of individuals, and provide useful feedback to the individuals and the community at

large. Furthermore, Gardner (1993a) draws a distinction between testing and assessment.

Assessment elicits information about an individual’s abilities in the context of actual

performance rather than by proxy using formal instruments in a de-contextualised setting.

Gardner urges for making assessment a natural part of the learning environment.

Assessment is then built into the learning situation much like the constant assessment of skills

that occurs in apprenticeship or the self-assessment that occurs in experts who have

internalised as standard of performance based on the earlier guidance of teachers. The

ecological validity of assessment is also an issue according to Gardner (1993). Predictive

validity of traditional intelligence tests may be psychometrically sound, but its usefulness

beyond predicting school performance is questionable. Therefore, prediction could be

improved if assessments more closely approximated real working conditions. Instruments for

measuring intelligence should also be “intelligence-fair” (Gardner, 1993:176). Consequently,

we need to reduce the bias toward measuring intelligence through logical/mathematical and

linguistic abilities and move toward looking more directly at a specific intelligence in

operation (e.g., assessing for spatial intelligence by having an individual navigate his or her

way around unfamiliar territory). Gardner acknowledges that this approach to assessment

may be difficult to implement.

Gardner (1993) emphasized two additional points that are critical about assessment. The

first is that the assessment of intelligence should encompass multiple measures. Relying on a

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single 1Q score from a WISE0III (Wechsler Intelligence Scale for Children) without

substantiating the findings through other data sources does the individual examinee a

disservice and produces insufficient information for those who provide interventions.

Secondly, all assessments and resulting interventions must be sensitive to individual

differences and developmental levels. Finally, Gardner is in favour of assessment for the

primary purpose of helping students rather than classifying or ranking them.

While these views about assessment are intuitively sensible, Sternberg (1991) argues

that the naturalistic approach is a “psychometric nightmare” (Sternberg: 1991:266).

Quantifying performance on these sorts of assessments is difficult; objectivity is

questionable, and cultural bias is still a problem. Hard data is the scientific “gold standard”

and psychometric soundness is a prerequisite. Therefore, Sternberg (1991) hesitates in

endorsing this approach to assessment on the basis that we would simply be replacing one

flawed system of measurement with an approach that is equally problematic. Recent research

on MI Theory-based assessments (Plucker, Callan & Tomchin, 1996 ) provides evidence in

support of Sternberg’s concern about psychometric quality.

The discussion of the conceptual framework was considered as indicated below.

Identifying gifted children, with the intention of assisting them to attain their fullest potential,

is not a straightforward pursuit. There are many theories regarding the characteristics that

may be displayed by gifted children, just as there are many definitions of intelligence, which

may be considered the core of giftedness. Whether intelligence is considered strictly in

academic terms or in a more holistic fashion directly affects the manner in which an

individual may describe and identify giftedness.

Charles Spearman, cited in Bartholomew (1995) considered intelligence to be a general

ability that specific talents could be built up; whereas Robert Sternberg believed and

presented the theory that intelligence could be grouped into three specific areas:

componential, experiential, and contextual. This theory was called the triarchic theory of

intelligence (Sdorow 1998). The multiple intelligence theory of Howard Gardner may be

considered the most advanced exploration of human intelligence. Gardner claims there are

seven different kinds of intelligence: linguistic, logical-mathematical, spatial, musical,

bodily- Kinesthetic, intra-personal, and interpersonal (Krechevsky & Gardner 1990). These

three definitions of intelligence act as a fundamental premise for developing an agreeable list

of gifted characteristics may be developed in order to assist in the identification of the gifted.

Upon investigation it would appear that gifted characteristics are divided into two main

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symbiotic groups, cognitive abilities and emotional stabilities (Harrison 1998). Both of these

areas require a supportive environment if the realization of an individuals potential is to be

accomplished. Too often only the negative characteristics of gifted children are dwelled upon,

hindering the identification of further positive factors and the development of such (Vialle &

Konza 1997). In an attempt to create a comprehensive positive list of characteristics, the area

of affirmative qualities must be addressed primarily.

An advanced problem solving ability appears to be a principal characteristic amongst

those considered gifted. Displaying and employing convergent and divergent thought

processes with a full understanding of the procedure, gifted children appear to be highly

innovative (Vialle & Konza 1997). Part of this heightened problem solving ability stems from

the early comprehension the gifted develop for minor symbolic internationalism. Early

reading ability is representative of this capacity (Vialle & Konza 1997). Developing an early

affinity for symbols and their relationships to each other aids the individual in comprehending

complex and sophisticated concepts, whether emotional or cognitive, subjective or objective.

A displayed early ability to draw may also be used as an identifying characteristic of a

gifted individual. As with reading, drawing displays an understanding of symbols and their

capacity to be manipulated in order to convey information, functionally as well as

philosophically (Harrison 1998). Whether these advanced manipulative abilities are

encouraged by emotional expansion or eager cognitive development is an argument

paralleling the nature versus nurture debate, and one that is equally futile. From a personal

perspective, cognitive expansion would appear to stem from emotional need, with

manipulation of symbols being the accepted method of interaction and therefore the area that

appears hyper-developed amongst those considered gifted. With this in mind, the awareness

of differing perceptions, and the methods with which they can be manipulated would have to

be an area included in the description of gifted individuals, and in a listing of identifying

characteristics.

Dr. Annemarie Roeper, cited in (Silverman, 1993) acknowledges the awareness of

perception in her definition of giftedness. This awareness leads to what may be termed

sensitivity, an area that is particularly vulnerable to outside influences. If directed in an

appropriate manner, these sensitivities may lead to optimal development of the gifted

individual (Silverman 1993). Kezimierz Dabrowski in Silverman (1993) describes these

heightened sensitivities as intensities, and explains them in terms of overexcitabilities.

Dabrowski divides the over excitabilities of an individual into five areas: Psychomotor,

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Sensual, Intellectual, Imaginational and Emotional, Over excitabilities must not be

misinterpreted as hyperactivity, as hyperactivity implies a lack of control and focus, two areas

that are not inherent in the gifted. Dabrowski recognized Emotional Intelligence, or the

productive development of Emotional Over excitability, as the root of all other valid

expansion of intelligence and possible giftedness. Unfortunately, from a personal perspective,

Dabrowski attached culturally specific moral elements to his theory of emotional

development, an act that has rendered his theory rather culturally biased.

At this point the main characteristics of gifted children would appear to be, innovative

thinking, displayed by advanced manipulation of symbols (reading and drawing),

sophisticated awareness of differing perceptions, heightened sensitivities, and displayed Over

excitabilities. Another characteristic that appear inherent in those of a gifted disposition

would appear to be entelechy (Lovecky 1993). Entelechy may be defined as a form of

motivation that is personally developed, employed to assist oneself in realizing one’s fullest

potential. The theory of self-actualization presented by Maslow (1954) encourages this form

of motivation, with the development of Rotter’s (1966) internal locus of control being a

primary concern. Personal responsibility for one’s own learning and development may be

considered a key element in those who are truly gifted. This does not mean that initially a

gifted child should not receive positive guidance, but it does explain what some observers

describe as an apparent “will to be” (Lovecky 1993) within gifted individuals.

The characteristic of heightened sensitivities warrants further expansion due to its

ambiguous sub structures, in particular the area of moral sensitivity. Moral sensitivity is a

commonly accepted identifying factor of giftedness in children; early moral concerns imply

an advanced moral development (Lovecky 1997). Due to Silverman’s (1993) observation

that the fundamental aspect of Dabrowski’s, and Lawrence Kohlberg’s, expansion of Jean

Piaget’s theories regarding moral development being altruistic behaviour, it is possible to

immediately identify ethnocentric bias. Altruism is not a globally accepted virtue – by some it

is even considered nihilistic (Rand 1964) - therefore such a base for identifying moral

advancement is extremely limited. Considering moral development from the standpoint of

Maslow, removing moral ideals and replacing them with personal values, a more

encompassing theory may be presented.

While the five key gifted characteristics, when nurtured appropriately, can lead to a

very fulfilling process of personal development, they can also pilot the individual towards

nihilistic tendencies when maltreated. Anti-social and obsessive-compulsive behaviours, as

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well as self-imposed extreme isolation, are some of the unfortunate side effects suffered by a

misdiagnosed or rejected gifted child (Vialle & Konza 1997). The gifted child may also suffer

inner tension, when rates of cognitive, emotional and physical developments do not coincide

with each other (Silverman, 1993). Over-sensitivity, especially in the area of emotional

intelligence can also lead to feelings of anxiety and guilt, both psychologically damaging

elements (Silverman 1993). Unaddressed moral sensitivities regarding injustice can also be

an area of much discomfort in the gifted individual, especially when personally held peers, or

concurrent does not readily accept value paradigms with common morality (Lovecky 1997).

These negative characteristics occur directly due to misdiagnosis and neglect of gifted

children and their needs. If a gifted child is correctly identified, and has their needs met and

constructively challenged, there should be no reason a gifted child should suffer any anxiety

or frustration (Gallagher Harradine & Coleman 1997).

When considering the views regarding the identification and support of the gifted,

Clark’s (2002) definition of intelligence must be contemplated. Clark believes that

intelligence is a combination of an individual’s intuitive, cognitive, physical and affective

performance, which would put her attitude more in line with that of Gardner, rather than

Spearman, although Clark states that Gardner either misunderstands, or misrepresents, the

interactive nature of the separate intelligence forms. Clark pays particular attention to the area

of creativity, as an identifying factor of giftedness as well as a means to develop intelligence,

recognizing J. P. Guilford as the initiator of this theory (Clark 2002). According to Guilford,

in Barron and Harrisson (1981) creativity is a form of problem solving that produces

innovative and constructive solutions to problems. Clark believes that creativity should not be

considered only from a cognitive positivist stance, but from a more holistic perspective

(Clark 2002).

Although Clark admits that the concepts presented by Dabrowski are very useful for

those wishing to analyse giftedness, she does not mention the altruistic factors of his theory.

In fact, Clark describes personal value development more in line with the opinions of Maslow

with the omission of Dabrowski’s moralism. Clarks does not agree with altruism, or indeed

moralism, being a key element of giftedness. Clark even goes as far as to state that a child

raised in an environment of fixed beliefs suffers from oppressed creativity, and therefore

lacks the very driving force that encourages further intellectual growth. Clark prefers to focus

on the sensitivities shown by the gifted, regarding social states, describing a more positive

regard for self and others concerning personal liberties and rights. Selflessness, or in fact any

68

moral stance, is not mentioned in Clark’s exploration of personal value development (Clark

2002). Clark also chooses not to dwell on the aspect of behavioural problems, when

describing the interactive qualities of the gifted. Clark takes a more objective, less

judgmental, perspective towards what may be considered by some, as anti-social or disruptive

behaviourism. This idea is reinforced when Clark describes the non-conformist attitudes

sometimes displayed by the gifted, but chooses not to condemn the action. In fact Clark

presents the thought that the imposing of irrational conformity has detrimental effects on the

intellectual advancement of the individual (Clark 2002). Again, this stance is more in line

with the objective description of subjective self-actualisation presented by Maslow, than the

absolute, expected moral development presented by Dabrowski.

It may be said that Clark takes a more objective, as well as holistic, position when

describing the gifted than is often displayed by her contemporaries. While many may view

this stance as contradictory, from a post-modern perspective, it is the viewpoint that allows

for the greatest expansion. Creating a more objective, comprehensive and unbiased list of

gifted characteristics will assist in a more positive identification process. Constructing

detection criteria from a morally normative classification foundation creates many deviant

components, which from an objective stance would not exist. With the removal of the deviant

label from the observable non-conformist behaviours displayed by the gifted, there would be

less chance of more profound anti-social conduct being formed.

Without the composition of detection criterion an important component of specific

education would be unrecognised, resulting in the failure to cater for, and assist in, the

realisation of an important element of society. In the interest of equal opportunities for all

children, fixed moral codes and anti-elitist attitudes need to be eliminated. The damaging

social context within which gifted children often find themselves in hinders both the

development of the child as well as their sphere of influence (Vialle & Konza 1997).

Environments of conformity in no way benefit the gifted child (Clark 2002). Unbiased

recognition of the gifted, in accordance with an objective/holistic form of identification,

needs to be followed by an authoritative form of guidance that allows the individual to

develop to their fullest potential, unhindered by irrational moral codes.

As in any form of characteristics list, the creation of such can only help in the

identification of subjects. The problems arise when the register of defining characteristics is

biased or imposing, and when those in a position to identify are unfamiliar with the protocol

or even the reality of the concept. For a list of characteristics to be of value for assisting in the

69

recognition of gifted children, it must become common within the context of not only

schooling, but also parenting. Long held derogatory beliefs need to be confronted with a

positive process of identifying and assisting the gifted, supported by rigorous data obtained

and presented in an objective manner. If the process of re-educating and reforming the social

context within which children are primarily socialised was successful, not only would the

circumstances surrounding the gifted child be made more favourable, but the assisted

development of more gifted children from birth would also be possible: a situation that, from

a personal perspective, would greatly improve.

(C) Empirical Studies on Giftedness:

Agulewicz and Eliot (1986) conducted a study on the predictive validity of the scales

for rating the behavioural characteristics of superior students of gifted children from three

distinct socio-cultural groups. The predictive validity of a recently published behavioural

rating scale for identifying gifted and creative students (scale for rating the behavioural

characteristics of superior students) SRBCSS was investigated for three distinct ethnic socio-

economic groups.

A total of 402 students in grades 3 through 6 were used in the study. Students were

categorized as low, mid and high socio-economic groups.

Regression analyses were computed between SRBCSS and both the Stand ford achievement

test. The result indicated low to moderate relationship between variables for Anglos from

mid-high and low socio-economic backgrounds. Correlations were higher for a group of low

socio-economic Hispanics, with the highest correlations being between reading

comprehension sub-test of the SAT and the creative scales of the SRBCSS.

The above study bears some semblance of the present study in that it is purely

exploratory – using an already developed instrument to identify the mathematically

precocious pupils. There remains an uncertainty as to whether the scale serves this purpose.

This is so because the author’s intention in developing the SRBCSS was to develop an ad-

hoc/adjacent measure in identifying gifted students.

The finding revealed that SRBCSS might be very good at the identification of gifted Hispanic

students. The scales also may be useful in the investigation of giftedness among students of

various socio-cultural groups.

In another factors underlying teachers’ perceptions of highly gifted students: cross-

cultural study, Busse et al (1986) conducted a study with 434 West Germany students and

70

446 American High School students. The teacher taught nature language. All teachers

completed a questionnaire in which they rated their nominees on 83 characteristics. The inter-

correlations of the items were factor analysed, Separated into two samples, to yield seven

German and five American factors. This study is related to the present study in the listing and

correlation of some of the traits that make up Mathematics precociousness and how to

identify the mathematically precocious children in the two cultures –Ebonyi States consisting

principally of a mixture of other cultures.

The reviewed study tried to look at the various definition of giftedness and models of

identifying the gifted. This is important because the present study is striving to develop and

standardize an instrument for identifying mathematically precocious children in Nigeria, a

different culture.

In another study reported by Weiss (1994) about 2.8 millions East German children

aged 10 to 18 years participated in nine nationwide Mathematical competitions. The 1329

most successful participants of above average IQ of 130 and above were selected for the

study in 1970. In other follow- up studies in 1983 and 1993, data on the background of the

students were gathered from the 23000 relatives of the children. Due to the law prohibiting

the use of IQ testing then in East Germany the IQ of the parents were estimated from their

occupations. Data gathered from the files of the children indicated their aspiration to obtain

university degrees as mathematicians, physicists, engineers and experts in finance. The first

follow –up study in 1983 confirmed that 92 percent of all participants did obtain university

degrees, 7 percent obtained degrees in non- mathematically- oriented fields such as medicine,

biology or the humanities, and 1 percent had no degree at all.

About 43 percent of the fathers of these gifted children belong to the same group with

professional qualifications comparatively as high as those of the 92 percent of the students. In

addition 24 percent of the fathers had university degrees in less mathematically oriented

fields.25.5 percent of the fathers were clerks or skilled workers in jobs such as book keeping,

mechanics tool fitting or draughtsmanship. Only 7.5 percent of all were skilled workers with

jobs such as mason and butcher. With regard to the mothers, the result was not clear: 37

percent maintained jobs typically done by females such as secretary / steno typists, book-

keeping, teaching and laboratory assistants and requiring above average intelligence. Some

mothers were complete housewives without any profession. The following are the empirical

findings:

i. In cases where gifted children had a father who was a graduate in Mathematics,

71

physics or engineering, all sibs of the participants were above average in ability. In such a

family the mother could belong to any profession or be a housewife.

ii. In cases where the gifted children had a father who did not belong to the oriented

professions, the sibs could have any job or profession. Indeed, 14 percent of these sibs belong

to jobs requiring no more than average intelligence.

iii. Parents who belonged to the same high IQ group as the gifted children nearly always

had children who were all of the same above average IQ.Unskilled parental pairs mostly only

had children in unskilled jobs. Parental pairs where both spouses had an estimated IQ of

about 110 had children who were scattered over all possible jobs and professions. The

reviewed study indicated the existence of a strong relationship between mathematical –

technical giftedness in school and achievement in life. The review indicated that there was

strong relationship evidence from the distribution of high professional achievement among

the relatives that such achievement needs not only nurture but also an appropriate genetic

background, which seems to be transmitted as a simple median trait. The review has much in

common with the present study in that the present investigated the influence of parental

education on the functioning of the items of the instrument in Ebonyi state.

Nokelainen (2004) examined the influence of self-attributions and parental altitude to

the development of mathematical talent with a self- report questionnaire administered on

three distinct groups of mathematical gifted Finnish students (n= 203) and their parents (n=

188). The first group represents highly able adults who have participated in internal Olympics

in Mathematics. The second group was constituted from students of polytechnics institute

who study Mathematics as part of their studies. The third group, pre-finalists, consisted of

secondary school students who take part in national competition in Mathematics.

All the student participants completed self- confidence attitude (SAAS) questionnaire.

The instrument used a six- point Likert scale ranging from strongly disagree to strongly

agree. The instrument included 18 items measuring students’ abilities and effort attributions,

based on Weiner’s (1996) attribution theory. Four dimensions: (1) ‘success due to ability’ (2)

‘Failure due to lack of ability ‘ (3) “ success due to effort “ and (4) “ Failure due to lack of

effort “

The parents completed inventory of parental influence questionnaire. The instrument

is five- point Likert scales ranging from strongly disagree to strongly agree. The instrument

included 39 items measuring the following five dimensions: (1) Pressure (2) Psychological

support (3) Help (4) Press for intellectual development and (5) Monitoring/time

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management.

The research questions formulated to guide the study included:

(1) Is the self- attribution of the three groups of mathematically gifted children influenced by

three-group membership, gender and level of giftedness?

( 2 )What are the most important forms of the parental influence?

How parental influences differ in the three groups?

Data generated were analysed statistically in the following four stages:

First, variable selection was conducted on the students and parent data to see if the items are

technically applicable for linear statistics computations. Second, the one- way Analysis of

variance was conducted on student and parent data to determine the level of differences

between groups. Third, explorative factor analysis was conducted on the student data only to

see if the four dimensions of Saas are present. Finally, Bayesian classification Modelling was

conducted to find the predictors of group membership among the self- attribution scale and

background variable with classification modes.

The results showed that the Olympics and pre-finalists did not connect hard work to

mathematical ability. Group effort was shown to be more important factor of success than

ability. The polytechnics had more parental pressure and less psychological support than

Olympians and pre-finalists. Olympians’ parent reported smaller frequencies of parental help

for homework and studying than the polytechnics and pre-finalists. Olympians and pre-

finalists parents emphasised more the value of books and reading than polytechnic parents

did. Polytechnics and pre-finalists’ parents were monitoring more their children’s behaviour

regarding homework, studying and T.V. The above reported study has many things in

common with the present study. The reported study investigated factors that contribute to the

mathematical giftedness of children. The current study, on the other hand, considered the

statuses of gender and parental educational level as variable that may contribute to the

mathematical giftedness of primary school pupils in Ebonyi state. Although the area and the

scope of study of the cited study are different, it is the belief of the researcher that the result

would reveal the place of parental influence in the development of giftedness in a

disadvantaged educational setting such as Ebonyi state.

Furthermore, Edikpa ( 2006 ) developed and validated a 35-item Decision-making skill

inventory for secondary schools. The instrument was subjected to both face and factor

validations. The specific objectives he wanted to accomplish were to:

Assess the validity of the items of the Decision – making skill inventory for secondary

73

schools

Determine the reliability index of the items of the decision- Making Inventory

Determine the influence of gender on the Decision – making skill inventory. The study,

an instrumentation research design by survey, covered the five existing Education Zones

in Anambra State.

As a guide towards the successful completion of the study the following research questions

were used:

How valid are the items of the Decision-Making skill inventory in terms of their factor

loadings?

What is the reliability coefficient of the Decision – making skill Inventory?

What is the influence of gender on the Decision – Making Skill Inventory?. The

instrument was subjected to both face and factor validations using principals drawn from

Delta state. The responses of these principals were subjected to construct validation

exercise. The construct validation reduced the number of items to thirty-five.

The instrument was administered on a total of three hundred and twenty – three

secondary principals in Anambra State. The principal factor and the normal Varimax rotation

of factor Analysis were used to answer research question one, Cronbach Alpha estimates

were used to asses the reliability index and the arithmetic and standard deviation were used to

answer research question three.

The results indicated that the Decision – Making Skill Inventory is valid, has a very reliability

index and has very minimal gender influence. The reviewed study resembles the present

study in that both studies are instrumentation research designs or development studies. The

reviewed developed and validated an attitudinal instrument whereas the present study

developed and validated an aptitude test.

(D) Summary of Literature Review

The concept of giftedness and talentedness in general and mathematical precociousness in

particular is relatively new in the Nigerian socio-cultural/socio-political context.

Nonetheless, its immediate and distant importance outweighs other considerations in the

identification processes. The concept and theoretical foundations of mathematical

precociousness were considered and they indicate that although giftedness in general is a

multi-dimensional phenomenon, which cannot as a result be identified with a single I. Q. test.

Mathematical precociousness, on the other hand, can be identified with a single factor

instrument like the MAGII. The review differentiated among some common terms often used

74

to describe giftedness in a specific area, which have similar meaning with giftedness. These

terms include high achiever, talentedness. It indicated that pupils capable of high

achievement/performance in an area either singly or in combination could be regarded as

gifted. The review went further to enumerate these areas as: General intellectual ability,

specific academic ability, creative/productive thinking, leadership visual and performing arts

and psychomotor ability. The study concentrated on specific academic ability and developed

its instrument based on the following constructs which were considered very important

measures of mathematical precociousness of a child namely: numeric ability; quantitative

ability measure; spatial ability measure; and creative thinking ability measure.

Both the general trait, attributes and characteristics of giftedness in particular and

traits, attributes and characteristics of mathematical precocious ness were reviewed from

teacher nomination form and rating scale inventory was drawn.

Tests needed for the identifications were reviewed and there was an indication that

identification is also multidimensional and the processes involved include: teacher

nomination, peer nomination, honour roll, creativity student council, Mathematics ability

scale rating. The literature showed that paper and pencil test like Mathematics ability tests

and other achievement tests are very effective compared with other subjective non-test

methods like teacher and peer nomination.

The importance of validity and reliability and also gender influence on mathematical

giftedness were reviewed. Available literatures indicate that there are more males than

females that are found to be either creative or gifted in Mathematics, although it is not

restricted to any gender. Also, the influence of socio-economic status specifically parental

education status and the attitude of the student towards Mathematics were reviewed and it

indicated that children from high status homes are better only in verbal area than those from

the lower socio-economic status. The situation as it concerns Mathematics is not yet clear.

Other empirical studies were reviewed and it was discovered that there are limited

literatures in this area. The few available ones are foreign. Thus there is the need to develop

and validate an instrument for Nigerian primary schools (MAGII). The study seeks to

contribute its quota in encouraging the indention and selection of the gifted in general and the

mathematically precocious children in the Nigerian primary schools in particular.

75

CCHHAAPPTTEERR TTHHRREEEE

RESEARCH METHODOLOGY This chapter discussed the research methodology. Specifically it focussed on the

various steps and activities the researcher adopted in carrying out the study. It discussed the

design of the study, area of the study, population of the study, the nature of the sample and

the sampling techniques, instrument for data collection, validation of Instrument used for data

Collection, reliability of instrument used for data collection and method of data analysis. The

various steps the researcher adopted in collecting the needed data for the study were

discussed.

Design of the study

The study was an instrumentation research design. An instrumentation research

design, according to Abonyi, Okereke, Omebe and Anugwo (2006), is a research design in

which the researcher aims at developing, validating/ standardising and recommending an

instrument for a specific educational purpose. The present study is an instrumentation

research design because the researcher developed and validated an instrument for the

identification of pupils who are mathematically precocious in Ebonyi state Primary School

System.

Area of the Study

The study was carried out in Ebonyi State of Nigeria. Ebonyi State is one the States of

Nigeria. Ebonyi State was created out of Abia and Enugu States respectively in 1996. The

newness of Ebony State and the level of development within the educational sector make it

lack basic human and materials resources necessary to tackle the challenges posed to

education in the 21st century. One aftermath is, therefore, the classification of the state as

being educational disadvantaged by the Federal Government. Inspite of this backwardness

there are a lot of gifted children from the state. However, her backwardness in the educational

sectors makes it develop very low interest, action and attention towards the Gifted and

Talented Children Education Programme. Major fallout of this low action and interest

towards the gifted and Talented Children Education in the state is a total absence of an

identification instrument within the state especially at the local government levels. The choice

of this state is a matter of educational development and advancement in that the results of the

study yielded an instrument that could be used for the identification of the crop of

76

mathematically gifted pupils now abound within the Ebonyi state Primary school system. .

Both government and privately owned primary schools were made use of.

Population of the Study

The population for the study comprised all the primary six pupils, which were nominated by

their teachers as being mathematically gifted in Ebonyi State. The numbers of approved

primary schools in Ebonyi States in 2005-2006 academic years according to the Ebonyi State

Universal Primary Education Board (ESUPEB, 2006) is seven hundred and thirty one

primary schools (731). In Ebonyi state, there are three education zones namely: Ebonyi

Central, Ebonyi North and Ebonyi South.

The distribution of these existing primary schools in the state are indicated in table 1.0 below.

Sample and Sampling Techniques

The sample for the study was drawn through the multistage sampling technique adopting

different and varied sampling techniques at each of the following stages. At the first stage, the

entire state was stratified along the existing education zones, namely: Ebonyi north, Ebonyi

Central and Ebonyi south using the stratified random sampling technique. At the first stage,

the simple random sampling technique was used to select one education zone (i.e. Ebonyi

South) out of the three existing education zones of Ebonyi state for trial testing. To avoid

sensitising the respondents the other two remaining zones were selected for the final

administration of the final instrument (MAGII) using the simple random sampling technique.

The proportionate stratified sampling technique was used at the third stage to select only ten

percent (10%) of the entire school population in Ebonyi North and Ebonyi central education

zones for the final administration of the instrument (MAGII). The purposive sampling

technique was used at the fourth stage to draw the subjects for the study in that all the pupils

nominated by their teachers as being mathematically gifted were used. The school population

and the number of schools used for the study are presented in table 1.0.

TABLE 1.0: School Population and the Number Sampled In Ebonyi State.

Ebonyi State Education

Zone

School

Population

Number Of School

Sample

bonyi South 213 21

Ebonyi Central 220 22

Ebonyi North 298 _

TOTAL 731 43

77

SOURCE: ESUPEB RECORDS, 2006.

Instrumentation

For the successful accomplishment of this work the researcher developed one instrument, the

instrument for identification of mathematically gifted pupils which is the major instrument

anticipated, and two other instruments, namely: the teacher nomination and rating Scale and

the pupils’ questionnaire. The teacher nomination and rating Scale were to provide

information on the extent the behavioural characteristics of pupils relate to the mathematical

giftedness. The pupils’ Questionnaire on the other hand was developed to provide

information relating to the variables in the study, namely: gender and parental educational

status. The teacher nomination and rating scale and the pupils’ questionnaire were subjected

to face validations.

The development of the MAGII was based on four distinct psychological traits of

mathematical giftedness namely: Numeric ability, quantitative ability measure, creativity

ability measure and spatial ability measure. A total of 120 items were developed with the

assistance of specialists under the four constructs. The researcher reviewed some foreign

tests, which were, of course, unfit because they were culturally biased. Some other local tests

were reviewed. These help in developing the items for the sub tests and the entire MAGII.

Numeric Ability Measure

Hornby (2000) used “Numeric” as adjective derived from the word ‘Numeracy

‘Numeracy means literacy with numbers. The numeric ability measure subscale was thus

included to measure the numeric ability or the numeracy level of the mathematically gifted

pupils. The researcher developed a total of forty items in this subtest with the help of experts

in this area. These items were shown to some primary school teachers in Ebonyi South before

inclusion. The useful advice offered by these experts enabled the researcher to drop ten items

from the original draft. The remaining thirty items of the section that survived the face

validation exercise were further subjected to factor validation using the Cronbach approach.

In accordance with the existing subscales of the instrument, only four factors were extracted.

Only item(s) of the instrument that recorded a factor loading of 0.35 and above and loaded

simply on the factor were selected as items of the instrument under this subscale. Out of the

thirty items of the instrument that survived the face validation, twenty-one recorded a factor

loading of 0.35 on this factor. It was hoped that the performance of the mathematically gifted

78

pupils in this section would indicate their interest.

Spatial Ability Measure

Hornby (2000) used spatial synonymously as relating to size, shapes and position. The

spatial ability measure subscale was developed to aid the researcher to measure the ability of

the mathematically gifted pupils’ ability in handling problems relating to sizes, shapes and

positions e.t.c. It helps to determine how the spatial ability of the pupils could contribute to

their mathematical giftedness. A total of thirty items were developed under this subscale and

these items were sent to experts for review. The useful advice of these experts enabled the

researcher to drop five items. The twenty-five items Subscale that survived the face

validation exercise were further subjected to factor validation using the Cronbach Apha

approach. Seventeen items met the minimum condition for inclusion as items under this

subscale.

Quantitative Ability Measure Subscale

‘Quantitative’ is used here as a short form for ‘Quantitative reasoning’ or’

Quantitative aptitude’. Hornby (2000) sees ‘Quantitative’ as relating to quantity or amount.

The quantitative ability measure subscale was thus included to measure the mathematically

gifted pupils’ ability in handling problems in number/ quantity relationships. The essence of

this scale therefore is to ascertain the extent the pupils’ reason mathematically. The

researcher developed a total of thirty items under this subscale and these items were sent to

experts for review. Twenty items survived the face validation exercise. The twenty items

were subjected to factor validation using the Cronbach Alpha method. Out of the total of

twenty-five items, twelve items of the instrument recorded a factor loading of least 0.35 and

simply on this factor. These twelve items were selected into the instrument under the

quantitative ability measure subscale.

Creativity Subscale

This subscale was developed to help determine the creativity level and how creativity

could contribute to the mathematical ability of the mathematically gifted pupils. The

researcher developed the twenty items in this section and these items were sent to experts in

Mathematics for review.

All the items survived this stage of validation. They were further subjected to factor

79

validation using the Cronbach Apha method. A total of thirteen items satisfied the necessary

and sufficient condition for their inclusion as the items of the instrument.

The Teacher Nomination Form and Rating Inventory

The instrument was developed to enable the class teachers to nominate the pupils they

considered mathematically precocious through their behavioural characteristics. The

instrument consists of two major sections: the biography section for the bio-data of both the

pupils and teachers, known as part A and the part B of the instrument contains ten (10)

behavioural traits of mathematically precocious pupils.

This section of the instrument was constructed as a kind of rating schedules for

teachers. The traits so specified were rated accordingly using Nworgu’s (1991:117) modified

five-point Likert like scale. The traits were rated as follows:

4 – Exceptional

3 – Much

2 – Moderate

2 – Little

0 – Undecided

The instrument was developed using the characteristics of mathematical precocious

ness derived from books and journals. The traits so identified were submitted to teachers,

experts in Psychology, special educationists and measurement and evaluation experts for

scrutiny. In all, a total of ten characteristics selected by these experts and teachers were used.

Some special educationists and psychometricians further scrutinized the list.

Pupils’ Questionnaire

The questionnaire was designed for collecting personal data and information relating

to the variables on the mathematically gifted pupils within the Ebonyi State Primary school

system. Information needed from the pupils includes: pupils’ name of school, date of birth,

school location, parental background, occupation and socio-economic status based on some

list of vocations identified by the researcher. Pupils who were identified and nominated as

gifted by their classroom teachers completed the questionnaire. The data that were collected

with this questionnaire aided the researcher in classifying the subject in terms of the related

variables in the study.

The trial testing of the pupils’ questionnaire was carried out in Ebonyi South

80

education zone. Only ten percent of the entire primary school population in each of the

remaining zones of the two states drawn from the proportionate stratified sampling technique

was used in the study. The pupils for the study were sampled using the purposive sampling

technique; in that only pupils nominated by their class teachers as being mathematically

gifted were used.

Validity

The following three approaches were adopted in determining the validity of the

MAGII items. These approaches are: face, construct and concurrent validities.

(a) Face validation. (i) The MAGII: A draft of the instrument for the identification of

mathematically gifted pupils for Nigeria primary schools (MAGII) was subjected to face

validation by a team of three experts in Mathematics, Measurement and Evaluation, Guidance

Counselling. The critical comments by these experts were incorporated into the modification

and dropping of some of the items of MAGII.

Only items deemed fit by these experts were retained and used in the final draft of the

Mathematics giftedness identification instrument for Nigerian secondary schools.

(ii) The teachers’ nomination scale inventory and the pupils’ nomination scales were also

presented to these experts. These experts subjected the rating scale to scrutiny based on the

behavioural characteristics of mathematically precocious pupils listed in the behavioural

characteristics. Also, the pupils’ questionnaire was presented to these experts for scrutiny

and face validation. Their corrections/modifications to the items were incorporated into the

final draft.

(b) Construct Validity

The items of the MAGII were subjected to construct validity by analysing the one hundred

and twenty items factorally. The factor analysis aided the researcher to place the items under

the appropriate principal factors. These factors are numeric ability measure, quantitative

ability measure, creative/productive thinking ability measure and spatial ability measure.

Items of the MAGII with a factor loading of 3.5 and above on each of these principal factors

were selected into the final draft of the instrument. Out of the one hundred and twenty (120)

items of the MAGII, only sixty- three items survived. The number of items that survived in

each section of the MAGII is as indicated in the table 2.0 below

Table 2.0: Number of Items That Survived After Validation.

81

Sub test Number of items in the

original test

Number of items that survived in

each section

Numeric 40 21

Spatial 20 12

Quantitative 30 17

Creativity Thinking 30 33

Total 120 63

These Sixty - three item versions of the instrument (i .e MAGII) form the final draft of the

instrument, which aided the researcher in collecting pertinent data for the study.

Concurrent Validity: In order to ascertain exactly what MAGII is doing with respect to the

giftedness of the pupils, the finial draft of the MAGII and the 1999 version of the National

Examination Council of Nigeria (NECO) G.I F.T. Instrument was concurrently administered

on a total of thirty (30) primary six pupils drawn from the same Ebonyi North education

zone. The score of these primary six pupils from these two instruments were correlated using

the Spearman’s correlation technique. This yielded an alpha value of 0.9, 0.91, 0.84, 0.92 for

the sub tests respectively and 0.92 for the entire test. These indicate a high concurrent validity

of the MAGII. The result indicates that each of the subscale of MAGII as well as the entire

test predict mathematical precociousness of the pupils.

Reliability

Reliability of an instrument is the extent to which an instrument measures whatever it

is measuring.

Therefore, the stability of the MAGII was established using the test retest approach. The

MAGII was administered on a total of 30 primary six pupils nominated by their teacher as

being mathematically precocious from central school, Onueke, Amuzu primary schools I and

II respectively within Ebonyi Central education zone on the twentieth of November, 2004. On

the sixth of December 2004 the MAGII was administered on the group of primary six pupils.

The scores obtained on these two occasions were correlated using the Spearman’s Rank

Order correlation technique. This yielded alpha values of 0.8, 0.71, 0.98, and 0.63

respectively for the sub tests and 0.6 for the entire instrument. This indicates that the MAGII

is highly stable.

Trial Testing

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The items of these instruments were pre-tested. The instruments were administered to 50

primary six pupils nominated as being mathematically gifted from Ezillo axis of Ebonyi

Central education zone between fifteenth and seventeenth December, 2004. The sample used

consisted of 15 girls and thirty-five boys. The trial test enabled the researcher to make further

modifications/corrections to the options of the items. Also ambiguities due to sentence

structure were removed.

Final Administration of the MAGII

The final draft of the MAGII was administrated to all the primary six pupils from forty- three

(43) primary schools pupils selected for the study from the two remaining education zones of

the state irrespective of whether the pupils were nominated or not. A total of one thousand

five hundred copies were printed and distributed. One thousand were recovered from the

pupils. However only the scripts of five and one pupils actually nominated were marked and

the results used for analysis. The final administration of the MAGII was done as follows:

(1) The test booklet and the answer booklets were distributed to the pupils first.

(2) The instructions were read from the booklets.

(3) The examples given were read and explained.

(4) The pupils were allowed a short period of time to ask questions not properly

understood by them.

(5) Having completed the above sequence, the pupils were allowed to commence work

During the examination, the teachers (examiners) apart from answering questions from the

pupils, when necessary, also checked for character. The pupil’s questionnaire was

administered as well.

In order to answer the research questions the individual items were scored

dichotomously either as right or wrong. Each item correctly responded to by the pupils earned

seven marks; each item wrongly responded to earned a zero mark. A Total of the marks

earned by each pupil on the subscale and on the entire were reduced to 100 by applying the

formula:

; 100 test ain items of No

test ain correctly got items ofnumber Total earnedMark x

Method of Data Analysis

The research work was an instrumentation research study, which involved hypotheses

83

testing. The data generated as a result of the MAGII were analysed descriptively and

inferentially. Research question 0ne was analysed and answered with the principal factor and

the Varimax rotation of factor analyses. Cronbach Alpha estimates were used to answer

research question two in terms of assessing the reliability. Other research questions were

answered using the descriptive statistics of the mean and standard deviations. The hypotheses

were tested at the 5% level of significance depending on their individual requirements as

indicated below:

Hypothesis One

This sought to determine whether the difference in the extent the individual items of the

instrument for the identification of pupils mathematically gifted in Ebonyi State Education

System function with respect to gender is significant. Gender as a variable could be classified

into two exclusive and exhaustive categories namely: male and female. There are a lot of

parametric and nonparametric statistics, which could be used to test the hypothesis.

However, since the functioning of the individual items with respect to gender was considered

in terms of the parameter, arithmetic mean, the nonparametric statistical alternatives were

ruled out. Out of the parametric statistical techniques, only the t- and z- tests statistics for the

difference between means of two populations are possible techniques to be used. The z- test

was used because of the large sample involved.

Hypothesis Two

The hypothesis sought to ascertain whether the difference between the proportions of items

that function differently as a result of gender and those that do not function differently is

significant at the 0.05 alpha level. The hypothesis is a test of difference between two

population proportions. Two population proportions of the pupils used for the study were

considered namely: the proportions that functioned differently and those that did not. Thus

the t-test and z- test of difference between two population proportions are possible statistical

techniques to be used. However, because of the largeness of the sample size the z-test of

difference between two population proportions was used.

Hypothesis Three

This hypothesis sought to ascertain whether the characteristics of the distribution of the

pupils’ scores as a result of gender are significant at the 0.05 alpha levels. The hypothesis was

84

to be tested with respect to gender. Gender is classified into two exclusive and exhaustive

categories, male and female. There are a lot of parametric and non-parametric statistical

techniques, which could be used to test the hypothesis. Owing to the fact that the

characteristics of the distribution are to be determined in terms of the parameter arithmetic

mean; the nonparametric statistical alternative techniques were not appropriate here.

However, based on the fact that gender has two categories, only the t- and z- tests of

significance between two population proportions are the only appropriate statistical

techniques for the test. The t- statistic was arbitrarily used to reduce monotony in the use of a

particular statistical technique.

Hypothesis Four

The hypothesis sought to ascertain whether the difference in the extent the individual items of

the instrument functioned as a result parental educational status is significant at 0.05 alpha

levels. This hypothesis was tested with respect to the variable, parental educational level.

Parental Educational Level was classified into three exclusive and exhaustive categories

namely: low, middle and high. There are lots of parametric and nonparametric statistical

techniques, which could be used for the test. The test is based on the parameter, arithmetic

mean. The non-parametric statistical alternatives were considered more suitable for use here.

The One- Way Analysis was used since it is the only parametric statistical technique that

could be used when the variable on which the hypothesis is based has three or more exclusive

categories.

Hypothesis Five

The hypothesis sought to ascertain whether the difference between the proportions of items

that functioned differently as a result of parental educational status and those that do not

function differently is significant at the 0.05 alpha levels. The hypothesis is a test of

difference in two population proportions because only proportions that functioned differently

and those that did not function differently were considered. Thus the t-test and z- test of

difference between two population proportions were possible statistical techniques to be used.

However, because of the largeness of the sample size the z-test for the significance of the

difference between two population proportions was used.

85

Hypothesis Six

The hypothesis sought to ascertain whether the characteristics of the distribution of the

pupils’ scores as a result of parental educational level are significant at the 0.05 alpha levels.

The variable parental educational status was classified into three exclusive categories in the

study. A lot of parametric and nonparametric statistical techniques are available. Since the

characteristics of the distribution of the pupils’ scores were to be ascertained using the

arithmetic means of the three groups, the non-parametric statistical techniques were

considered inappropriate. However, out the numerous parametric statistical techniques, the

One- Way Analysis was considered most appropriate for use since it is the only parametric

statistical technique applicable when the variable of interest has three 0r more exclusive

categories.

Hypothesis Seven

The hypothesis sought to ascertain the whether the difference between teacher nomination

scores and the scores of the pupils on instrument is significant at the 0.05 alpha levels. There

are a lot of parametric and nonparametric statistics that could be used to test hypothesis.

However, since the test is that of testing the significance of the difference between the means

of two populations the nonparametric statistical alternatives were considered inappropriate

for use in this case. Two independent samples were involved namely, teacher nomination

scores and the Pupils’ scores on the instrument. Thus, the t-test statistics and z- test statistics

were the only parametric statistical concepts left for consideration. The t- test statistics was

used.

Hypothesis Eight

The hypothesis sought to ascertain whether the interactive effects of gender and parental

educational status are significant at the 0.05 alpha levels. The hypothesis sought to test the

significance of the interactive effects of two independent variables, namely gender and

parental educational level each of which has two and three levels. Therefore the test was

considered to be similar to 2x3 factorial design. Accordingly, the Two – Way Analysis of

variance was considered highly appropriate for use here.

86

CHAPTER FOUR PRESENTATION OF THE RESULTS

This chapter presents the results of data analysis based on the research questions and the hypotheses that guided the study. The results are presented in tables according to the respective research questions and hypotheses. Research Question 1 What is the validity of instrument for the identification of pupils who are mathematically gifted within the Ebonyi State Primary School System? The data collected for the study was subjected to factor analysis using the principal component and factor matrix. The summary of the data from the factor loading for all the ninety – one items of the instrument for the identification of mathematical giftedness within the Ebonyi state Primary school system that out of the eight factors extracted by computer only four have items sufficiently loaded on them They are factors 2, 5, 6 and 8 respectively. Out of the ninety- one item used for the study, sixty- three recorded at least factor loading of 0.35.This based on Meredith (1969) recommendation that the minimum loading of any item should be 0.35 and the minimum number of items per factor should be four. For the four factors and their corresponding items factor loading and communality.( see Appendixiii) Research Question 2 What is the reliability index of the subscale and the entire test? In order to answer this research question, the Kuder- Richardson formula 20 was applied. Table 4.0: Proportion of the Pupil Failing/Passing each Item of the Numeric Subtests of the Instrument

Item

/No

No

pass

ing

No

faili

ng

Prop

ortio

n pa

ssin

g

Prop

ortio

n fa

iling

Prod

uct P

q

1 401 100 0.80 0.20 0.20 2. 281 220 0.6 0.44 0.25 3. 306 195 0.61 0.39 0.24 4. 366 135 0.73 0.27 0.20 5. 135 396 0.27 0.73 0.2 6. 215 285 0.43 0.57 0.25 7. 306 195 0.60 0.40 0.23 8. 105 396 0.21 0.80 0.2 9. 100 401 0.12 0.80 0.16

87

10 200 301 0.40 0.60 0.23 11. 150 351 0.30 0.70 0.21 12. 170 331 0.34. 0.66 0.22 13. 185 316 0.37 0.63 0.23 14. 286 215 0.57 0.49 0.25 15. 165 336 0.33 0.67 0.22 16. 180 321 0.36 0.64 0.23 17. 130 371 0.26 0.74 0.19 18. 150 351 0.30 0.69 0.21 19. 220 281 0.44 0.56 0.25 20. 240 261 0.48 0.58 0.25 21. 180 321 0.36 0.64 0.23

= 0.83 TABLE 5.0: Proportion of the Pupils that Fail/Pass each of the Items on the Spatial Subscale

S/N

O

NO

PA

SSIN

G (p

)

NO

FA

ILIN

G

PRO

POR

TIO

N

PASS

ING

PRO

POR

TIO

N

FAIL

LIN

G

PRO

DU

CT

PQ

22. 306 195 0.61 0.39 0.24 23. 331 200 0.67 0.34 0.22 24. 351 150 0.70 0.30 0.21 25. 386 115 0.77 0.23 0.17 26. 331 200 0.66 0.35 0.23 27. 251 250 0.50 .50 0.27 28. 276 225 0.55 0.45 0.25 29. 240 261 0.50 0.53 0.25 30. 175 326 0.35 0.65 0.23 31. 200 301 0.40 0.61 0.24 32. 95 406 0.19 0.81 0.15 33 120 381 0.24 0.96 0.18 = 0.85

88

S/N

o

No

pass

ing

No

faili

ng

Prop

ortio

n pa

ssin

g

Prop

ortio

n fa

iling

Prod

uct P

Q

34. 80 421 0.16 0.84 0.14 35. 110 391 0.22 0.78 0.17 36. 316 185 0.63 0.37 0.23 37. 250 251 0.50 0.50 0.25 38. 235 266 0.47 0.53 0.25 39. 326 175 0.66 0.35 0.23 40. 140 361 0.28 0.72 0.20 41. 145 366 0.29 0.71 0.21 42. 125 376 0.25 0.75 0.19 43. 105 396 0.21 0.79 0.17 44. 95 406 0.19 0.81 0.15 45. 115 386 0.23 0.77 0.18 46. 235 266 0.47 0.53 0.25 47. 291 210 0.58 0.42 0.24 48. 250 251 0.50 0.51 0.25 49. 200 301 0.40 0.60 0.24 50. 230 271 0.46 0.54 0.25 = 0.83

89

Table 6.0:Proportion of pupils passing / failing each item of the creativity subscale

Item

/NO

No

pass

ing

No

faili

ng

Prop

ortio

n pa

ssin

g

Prop

ortio

n fa

iling

Prod

uct

PQ

51. 266 235 0.53 0.47 0.25 52. 351 150 0.70 0.30 0.21 53. 281 220 0.56 0.45 0.25 54. 235 266 0.47 0.53 0.25 55. 210 291 0.42 0.59 24 56. 175 326 0.35 0.65 0.22 57. 110 391 0.22 0.77 0.17 58. 210 291 0.42 0.58 0.24 59. 391 110 0.78 0.22 0.17 60. 130 371 0.26 0.74 0.19 61. 170 331 0.34 0.66 0.22 62. 180 321 0.36 0.64 0.23 63. 190 311 0.38 0.62 0.24 = 0.85 Data on the proportion of the pupils who pass/fail each item of the instrument for the identification of mathematical giftedness in Ebonyi State Primary school system showed that: = 0.81 Data on table 4.0 above show each item of the subscales and of the entire instrument for the identification of mathematical giftedness in Ebonyi State primary school system. The data affirm that the reliability of Indices for the numeric, spatial, quantitative and creative thinking subscales are: 0.83, 85 ,0. 83 and 0.85 respectively. Also, the data show the reliability index for the entire MAGII to be 0.98. These reliability indices are reasonably high enough to warrant the use of the instrument as a G. I F T. instrument in Ebonyi state. Research Question 3 To what extent do the items of the instrument for the identification of mathematical giftedness within Ebonyi State Primary school system function differently as a result of gender?

90

Table 8.0: The Mean and standard deviation on the Influence of Gender on the pupils’ Performance on the Instrument S/NO GENDER MALE FEMALE X SD X SD 1. 5.79 2.81 5.99 6.47 2. 4.57 2.35 3.57 3.12 3. 3.95 3.48 4.14 3.45 4. 5.19 3.08 4.95 3.19 5. 5.67 3.60 4.79 3.39 6. 4.14 3.45 4.59 3.34 7. 4.05 3.47 4.41 3.39 8. 1.15 2.60 1.78 3.06 9. 1.57 2.93 1.23 2.67 10. 2.57 3.39 2.85 3.47 11. 1.76 3.05 2.45 3.35 12. 2.05 3.20 2.68 3.41 13. 2.00 3.17 3.14 3.49 14. 3.24 3.50 3.95 3.48 15. 2.24 3.28 2.41 3.34 16. 2.33 3.31 2.68 3.14 17. 1.76 3.05 1.77 3.05 18. 4.10 3.46 2.55 3.38 19. 2.76 3.43 3.32 3.51 20. 3.29 3.51 3.45 3.57 21. 1.90 3.13 3.11 3.49 22. 4.24 3.43 4.32 3.41 23. 4.62 3.33 4.67 3.31 24. 4.81 3.26 5.00 3.17 25. 5.33 2.99 5.5 2.88 26. 4.19 3.45 4.91 3.21 27. 3.86 3.49 3.14 3.49 28. 4.14 3.45 3.64 3.51 29. 3.67 3.51 3.00 3.48 30. 2.38 3.33 2.50 3.37 31. 3.05 3.48 2.50 3.37 32. 0.48 1.77 2.09 1.78 33. 1.43 2.83 1.90 3.13 34. 0.76 2.19 1.50 2.88 35. 0.48 1.77 2.14 3.23 36. 5.05 3.15 3.82 3.50 37. 3.14 3.49 4.73 3.29 38. 2.76 3.43 3.82 3.50 39. 6.05 2.41 3.18 3.50 40. 2.14 3.24 1.77 3.05 41. 1.52 2.90 2.45 2.77 42. 1.90 3.13 1.55 2.91

91

43. 0.62 1.99 1.86 3.10 44. 0.86 2.30 1.73 3.02 45. 2.19 3.26 1.05 2.50 46. 3.14 3.49 3.41 3.51 47. 4.00 3.48 3.41 3.51 48. 3.52 3.57 3.41 2.51 49. 3.05 3.49 2.91 3.46 50. 3.29 3.51 3.10 3.50 51. 4.15 3.45 3.32 3.51 52. 4.90 3.22 4.91 3.50 53. 3.81 3.50 4.36 6.84 54. 3.24 3.50 3.32 3.51 55. 2.95 3.47 1.91 3.13 56. 1.33 2.76 1.95 3.15 57. 3.71 3.51 2.14 3.25 58. 3.71 3.51 2.14 3.23 59. 6.05 2.41 4.86 3.23 60 4.34 2.12 4.31 2.32 61 3.76 3.42 3.760 3.44 62. 1.14 2.60 2.41 3.34 63 2.24 2.12 2.30 2.13 Data on table 8.0 provided answers to research question 2. The data affirm that there are established pattern with respect to gender differences on the pupils’ performances in all the items of the instrument .In particular, the data show that the performances of the pupils were gender sensitive in favour of the male pupils on the following items: 2, 9, 19, 27, 36, 39, 40, 41, 42, 45, 49, 53, 55, 57, 58, and 59 respectively. The data also show that the performances of the pupils were gender sensitive in favour of the female pupils on the following items: 1, 3, 4, 5, 6, 8, 10-18, 20-26, 28, 30, 32-35, 37, 38, 43-44, 46-47, 50, 51, 52, 54, 56,and 60. The rest of the items of the instrument were found not to have functioned differently as a result of gender. In summary, gender partitioned the entire items of the instrument into two exclusive sets of items: those that functioned differently as a result of gender and those that do not function differently as a result of gender. Research Question 4 What are the characteristics of the distribution of pupils’ scores on the subscales and on the entire instrument for the identification of mathematical giftedness within Ebonyi State primary school system as a result of gender?

92

Table 9.0: Mean And standard deviation on the Gender Influence On the Characteristics of the Distribution of the Pupils’ Score on the Subscales and On the Entire Test .

Scal

es

Gen

der

N

Mea

n X

Stan

dard

de

viat

ion

SD

Numeric Male 245 42.15 18.6 Female 256 41.87 16.62 Spatial Male 245 50.05 19.19 Female 56 48.04 16.3 Quantitative Male 245 42.15 18.66 Female 256 41.82 16.62 Creativity thinking Male 245 48.05 21.92

Female 256 53.5 29.07 Entire test Male 245 41.37 15.23 Female 256 41.15 10.57

Data on table 9.0 illustrate the extent to which the items on the subscales and on the

entire instrument function as a result of gender. The data affirm that more female pupils than

male pupils’ were suspected of their gifts in Mathematics and then nominated to participate in

the study in Ebonyi State Primary School System within the 2005/2006 academic session.

The data also support the fact that the performances of the suspected pupils were gender

sensitive on the entire instrument for the identification of mathematical giftedness within the

Ebonyi State Primary School System. The data show that the male students score relatively

higher than their female counterparts on the entire instrument.

On the numeric, spatial, quantitative subscales the male pupils recorded mean

performances of: x = 42.15, SD = 4.24; x=50.05 and SD=4,24; and x=42.15 and SD=4.34

respectively which were found to be systematically better than the corresponding

performances of: X = 41.82, SD = 16.62; X = 48.04; SD = 15.5 and X = 41.82, SD = 16.62

recorded by the female pupils on the same scales. On the creativity thinking subscale the

female pupils recorded a mean performance of: X = 53.5, SD = 29.01 which was found to be

comparatively better than a corresponding mean performances of X = 50.83, SD = 25.94

recorded by their male counterpart.

93

Finally, on the entire instrument the distribution of the pupils’ scores depicted marginal and systemic gender in the patterns of the pupils’ achievement on the instrument. On the test, the male pupils recorded a mean performance of X = 41.37, SD = 13.73 and their female counterpart recorded a mean performance of X = 41.15 and SD = 10.57. The difference in the mean performance was found to be systematic. In all, the pupils’ scores on the subscales depicted lack of uniqueness in the way and manner the items are distributed across the subscales of the instrument. The pupils’ scores on the entire instrument showed slight and systematic differences as a result of gender. Research Question 5: To what do the items of the instrument function differently as a result of parental educational level? Table 10.0: Mean And Standard Deviation on the Influence of Parental Educational Level on the Performance of Pupils on the Instrument Item No. Parental Educational Level Statistics Low Middle High 1 X 5.72 5.14 3.33 SD 2.31 3.12 4.04 2. X 3.92 4 4.67 SD 3.48 3.52 4.04 3. X 3.86 4.52 2.33 SD 3.49 3.38 4.04 4. X 4.98 6.53 4.67 SD 3.18 1.78 4.04 5. X 1.73 5.02 2.33 SD 3.03 3.18 4.04 6. X 3.15 1.81 4.67 SD 3.49 3.11 4.04 7. X 1.93 2.98 2.33 SD 3.48 3.50 4.04 8. X 1.98 0.78 0.00 SD 3.16 2.24 .00 9. X 1.54 1.30 2.33 SD 2.91 2.76 4.04 10. X 2.66 1.54 2.33 SD 3.40 2.94 4.04 11. X 2.26 1.30 0.00 SD 3.28 2.76 0.00 12. X 2.54 3.23 2.33 SD 3.37 3.52 4.04 13. X 2.77 1.79 0.00 SD 3.43 3.09 0.00 14. X 2.90 3 0.00 SD 3.46 3.51 0.00 15. X 2.18 2.1 2.33

94

SD 3.25 3.25 4.04 16. X 2.02 1.83 0.00 SD 3.9 3.12 0.00 17. X 2.00 1.32 0.00 SD 3.17 2.78 0.00 18. X 2.24 1.11 0.00 SD 3.27 2.59 0.00 19 X 3.74 2.64 4.67 SD 3.45 3.43 4.04 20. X 3.11 1.79 2.33 SD 3.49 3.09 4.04 21. X 2.56 0.49 2.33 SD 3.38 1.80 4.04 22. X 4.82 3.80 2.33 SD 3.25 3.53 4.04 23. X 4.57 4.42 2.33 SD 3.34 3.42 4.04 24. X 4.02 4.42 4.67 SD 3.47 3.42 4.04 25. X 5.50 4.72 4.67 SD 2.88 3.32 4.04 26. X 5.20 4 4.67 SD 3.06 3.51 4.04 27. X 2.00 4.14 4.67 SD 3.17 3.48 4.04 28. X 4.14 3.38 4.67 SD 3.45 3.56 4.04 29. X 4.11 3.62 4.67 SD 3.43 3.56 4.04 30. X 2.37 3.38 4.67 SD 3.32 3.56 4.04 31. X 3.06 3.38 2.33 SD 3.48 3.56 4.04 32. X 0.87 0.72 0.00 SD 2.32 2.17 0.00 33. X 1.00 1.21 2.33 SD 2.41 2.69 4.04 34. X 4.48 0.48 0.00 SD 3.37 1.81 0.00 35. X 1.72 1.45 0.00 SD 2.57 2.89 0.00 36. X 2.69 6.28 2.33 SD 3.41 2.17 4.04 37. X 3.54 5.79 2.33 SD 3.51 2.69 4.04 38. X 3.19 5.55 2.33 SD 3.49 2.89 4.04 39. X 2.34 2.90 4.67

95

SD 3.31 3.57 4.04

40. X 3.91 7. 4.67 SD 3.48 0.00 4.04 41. X 3.11 2.41 0.00 SD 3.49 3.39 0.00 42. X 1.35 1.93 0.00 SD 2.76 3.18 0.00 43. X 1.35 6.58 0.00 SD 2.76 1.81 0.00 44. X 0.99 5.6 2.33 SD 2.45 2.84 4.04 45. X 0.76 4.32 2.33 SD 2.08 3.57 4.04 46. X 3.46 2.12 2.33 SD 3.51 3.25 4.04 47. X 3.65 2.68 2.33 SD 3.50 3.45 4.04 48. X 4.53 2.56 4.67 SD 3.35 3.41 4.04 49. X 4.16 2.59 4.67 SD 3.44 3.42 4.04 50. X 1.74 3.23 2.33 SD 3.03 3.52 4.04 51. X 3.42 4.77 4.67 SD 3.51 4.28 4.04 52. X 5.83 3.95 4.67 SD 2.61 3.51 4.04 53. X 4.67 3.88 4.67 SD 3.31 3.40 4.04 54. X 3.61 2.28 4.67 SD 3.51 3.32 4.04 55. X 2.32 1.4 4.67 SD 3.3 2.83 4.04 56. X 2.35 1.33 2.33 SD 3.31 2.78 4.04 57. X 2. 40 0.80 0.00 SD 3.33 1.12 0.00 58. X 2.79 2.71 2.33 SD 3.43 3.47 4.04 59. X 1.87 2.77 2.33 SD 3.09 3.42 4.04 60. X 1.85 0.68 2.33 SD 3.09 2.10 4.04 61. X 2.58 2.10 4.67 SD 3.38 3.21 4.04 62. X 2.76 2.77 4.67 SD 3.43 3.43 4.04

96

63 X 3.56 3.23 4.32 SD 2.43 4.23 1.21 Data on table 10.0 describes the extent the individual items of the instrument function differently as a result of the pupils’ parental education level. There was no definite trend or pattern in the way the individual items function as a result of pupils’ educational background. However, the data on the same table show that pupils’ performances on items1, 7, 8, 10, 11, 12, 13, 16, 17, 20, 21, 22, 23, 25, 26, 34, 35, 46, 47, 53, 54, 56, 57, 58, and 60 favour pupils nominated from low educational backgrounds. Performances of the pupils on items: 3, 4, 5, 14, 31, 36, 37, 38, 40, 42, 43, 44, 45 and 50 favour pupils nominated from middle educational backgrounds and performances in items 2, 6, 9, 15, 19, 24, 27, 28, 30, 33, 39, 48, 49, 51, 52, 55, 61, 62 and 63 favour pupils from high educational backgrounds. In summary, the performances of the pupils on individual items of the instrument favour one level of parental educational status or the other. Performances of the pupils in the remaining items did not favour any of the different levels of parental educational levels. In all, pupils’ performances partitioned the items into those that functioned differently as a result of parental educational status and those that do not. Research Question 6 What are the characteristics off the distribution of the pupils’ scores on the subscales and on the entire instrument as a result of parental educational status? Table 11.0: Mean And standard Deviation On The Influence Of Parental Educational Level (Status) On The Characteristics Of The Distribution Of The Pupils’ Scores On The Subscales And On The Entire Test (MAGII)

Scal

es

Pare

ntal

Ed

ucat

iona

l lev

el

N

X

SD

Numeric Low 460 41.46 17.25 Middle 38 47.79 21.1 High 3 48 21.1 Spatial Low 460 48.33 17.62 Middle 38 57.45 18.06 High 3 49.33 15.37 Quantitative Low 460 48.33 25.91 Middle 38 57.45 14.04 high 3 49.33 9.7

97

Creativity Low 460 50.6 26.25 Middle 38 52.79 22.93 High 3 61 8.66 Entire test Low 460 40.86 12.23 Middle 38 45.9 11.48 High 3 44 0.27

Data on table 11.0 illustrate the characteristics of the distribution of the pupils’ scores on the subscales and on the entire instrument for identification of gifted pupils in Ebonyi state as a result of parental educational status. There was no identified pattern in the pupils’ performances on the subscales and the entire instrument as a result of the pupils’ parental educational background. Nonetheless, the data show that the pupils’ drawn from the middle parental educational background recorded mean performances of X = 57, SD = 4.06, X = 57.45, SD = 3.04 on the spatial and quantitative subscales respectively. These performances were found to be the best with respect to the subscales. On the numeric and Creativity thinking subscales pupils nominated from the high parental educational backgrounds recorded mean performances of X = 48, SD = 3.9; X = 61, SD = 2.66 respectively. These performances were found to be the best with respect to these subscales. Finally, on the entire scale the pupils nominated from the middle parental educational background recorded the best performance of X = 45 and SD =4.48. In summary, the characteristics of the distribution of the pupils’ scores indicate that the pupils drawn from the different levels of parental educational status performed differently within and across the subscales and the entire instrument. This result revealed that the specific educational status to which the pupils belong exerts differential influences on the pupils’ performances. Research Question 7 To what extent has the interactive effects of gender and parental educational level affected the pupils’ performances on the instrument. Table 12.0:Mean and standard deviation on the Interactive Effects of Gender and Parental Educational Status On Pupils’ Performances On The Instrument.

Gender Parental Educational Status Factor Low Middle High Total N

X SD

N X SD

N X SD

X=41.3 N = 245 SD=13.73 Male 221

40.61 9.41

24 48.32 7.81

0 0 0

98

Female 239 40.99 10.15

14 41.76 11.12

3 57.73 13.13

X = 41.15 N = 256 SD=10.56

Total 460, 40.81 12.2

38, 45.9 11.11

3, 51.73 ,12.3

SD=501 41.26 9.67

The study involves two independent variables namely; gender and parental educational level. Gender and parental educational level in turn consist of two and three levels respectively. The problem was thus investigated using a (2 x 3) factorial design. When the two main effects, gender and parental educational level, were separately considered, the data show that the male pupils obtained a mean score, X = 41.37 and SD = 13.73 and their female counterpart obtained a mean score of X = 41.15 and SD = 10.56. The data show that the male pupils performed systematically better than their female counterparts on the instrument. The data on table 12.0 also affirm that the pupils from the different levels of parent educational background: low, middle and high recorded mean performances of: X = 40.81 and SD = 12.2, and SD = 11.47 and X = 51.73 and SD = 12.73 respectively. The data thus show that pupils from the high educational background recorded the best performance on the instrument. Also, the data generated on how the different levels of the first independent variable (gender) interact with the different levels of the second variable (parental education level) showed that: (i). Female pupils identified from low parental educational background performed better than their male counterparts from similar background on the instrument. (ii). Male pupils from the middle parental educational backgrounds performed

comparatively better than their female/male counterparts from similar parental background on

the instrument.

Finally, the same data indicated that: (i). Male pupils from the middle parental education status recorded the best performance

on the instrument comparing the pupils’ performances across the different levels of parental

educational level.

(ii). Female pupils from the high parental educational background recorded the best

performance on the instrument comparing the pupils’ performances across the different levels

of parental educational status.

There is actually a difference in the mean performances of the pupils as a result of the

99

interactive effects of gender and parental educational status. Research Question 8 What are the magnitudes and directions of the pairwise inter correlation coefficients among the subscales and the entire scale for the identification of giftedness within the Ebonyi State Primary School System. Table 13.0:Pairwise Correlational Matrix Of The Subscales And The Entire Instrument For The Identification Of Giftedness Within Ebonyi State Primary School System. Scale Numeric Spatial Quantitative Creativity

thinking Entire test

Numeric 1 0.53 0.16 -0.01 0.53 Spatial 0.53 1 0.19 0.06 0.55 Quantitative 0.16 0.19 1 0.19 0.39 Creativity thinking -0.01 0.06 0.19 1 0.40 Entire test 0.53 0.55 0.39 0.39 1 The data presented on table 13.0 above represent the pair wise correlation matrix of the subscales and the entire instrument for the identification of mathematical giftedness within the Ebonyi State Primary School system. The data affirm that: (i). The correlation coefficient between the creativity and numeric subscales is -0.01. This was found to be small in magnitude and negative in direction. This shows a small inverse relationship between the pupils’ performances on the two subscales of the instrument. This means that pupils who score highly on the creativity thinking subscale scored disappointingly very lowly on the numeric subscale or vice versa. In other words, the performances of the pupils are varying in opposite direction. The two respective subscales predict different psychological constructs of the pupils yet to be determined. (ii). The correlation coefficient between spatial and numeric subscales is 0.53. This was found to be positive and moderate in size. This means that the performances of pupils on these subscales vary moderately in the same direction. Differently put pupils who performed moderately well in one subscale also performed moderately well in the other sub scale and or vice versa. (iii). The correlation coefficients between the subscales creativity thinking and quantitative subscales, numeric and quantitative subscales and creativity thinking and spatial subscales are obtained as: 0.19, 0.16 and 0.06 respectively which are considerably small in magnitude and positive in direction. These values enabled the researcher to conclude that there is a very small direct relationship between the performances of the pupils on these respective subscales and vice versa. In other words, the performances of the pupils on the subscales are slightly positive and have minimal functional relationship. The respective pairs of subscales are

100

minimally related in the way and manner they predict the mathematical giftedness of the pupils. Finally, the pairwise correlation coefficients between the subscales and the entire test; entire versus creativity thinking, entire versus numeric, entire and quantitative, and entire and spatial were found to be: 0.40, 0.53, 0.39 and 0.55. These show that the relationships between the entire and each of the respective subscales are positive and moderately related. The results affirm that performances of the pupils on the subscales are related moderately to their performances on the entire scale. The data also affirmed that the pupils’ performances on the spatial and numeric subscales wear more semblances to the performances of the pupils on the entire scale. Research Question 9 What are the magnitude and direction between teacher nomination scores and the scores of the gifted pupils on the instrument? Table 14.0: Pairewise Correlation Matrix Between The Teachers’ Nomination Scores And Their Scores On The Instrument.

Scal

e

Cre

ativ

ity th

inki

ng

H

Num

eric

Qua

ntita

tive

Spat

ial

Teac

hers

no

min

atio

n

4.

Creativity thinking

1

0.40 -0.01 0.19

0.06

-0.11

5.

H

0.40 1

0.53

0.39

0.55

-0.13

1.

Numeric

-0.01 0.53

1

0.16

0.53

-0.15

3. Quantitative 0.19 0.39

0.16

1

0.19

-0.14

2. Spatial

0.06 0.55 0.53 0.19 1 -0.07

6. Teacher nomination -0.11 -0.13 -0.15 -0.14 -0.07 1

The data on table 14.0 above represent the pairwise correlation coefficient between the teacher nomination scores and scores of the pupils on the instrument. There is generally no special trend or pattern in the data. The data, however, indicate that the correlation

101

coefficients between teacher nomination scores and pupils’ scores on the entire test, teacher nomination scores and the pupils’ scores on the creativity thinking, teacher nomination and the pupils’ scores on the numeric, teacher nomination scores and pupils’ scores on the spatial subscale, and teacher nomination scores and the pupils’ scores on the quantitative ability measure subscales to be: -0.11, -0.15, -0.07 and -0.14 respectively. These correlation coefficients are small as well as negative in direction. These values imply very minimal inverse relationship between the performances of the pupils on the subscales and/ or the entire test and their performances on the teacher nomination procedure. The same data indicate the correlation coefficient between the teacher nomination scores and the scores of the pupils on the entire test as – 0.13. The implication of the result is that there is a very minimal inverse relationship between the teacher nomination procedure and the pupils’ performances on the test. This means in effect that the teacher nomination scale is predicting something different from what the instrument did. Finally, none of the pairwise correlation coefficients was found to be zero. This implies the existence of some kind of functional relationships between the performances of the pupils on the entire and on the subscales and the performances of the pupils on the nomination procedure. The implication is that neither the subscales nor the entire instrument is redundant in predicting the pupils’ giftedness. Put differently, there are indication that all the subscales and the instrument can exist as separate constructs of mathematical giftedness. Hypothesis 1: HO1: There is no significant difference in the extent the individual items of the instrument functioned as a result of gender. Table 15.0: Z-Statistics Values on the Gender Influence on the Functioning On the Individual Items.

S/ N

G

END

ER

ALP

HA

Z-TE

ST

VA

LUES

INTE

RPR

ET

ATI

ON

Z-ca

l

Z -c

rit.

1 Male 0.05 -0.72

1.96 ** Female 0.05 1.96 2 Male 0.05

\-0.84 1.96 **

Female 0.05 1.96 3. Male 0.05 -0.46 1.96 **

102

Female 0.05 1.96 4. Male 0.05

0.65 1.96 **

Female 0.05 1.96 5. Male 0.05

\-1.86 1.96 **

Female 0.05 1.96 6. Male 0.05

\-1.15 1.96 **

Female 0.05 1.96 7. Male 0.05

-0.91 1.96 **

Female

0.05 1.96

5 Male 0.05 -1.92

1.96 ** Female 0.05 1.96 9. Male 0.05

1.07 1.96 **

Female 0.05 1.96 10. Male 0.05

-0.97 1.96 **

Female 0.05 1.96 11. Male 0.05

-1.87 1.96 **

Female 0.05 1.96 12. Male 0.05

-1.66 1.96 **

Female 0.05 1.96 13. Male 0.05

-2.95 1.96 **

Female 0.05 1.96 14. Male 0.05

-1.78 1.96 **

Female 0.05 1.96 15. Male 0.05

-0.45 1.96 **

Female 0.05 1.96 16. Male 0.05

-0.90 1.96 **

Female 0.05 1.96 17. Male 0.05

-0.03 1.96 **

Female 0.05 1.96 18. Male 0.05

3.93 1.96 **

Female 0.05 1.96 19. Male 0.05

-1.39 1.96 **

Female 0.05 1.96 20. Male 0.05

-0.42 1.96 **

Female 0.05 1.96 21. Male 0.05 -3.15 1.96 *

103

Female 0.05 1.96 22. Male 0.05 -0.20 1.96 ** Female 0.05 1.96 23. Male 0.05

1.40 1.96 **

Female 0.05 1.96 24. Male 0.05

-0.51 1.96 **

Female 0.05 1.96 25. Male 0.05

-0.49 1.96 **

Female 0.05 1.96 26. Male 0.05

-1.87 1.96 **

Female 0.05 1.96 27. Male 0.05

1.79 1.96 **

Female 0.05 1.96 28. Male 0.05

1.26 1.96 **

Female 0.05 1.96 29. Male 0.05

1.66 1.96 **

Female 0.05 1.96 30. Male 0.05

-0.31 1.96 **

Female 0.05 1.96 31. Male 0.05

1.39 1.96 **

Female 0.05 1.96 32. Male 0.05

-5.36 1.96 *

Female 0.05 1.96 33. Male 0.05

-1.40 1.96 **

Female 0.05 1.96 34. \Male 0.05

-2.49 1.96 *

Female 0.05 1.96 35. Male 0.05

-5.49 1.96 *

Female 0.05 1.96 36. Male 0.05

3.20 1.96 *

Female 0.05 1.96 37. Male 0.05

-4.05 1.96 *

Female 0.05 1.96 38. Male 0.05

-2.64 1.96 *

Female 0.05 1.96 * 39. Male 0.05

8.24 1.96

Female 0.05 1.96 **

104

40. Male 0.05 1,02

1.96 Female 0.05 1.96 * 41. Male 0.05

-2.57 1.96

Female 0.05 1.96 ** 42. Male 0.05

1.03 1.96

Female 0.05 1.96 * 43. Male 0.05

-4.12 1.96

Female 0.05 1.96 * 44. Male 0.05

-2.80 1.96

Female 0.05 1.96

45. Male 0.05

-0.66 1.96 *

Female 0.05 1.96

46. \Male 0.05

-0.34 1.96 **

Female 0.05 1.96

47. Male 0.05

\-0.91 1.96 **

Female 0.05 1.96

48. Male 0.05

0.28 1.96 **

Female 0.05 1.96

49. Male 0.05

0.35 1.96 **

Female 0.05 1.96

50. Male 0.05

0.26 1.96 **

Female 0.05 1.96

51. Male 0.05

2.06 1.96 *

Female 0.05 1.96

52. Male 0.05

-0.01 1.96 **

Female 0.05 1.96

53. Male 0.05

-0.88 1.96 **

Female 0.05 1.96

54. Male 0.05

-0.20 1.96 **

Female 0.05 1.96

55. Male 0.05

-0.01 1.96 **

Female 0.05 1.96

56. Male 0.05

2.74 1.96 *

Female 0.05 1.96

57. Male 0.05

-1.82 1.96 **

Female 0.05 1.96 58. Male 0.05 4.06 1.96 *

105

Female 0.05 1.96 59. Male 0.05

3.59 1.96 *

Female 0.05 1.96 60. Male 0.05

-3.66 1.96 *

Female 0.05 1.96 61. Male 0.05

-1.81 1.96 **

Female 0.05 1.96 62. Male 0.05

-1.71 1.96 **

Female 0.05 1.96 63. Male 0.05

-0.91 1.96 **

Female 0.05 1.96 ** Significant at 0.05 alpha levels. * Not significant at 0.05 alpha level Data on Table 15.0 affirm that for items: 13, 18, 21, 32, 34, 35, 36, 37, 41, 43,44, 45, 51, 56, 58, 59, 60 each recorded a Z- calculated values which was found to have, by far, exceeded the corresponding critical value at the same level of significance and for the same degrees of freedom. Based on this, the Null hypothesis one as it separately affected the individual items of the instrument was rejected and its corresponding alternative accepted. The conclusion was that gender considerably affected the pupils’ performances on the items. The rest of the items of the instrument recorded table-critical values, which was found to be by far less than the corresponding computed table value. Again, the null hypothesis as it affected these items was accepted at the expense of its alternatives, which was respectively rejected. The conclusion was that gender did not considerably affect the pupils’ performances on these items. In all, gender partitioned all the items into the proportion that function differently as a result of gender and proportions that do not function differently as a result of gender. Hypothesis 2 Ho2: There is no significant difference in the proportion of the items that function differently and those that do not function differently at the 0.05 alpha level as a result of gender. Table 16.0: Z- test statistics on gender influence on the functioning of the individual items of the instrument

Sect

ion

Tot.

No

of It

ems

No

of I

tem

s th

at

func

tione

d di

ffer

ently

N

O. o

f Ite

ms

that

di

d no

t Pr

op.

Of

Item

s th

at

func

tione

d di

ffer

ently

PPr

op.

Of

Item

s th

at

did

not

func

tion

diff

eren

tly P

P 1 –

P2

Z-ca

lcul

ated

va

lue

Z-cr

itica

l val

ue

Inte

rpre

tatio

n

Numeric 21 2 19 0.1 0.9 -0.8 -2.15 1.645 * Spatial 12 1 11 0.08 0.92 -0.84 -1.61 **

106

Quantitative

17 9 8 0.53 0.47 0.06 0.25 **

Creativity thinking

13 5 8 0.38 0.62 -0.24 -0.84 *

Entire 63 17 46 0.27 0.73 -0.48 -3.38 ** **Significant at 0.05 alpha level *Not significant at 0.05 alpha level Data presented on table 16.0 affirm that the proportion of the items that functioned differently as a result of gender is P1 =0.1 and the proportion that failed to function differently as a result of gender is P2 =0.9. On subtraction, P1 -P2 = -0.8 was obtained. This show that the proportion of items of the numeric subscales that functioned differently is 0.8 less than the proportion that did not. Further, the hypothesis as it relates to this subscale was tested. A Z –test calculated value of –2. 33 was obtained. This, on comparison, was found to be less than the corresponding – Z0. 05 = - 1.645.The Null hypothesis was thus rejected at the 0.05 level of significance. The conclusion was that the proportion of the items of the Numeric subscale that functioned differently as a result of gender is significantly higher than the proportion that did not at the 0. 05 alpha level. Data generated on the quantitative, spatial and creativity thinking subscales show that the proportions of the items of these respective subscales that functioned differently as a result of gender are: 0.08, 0.53 and 0.38. On the same subscales, the proportion that did not functioned differently as a result of gender is: 0.92, 0.47 and 0.62. This yielded: -0.84, 0. 06 and –0.24 on subtraction as the respective differences between the proportion of the items of the respective subscales that functioned differently as a result of gender and those that did not. These values indicate that the proportion of the items of the respective subscales that functioned differently as a result of gender was 0.84, 0.06 and 0.24 less than, greater than and less than the proportion of the items of the same subscales that did not function differently as a result of gender. A test of significance was conducted on the respective values. These yielded Z- calculated value of: -1.61, 0.25 and –0.84 for the various subscales. Based on these values the Null hypotheses as they relate to the respective subscales were all accepted. The conclusion was that the difference between the proportion of the items of the subscales that functioned differently and those that did not function differently as a result of gender was not with respect to the respective subscales was not significant as a result of gender. On the entire instrument the difference between the proportion of items that functioned differently and those that did not function differently was observed to be – 0.48. This indicates that the proportion of the items of the entire instrument that functioned differently as a result of gender is 0.48 less than the proportion that did not. The test of significance of difference yielded a Z0. 05 calculated value of –3.38, which was found to be less than the corresponding critical value. Based on this the Null hypothesis was rejected. The conclusion

107

was that the proportion of the items of the instrument that functioned differently as a result of gender and those that do not function differently as a result of gender was significantly different. This implies that the proportion of the items of the entire instrument that function differently is significantly less than those that did not functioned differently as a result of gender. HO3 : There is no significant difference in the characteristics of the distribution of the pupils’ scores on the subscales and on the whole instrument as a result of gender. Table 17.0:t-Test Statistics For The Characteristics Of The Distribution Of The Pupils’ Scores On The Whole And Subscales As A Result Of Gender.

** Significant at 0.05 alpha level *Not significant at alpha level. Summary of the data presented on Table 17.0 above yielded for the numeric subscales a t- calculated value of 0.66. Comparatively this value was found to be by far less than the corresponding t- critical value of 1.96 at the 499 degrees of freedom and the 0.05 alpha levels. Based on this result the Null hypothesis as it affected the numeric subscales was

Scale Gender Perf

orm

anc

e X

SD t-ca

l

Alp

ha

t-cr

itica

l

Numeric

Male 42.29 5.34 0.66 0.05 1.96**

** Female 41.68 4.00 Spatial

Male 50.06 4.64 5.42 0.05 1.96** ** Female 48.04 3.56

Quantitative

Male 46.6 4.24 7.03 0.05 1.96**

** Female 44.04 3.9 Creativity thinking

Male 48.71 4.24 157.2 0.05 1.96**

** Female 52.86 4.21 Entire Test

Male 7.89 1.11 0.05 1.96**

** Female 41.15 6.79

108

accepted at the expense of its alternative hypothesis, which was consequently rejected. The conclusion made was that the characteristics of the distributions of the pupils’ scores on the numeric subscale as a result of gender were not significant at the 0.05 alpha levels. The t-test of significance of the Null hypothesis as it affected the spatial, quantitative, creativity thinking subscales yielded a t-calculated value of 5.42, 7.03, and 157.2 respectively for the subscales. Comparatively these values were found to be far less than the corresponding t-critical value of 1.96 at the 499 degrees of freedom and the 5% level of significance. Based on these results the Null hypothesis as it affected the respective subscales was accepted at the expense of their corresponding alternative hypothesis, which was consequently rejected. The conclusion was that gender significantly affected the pupils’ performances on the subscales at the 5percent level of significance. Finally, on the entire instrument a calculated t- value of 1.11 was obtained. This was compared to the corresponding t-critical value of 1.96, which was obtained at the 0.05 levels of significance and at the 499 degrees of freedom. Based on this result the Null hypothesis was accepted and its alternative rejected. The conclusion was that gender did not significantly influence the pupils’ performances on the entire instrument. Hypothesis 4 HO4: There is no significant difference in the extent the individual items of the instrument function differently as a result of parental educational status. Table 18 .0: One-way Analysis of Variance on the extent the individual items of the instrument functioned as a result of parental educational status S/N

Ed-L

evel

X SD FR F-ratio Critical

Interpretation

1. 1 5.72 2.32 2.95 2.99 ** 2 5.14 3.12 2.99

3 3.33 4.04 2.99 2. 1 3.91 3.48 2.99 ** 2 4 3.51 0.08 2.99 ** 3 4.67 4.04 2.99 3. 1 3.86 3.49 1.05 2.99 **

2 4.52 3.38 2.99 3 2.33 4.04 2.99 4. 1 4.98 3.18 2.99 **

109

2 6.53 1.98 3.48 2.99 3 4.67 4.04 2.99 5. 1 1.72 3.02 2.99 * 2 5.02 3.18 25.21 2.99 3 2.33 4.04 2.99 6. 1 3.15 3.49 2.99 ** 2 1.81 3.11 2.44 2.99 3 4.67 4.04 2.99 7. 1 3.93 3.48 1.73 2.99 ** 2 2.98 3.50 2.99 3 2.33 4.04 2.99 8. 1 1.97 3.16 2.41 2.99 ** 2 0.78 2.24 2.99 3 0.80 0.00 2.99 9. 1. I.54 2.91 0.25 2..99 ** 2. 1.30 2.76 2.99 3. 2.33 4.04 2.99 10. 1. 2.66 3.40 2.08 2.99 ** 2. 1.56 2.94 2.99 3. 2.33 4.04 2.99 11. 1. 2.36 3.28 2.32 2.99 ** 2. 1.30 2.76 2.99 3. 0.00 0.00 2.99 12. 1. 2.54 3.37 0.92 2.99 ** 2. 3.23 3.52 2.99 3. 2.33 4.04 2.99 13. 1. 2.17 3.43 2.45 2.99 ** 2. 1.79 3.09 2.99 3. 0.00 0.00 2.99 14 1. 2.90 3.46 1.07 2.99 ** 2. 3.00 3.51 2.99 3. 0.00 0.00 2.99 15 1. 2.18 3.25 0.02 2.99 ** 2. 2.10 3.26 2.99 3. 2.33 4.04 2.99 16 1. 2.04 3.19 0.68 2.99 ** 2. 1.83 3.12 2.99

110

3. 0.00 0.00 2.99 17 1. 2.00 3.17 1.34 2.99 ** 2. 1.32 2.78 2.99 3. 0.00 0.00 2.99 18 1. 2.24 3.27 3.03 2.99 * 2. 1.11 2.59 2.99 3. 0.00 0.00 2.99 19 1. 3.74 3.50 2.30 2.99 ** 2. 2.64 3.43 2.99 3. 4.67 4.05 2.99 20 1. 3.11 3.49 2.78 2.99 ** 2. 1.79 3.31 2.9 3. 2.33 4.41 2.99 21 1. 2.56 3.76 7.65 2.99 ** 2. 0.49 1.80 2.99 3. 2.33 4.04 2.99 22 1. 4.82 3.25 2.60 2.99 ** 2. 3.80 2.99 23 3. 2.33 2.99 23 1. 4.57 3.34 0.68 2.99 ** 2. 4.41 3.42 2.99 3. 2.33 4.04 2.99 24 1. 4.02 3.47 3.47 2.99 * 2. 4.42 3.42 2.99 3. 4.67 4.04 2.99 25 1. 5.50 2.88 1.39 2.99 ** 2. 4.72 3.32 2.99 3. 4.67 4.04 2.99 26 1. 5.20 3.07 2.66 2.99 ** 2. 4.00 3.51 2.99 3. 4.67 4.04 2.99 27 1. 2.00 3.17 9.05 2.9 * 2. 4.14 3.48 2.9299 3. 4.67 4.04 2.99 28 1. 4.14 3.45 11.99 2.99 * 2. 3.38 3.54 2.99 3. 4.67 4.04 2.99

111

29 1. 4.11 3.45 0.31 2.99 ** 2. 3.63 3.56 2.99 3. 4.67 4.O4 2.99 30 1. 2.37 3.32 1.86 2.99 ** 2. 3.38 3.56 2.99 3. 4.67 4.42 2.99 31 1. 3.06 3.45 0.18 2.99 ** 2. 3.06 3.6 2.99 3. 0.00 4.04 2.99 32. 1. 0.87 2.32 0.26 2.99 ** 2. 0.74 2.17 2.99 3. 0.00 0.00 2.99 33 1. 1.0 2.45 0.51 2.99 ** 2. 1.1 2.17 2.99 3. 2.33 4.04 2.99 34 1. 4.48 3.36 22.39 2.99 * 2. 0.48 1.81 2.99 3. 0.00 0.00 2.99 35. 1. 1.12 2.67 0.50 2.99 ** 2. 1.45 2,89 2.99 3. 0.00 0.00 2.99 36 1. 2.69 3.41 15.37 2.99 * 2. 6.28 2.17 2.99 3. 2.33 4.04 2.99 37 1. 3.54 3.51 5.89 2.99 * 2. 5.79 2.69 2.99 3. 2.33 4.04 2.99 38 1. 3.19 3.49 6.33 2.99 * 2. 5.56 2.89 2.99 3. 2.33 4.04 2.99 39. 1. 2.34 3.31 1. 06 2.99 ** 2. 2.90 5.09 2.99 3. 2.33 4.04 2.99 40 1. 3.91 3.48 11.37 2.99 * 2. 7.00 0.00 2.99 3. 4.67 4.04 2.99 41 1. 3.11 3.49 1.69 2.99 **

112

2. 2.41 3.39 2.99 3. 0.00 0.00 2.99 42 1. 1.35 2.76 0.95 2.99 ** 2. 1.93 3.18 2.99 3. 0.00 0.00 2.99 43 1. 1.35 2.76 49.59 2.99 * 2. 6.58 1.81 2.99 3. 0.00 0.00 2.99 44 1. 0.99 2.45 521.63 2.99 * 2. 5.60 2.84 2.99 3. 2.33 4.04 2.99 45 1. 0.75 1.25 38. 34 2.99 * 2. 4.32 3.51 2.99 3. 2.33 4.04 2.99 46 1. 3.46 3.51 2.88 2.99 ** 2. 2.12 3.25 2.99 3. 2.33 4.04 2.99 47 1. 3.65 3.50 1.35 2.99 2. 2.68 3.45 2.99 3. 2.33 4.04 2.99 48 1. 4.52 3.35 6.10 2.99 * 2. 3.56 3.41 2.99 3. 4.67 4.04 2.99 49 1. 4.16 3.44 4.17 2.99 * 2. 2.57 3.42 2.99 3. 4.67 4.04 2.99 50 1. 1.74 3.03 5.76 2.99 * 2. 3.23 3.58 2.99 3. 2.33 4.04 2.99 51 1. 3.42 3.51 2.98 2.99 ** 2. 4.77 4.28 2.99 3. 4.67 4.04 2.99 52 1. 5.83 2.61 9.13 2.99 * 2. 3.96 3.51 2.99 3. 4.67 4.04 2.99 53 1. 4.67 3.31 1.16 2.99 ** 2, 3.88 3.40 2.99

113

3. 4.67 4.04 2.99 54 1. 3.61 3.51 3.02 2.99 * 2. 2.28 3.32 2.99 3. 4.67 4.04 2.99 55 1. 2.32 3.30 2.57 2.99 * 2. 1.40 2.83 2.99 3. 4.67 4.04 2.99 56 1. 2.35 3.31 1.78 2.99 ** 2. 1.33 2.78 2.99 3. 2.33 4.04 2.99 57 1. 2.40 3.33 9.27 2.99 * 2. 0.18 1.12 2.99 3. 0.00 0.00 2.999 58 1. 2.79 3.43 0.03 2.99 ** 2. 2.71 3.47 2.99 3. 2.33 4.04 2.99 59 1. 2.86 3.45 0.42 2.99 ** 2. 2.77 3,34 2.99 3. 2.33 4.04 2.99 60 1. 1.85 3.09 2.77 2.99 ** 2. 0.68 2.10 2.99 3. 2.33 4.04 2.99 61 1. 2.58 3.38 0.88 2.99 ** 2. 2.10 3.02 2.99 3. 4.67 4.04 2.99 62 1. 2.76 3.43 0.46 2.99 2. 2.77 3.43 2.99 3. 4.67 4.04 2.99 63 1. 2.57 3.44 0.92 2.99 ** 2. 2.10 3.44 3. 2.77 3.32 **Significant at 0.05 alpha levels * Not Significant at the 0.05 alpha levels Data on table 16 .0 above show that items: 5, 21, 27, 28, 34, 36, 37, 40, 43, 44, 45, 48, 49, 50, 5, and 57 recorded F-ration computed values, which far exceeded the corresponding F-ration tab- critical values at the same level of significance and for the same degree of freedom. Consequently, the Null hypothesis as it affected each of the individual items was rejected and the alternative hypothesis accepted. The conclusion was that parental education status

114

significantly affected pupils’ performance on the items. On the rest of the items parental educational status did not significantly affect pupils’ performances on the instrument. Parental educational status partitioned the entire items into proportions that functioned differently as a result of parental educational status and proportions that did not function differently as a result of parental educational status. Hypothesis 5 HO5 : There is no significant difference between the proportions of the items of the instrument that function differently and those that do not function differently as a result of parental educational status at the 0.05 alpha level of significance. Table 19 .0: Z-Test Statistics on the Influence of Parental Educational Status on the Functioning Of the Individual Items of the Instrument

Sect

ion

Tot.

No.

of i

tem

s

No

of it

ems t

hat

func

tione

d di

ffer

ently

N

o of

item

s tha

t fai

led

to fu

nctio

n di

ffer

ently

Pr

opor

tion

that

fu

nctio

ned

diff

eren

tly

Prop

ortio

n th

at d

id n

ot

func

tione

d di

ffer

ently

P 1 –

P2

Z- c

alcu

late

d

Z –

criti

cal v

alue

Numeric 21 2 19 0.1 0.9 -0.8 -2.8 1.645*

Spatial 12 2 10 0.17 0.83 -0.66 -2.56 1.645* Quantitative 17 11 6 0.65 0.35 -0.3 1.19 1.645** Creative 13 2 11 0.15 0.85 -0.7 -2.08 1.645* Entire 63 17 46 0.27 0.73 -0.46 -3.33 1.645*

** Significant at 0.05 alpha level * Not significant at 0.05 alpha level The data on Table 19 .0 above show that the difference between the proportions of items that functioned differently and those that did not function differently as a result of parental educational status is-0.8 on the numeric subscale. This affirms that the proportion of the items of the numeric subscale that functioned differently was 0.8 less than the proportion that did not function differently as a result of parental educational status. The test of the corresponding hypothesis yielded a Z- test calculated value of-2.8, which is less than the corresponding Z-test critical value of –1.645. Based on this result, the Null hypothesis as it affected the numeric subscale was rejected and its alternative accepted. The conclusion made was that the difference between the proportions of the items of the numeric subscale that functioned differently and the proportion that did not function differently as a result of parental educational status was significant at the 5 percent significance level. Similar analysis techniques were applied to the spatial, quantitative and creativity thinking subscales. The results indicated that the difference between the proportions of the

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items of each of these subscales that functioned differently and the proportions that did not function differently as a result of parental educational status to be: -0.66, 0.3, -0.7 respectively. The test of the Null as it affected the items of the respective subscales yielded for each of the subscales a Z-test calculated value of: -2.56, 1.19 and -2. 08, which was respectively found to be: less than, less than and less than the respective Z0.05- critical value of –1.645, 1.645 and –1.645. Based on these results the Null hypothesis as it affected each of these subscales was rejected, accepted and rejected respectively. The conclusion was that there is a significant difference between the proportions of the items of the spatial, quantitative and creativity and productive thinking subscales that functioned differently as a result of parental educational status and the proportion that did not. Finally, on the entire instrument a Z- test calculated value of –3.3 was obtained which is less than a z-test critical value of –1.645.Based on this result the Null hypothesis as it affected the entire instrument was rejected and the alternative hypothesis upheld. The conclusion was that the proportion of the of the entire items of the whole instrument, which functioned differently differed significantly from the proportion of the items that did not function differently at the 5 percent level of significance as a result of parental educational status. The proportion of items of the instrument that functioned differently was significantly less than the proportion that did not at the 5 percent significant level. Hypothesis 6 HO6: The characteristics of the distribution of the pupils’ scores on the subscales and on the entire instrument is not significant at the 5 percent level of significance as a result of parental Educational status. Table 20 .0: A One- Way ANVOA Statistics on the characteristics of the distributions of the Pupils’ scores on the subscales and on the entire Instrument as a Result of Parental Educational Status.

Scal

es

Sour

ce o

f va

riat

ion

DF

Sum

of

Sq

uare

s

Mea

n Sq

uare

s

F-ra

tio

calc

ulat

ed F-

ratio

cr

itica

l

Dec

ision

Num

eric

Between-groups 2 3509.0101 17545050 5.7524 2.99 Reject

Within-groups 498 157891.7484 305.0035 Ho

Spat

ial

Between groups 2 3860.0570 30.0285 6.238 2.99 Reject

Within-groups 498 154085.6536 309.4089 Ho

Qua

ntita

tive

Between-groups 2 527.1542 263.5771 0.416 2.99 Accept

Within-groups 498 315556.2989 633.6471 Ho

116

Cre

ativ

e th

inki

ng Between-

groups 2 162.8286 81.414 0.1206 2.99 Accept

Within-groups 498 336315.0875 675.3315 Ho

Entir

e Te

st

Between-groups 2 1240.2301 620.1150 4.2181 2.99 Reject

Within-groups 498 73212.1191 147.0123 Ho

The summary of ANOVA statistics presented on table 20. 0 shows that F-ratio calculated values of 5.7524 and 6.238 were obtained for the numeric and spatial subscales respectively. These values were compared to corresponding table critical F-ratio values obtained at the same degrees of freedom and for the same 0.05 alpha levels of significance. Based on this the Null hypothesis as it affected each of these subscales was respectively rejected and their corresponding alternatives accepted. The conclusions made with respect to each subscale were that the characteristics of the distribution of the pupils’ scores on each of these subscales are significant at the 0.05 levels of significance as a result of parental educational status. In a similar fashion, the F-ratio calculated values for the quantitative and creativity thinking subscales are 0.416 and 0.1206 respectively which are far less than the table critical values of 2.99 for 2,498 degrees of freedom and 0.05 level of significance. Based on these results the Null hypothesis as it affected each of these subscales was respectively accepted at the expense of their corresponding alternative hypothesis, which was rejected. The conclusion made with respect to each of these subscales was that based on the characteristic of the distributions of the pupils’ scores on each of the subscales, the pupils’ performance is not significant at the 0.05 alpha levels of significance due to parental educational status. Finally, an F-ratio calculated value of 4.2181 was obtained for the characteristics of the distributions of the items of the entire instrument. This was compared to the corresponding F-ratio critical value of 2.99 obtained for 2.498 degrees of freedom and at the 0.05 levels of significance. The result of the comparison aided the researcher to reject the null hypotheses as it affected the entire instrument. The conclusion made was that the characteristics of the distributions of the pupils’ scores on the entire scale indicated that the pupils’ performances are significant at the 0.05 levels of significance due to parental educational status. Hypothesis 7 Ho7: The interactive influences of gender and parental educational levels on the achievement of the pupils on the instrument for the identification of mathematical giftedness are not significant at the 0.05 alpha levels of significance (P<0.05). Table 21.0: Source Table For Two–Way Factorial Analysis Of Variance Showing The

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Computed Sums Of Squares On The Scores Of The Pupils On The Instrument As A Result Of The Interactive Effects Of Gender And Parental Education Level

Source of Variation SS DF Mean Square Computed

F-ratio

F-critical-ratio

P

Main effects 957.464 3 319.155 2.166 2.60* < 0.05 Gender 6.054 1 6.054 0.04 3.84* < 0.05 Educational level

951.41 2 475.705 3.228 2.99 > 0.05

2-way Interaction (Gender and educational level) 405.044 1 405.044 2.749 3.84*

< 0.05

Explained 1362.508 4 340.627 2.312 2.37. > 0.05 Residual 73089.841 496 147.359 Total 74452.349 500 148.905 *Not significant at the 5% level of significance.

The data on table 21.0 provide evidence of the interactive influences of gender and parental

educational status on the pupils’ performances on the instrument for the identification of mathematical giftedness in Ebonyi State Primary School System. The data show for the independent variable gender, an F-ratio of 0.04 for the 1,500 degrees of freedom and for 5 at the 0.05 levels of significance. This value was compared to the corresponding table-critical value of 3.84 for the same degrees of freedom and at the same level of significance. The Null hypothesis as it affected gender singly was accepted and its alternative rejected. The conclusion was that gender did not significantly affected pupils’ performances on the instrument. The same reasoning and arguments enabled the researcher to arrive at the finding with respect to Parental educational level on pupils’ performance on the instrument. Parental educational status recorded a calculated F-ratio value of 3.228 for the 2,500 degrees of freedom and at the 0.05 levels of significance. This was again compared to the corresponding tabular critical value of 2.99 obtained at the 0.05 levels of significance and for the 2,500 degree of freedom. The Null hypothesis as it concerned parental educational status singly was rejected and its corresponding alternative accepted. The conclusion was that parental educational level is significant to the pupils’ performance on the instrument. Finally, the interaction effects were investigated, and accordingly an F-ratio was computed and found to be 2.749 at the 0.05 levels of significance and for 500 d.f. The corresponding table-critical value was found to be 3.84 at the same level of significance and for the same degrees of freedom. Comparatively, the F-ratio computed was found to be far less than the F-ratio critical value, the Null hypothesis was accepted and its corresponding alternative rejected. The conclusion was that the interactive effects of parental educational level and gender are highly not significant to

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the pupils’ performance on the instrument. Hypothesis 7 Ho7: The difference between the mean score of the gifted pupils on the instrument and mean teacher’s nomination score is not significant at the 5 percent level of significance (i.e. P<0.05) Table 22.0: Source table for the t-test statistics on the difference between the mean scores of the gifted pupils on the subscales and on the entire and the teacher’s nomination.

Subs

cale

Cal

cula

te

t-st

atist

ics

betw

een

TMSa

rd.

Alp

ha

t-cr

itica

l

Df

Inte

rpre

tatio

n

Numeric 26.70 0.05 1.96 1000 * Spatial 19.49` 0.05 1.96 1000 * Quantitative 23.70 0.05 1.96 1000 * Creativity 15.93 0.05 1.96 1000 * Entire test 35.12 0.05 1.96 1000 * * Not Significant ** Significant Data on table 22.0 show the significance of the difference between the mean scores of the pupils on the subscales and on the entire instrument for the identification of mathematically gifted pupils in Ebonyi State Primary School System and the teacher nomination scores. Evidence inherent in the table reveals that the difference between the mean scores of the pupils on the numeric, spatial, quantitative and creativity thinking subscales and the teachers’ nomination scores are respectively significant at the 5 percent level of significance. Further revelation from the table is that the difference between the mean scores of the pupils on the instrument for the identification of giftedness and the mean teacher’s nomination is significant at the 5 percent level of significance. The implication is that the teachers rated the pupils significantly higher than the direct evidence of their gifts, which they provided on the instrument. Summary of the Findings of the Study The following constitute a summary of the findings of this study: A) The items of the instrument for the identification of pupils mathematically gifted in the Ebonyi State School System are valid to be used as giftedness identification instrument (B). The reliability index of the subscales and the entire test is high enough to permit its use for the identification of mathematically gifted pupils in Ebonyi Primary School System. (C). Investigation of gender influence on the functioning of the items and on the characteristics of the distribution of pupils’ scores on the subscales and on the entire

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instrument show that pupils’ performances were found to exhibit gender parity across the subscales and on the entire instrument. Specifically: i. Gender partitioned the entire items of the instrument into the proportion that functioned differently as a result of gender and the proportion that did not function differently. ii. On the Numeric subscale and on the entire instrument the proportion of items that functioned differently is significantly different from the proportion that did not function differently at the 0.05 levels of significance. iii. On the spatial, quantitative and creativity and productive thinking subscales the proportion of items that functioned differently was not significantly different from the proportion that did not function differently as a result of gender at the 0.05 levels of significance. iv. Pupils’ performances on the Numeric subscale and on the entire instrument were not significantly affected by gender. v. Pupils’ performances on the spatial, quantitative and creativity thinking subscales were significantly affected by gender. (D) The influence of parental educational status on the functioning of the items and on the characteristics of pupils’ performances showed that: I. Parental educational status partitioned the entire items of the instrument into two disjoint exclusive classes, Proportion that functioned differently and proportion that did not function differently as a result of parental education level at the 0.05 levels of significance. ii. On the quantitative subscale the proportion of the items that functioned differently is not significantly different from the proportion that did not function differently as a result of parental educational status. iii. On the numeric, spatial and creativity thinking subscales and on the entire instrument the proportion of items that functioned differently is significantly different from the proportion that did not function differently as a result of parental education status. iv. Parental educational status was highly significant to pupils’ performances on the numeric, spatial and on the entire instrument. V) Parental educational status was not highly significant to pupils’ performances on quantitative and creativity thinking subscales. VI ) The interactive effects of gender and parental education status are not significant to the pupils’ performances on the instrument. (E) Pupils’ performances on the teacher nomination procedures were significantly better than the pupils’ performances on the on the subscales and on the entire instrument. ( F ) .The magnitudes and directions of the Interco relation coefficients showed : I. There was a very low inverse relationship between the pupils’ performances on the numeric and creativity and productive thinking subscales. ii. There was a moderate positive relationship between the pupils’ performances on the spatial and on the numeric subscales. iii. There was a considerably low positive relationship between the pupils’ performances on the creativity and productive thinking and quantitative subscales, numeric and quantitative subscales and creativity and productive thinking subscales respectively.

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CHAPTER FIVE

DISCUSSION OF FINDINGS, RECOMMENDATIONS, CONCLUSION AND

SUGGESTION FOR FURTHER STUDIES

The chapter contains the discussion of the findings of the study. The study recorded a lot of

inconsistencies; difficulties and unexpected results surfaced which need to be discussed. It is

very pertinent to set out the discussion of these results under the following headings:

a. Validity of the instrument

The first finding of the study is that the instrument is valid. It is a welcomed development.

The implication is that the instrument can yield a trustworthy measure of any child’s level of

mathematical giftedness in Ebonyi State primary School System. Enyi (2006) meant this

when he said that valid has to do with the trust we have in accepting the results obtained with

measuring instrument. The implication of the finding is that the MAGII can conveniently be

used to identify mathematical giftedness in Ebonyi state in particular.

b. Reliability Index of the subscales and the Entire Instrument

One of the findings of this study was that the reliability index for the entire instrument for the

identification of mathematical giftedness was calculated and given as 0.83, 0.85, 0.83, 0.83

and 0.81 respectively. This finding, although interesting, failed to conform to expectations.

This is so because as indicated in (Prometheus Society, 2006) although the technical quality

of a well-constructed instrument lies in inter - item internal consistencies of the items, the

reliabilities tend to increase with the age of the testee (Prometheus society 2006). The finding

also failed to correlate with the reality in the area of giftedness in which most reliability

indices obtained with K-R 20 for ages 2 to 17 and 18-23yrs range from 0.95 to 0.99 and

lower reliability values for children of lower ages (The Prometheus Society, 2006). The

nominees were of an average age of 16 years and reliability values higher than those values

obtained would have been a little better than the present reliability values. A probable

explanation for the failure of the present finding to correlate with the realities in the area of

giftedness is, first, most of the reliability indices in area of giftedness were obtained in service

areas different from the mathematical sciences and, secondly, large samples were studied.

The area of giftedness services for the present study is Mathematics. Further, the

group studied are disadvantaged pupils extracted from educationally poor backgrounds. Thus

the observed differences between those theoretically recommended values, which were

obtained with children of more advanced cultures, and the values obtained in the present

study are not totally ruled out. An additional discovery, which could explain the situation, is

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that most of the pupils used actually were of mixed ages and drawn from educational poor

backgrounds. Majority of these pupils are descendants of peasant farmers who know very

little about the importance of education. The implication of this finding therefore, is that the

government to fashion out ways and means of improving the status of her education as a

social instrument for faster and quicker development of the state should make more efforts.

c. Characteristics of Distribution of Pupils’ Scores

An interesting part of the finding here is that the participants recorded the highest mean score

on the creativity thinking subscale. The discovery did not conform to the expectations of the

present researcher. It is equally surprising. Naturally, the performance of the pupils ought to

be high in the numeric subtest because the content of the subscale was developed from the

primary school work and since the item are similar in content to that of their primary school

Mathematics syllabus; the mean scores of the participants were expected to be the highest in

this section. The study fails to conform to Ojerinde’s (2001) opinion that variation in content

of subject matter and other related factors may affect test scores and their correlation

coefficients on successive retesting. Further, Okereke (2006) in study observed that learners

of Mathematics are not usually properly disposed towards Mathematics questions requiring

the application of creative ability.A possible explanation for this discrepancy might be that

most of the teachers for these pupils use quantitative and verbal reasoning textbooks in their

normal class instruction; and their experiences with their various classroom instructions may

have accounted for this surprise result.

An Additional revelation from the study is that despite the special nature of the study

many participants obtained very low scores. This was not an expected result. The result also

casts serious doubts and challenges the authenticity of the nomination made at the school

levels. However, the only explanation of this result could be traced from the technical

qualities of the teacher- made tests used in the various schools. The teacher–made tests often

used as training instruments within the schools in Primary school System lack necessary

psychometric qualities to warrant their use as tests let alone their use as an identification

instruments (Abonyi, 2003, Okpala et al (1993). These tests are, in most cases, not printed

and yet used in most classrooms and schools in training the pupils. The pupils’ carry- over

experiences with these tests will probably be a good explanation for the low performances on

the instrument.

Hassan (undated) had observed that when a test or identification instrument lacks

necessary psychometric qualities, the scores so generated with the instrument and the

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decision taken based on the scores are faulty. The implication of these results probably is that

the Ebonyi State Government needs to empower the headmaster and principals of schools

with her Education System financially so as to enable them to render basic education services

expected of them.

Finally, an interesting finding is that girls rather than boys participated more in the

study. In fact many schools nominated girls as possible substitute for their male participants

in the study. This again was an unexpected and surprising finding especially when one

considers the service area concerned. The present study contradicted Pamberton (2004)

finding and observation that more boys than girls are offered to participate in gifted education

programmes. The only explanation to this finding is that the educational backwardness of this

state coupled with the Ebonyi state government campaign slogan that ‘Education is the only

solution to the state’s backwardness’ and the zeal to catch up with other states may have been

partially responsible for the gender sensitivity of the study in favour of the female folk. In

addition there are limited career options open to the womenfolk in comparison to their male

folk and thus embracing education is undoubtedly the only survival option left for most of the

women. The situation, although a welcome development, yet it calls for conceited efforts of

the Government of the state, State Educational Agencies and teachers to devise more gender

equity teaching strategies.

d. Gender Influence on the Functioning of the Items

A significant and an interesting finding was that there was no gender equity on the

pupils’ performances on the subscales and on the entire scale. Specifically, on the numeric,

spatial, quantitative subscales and on the entire test the male performed significantly better.

This suggests that performances of the pupils on these subscales far favour the males than the

female participants. This finding has a serious concern from the social justice perspective; it

has further and broader repercussions on the use of this instrument and thus should be

regarded as one of the limitation to the study. However, the finding supports the realities in

the area of giftedness in relation to the influence of gender to the gifted students’

mathematical achievement and ability (Pajares, 1996) and also conforms to the realities with

regard to school ability and achievement in Science, Technology and Mathematics (Okeke,

2006). The observed gender differences in achievement between the girls and the boys could

be attributed to the nature and pattern of the pupils’ career aspirations.

Currently, the wish of every Ebonyi State woman is to get educated in any area her

talent permits, provided such an area will enable her get employed on graduation. Most of

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them aspire to major in Management, Planning, Administration and Political Science all of

which has very minimal need for Mathematics.

An additional discovery in this section which also will serve as a limitation is that the

female performed significantly better than the males in the creativity thinking subscale. This

means that gender is a potent factor that will influence pupils’ performance on this subscale

of the instrument. This finding is quite unexpected. It also contradicts the realities in the area

of giftedness, Mathematics and Science and Technological education (Okeke, 2006, Pajaras,

1996). A major reason for the observed superior performance of the female pupils could be

that this subscale is less computational oriented. Another explanation could be that it

involves less mathematical reasoning. Majority of the participants are females and well near

the adolescence stage of development. Kerr (1997) strengthened this thus:

Adolescence brings changes in gifted girl’s aspiration, expectations, attitudes and

achievements. The changes that occur for girls today are subtler than those that occurred in

the past. Nevertheless, the theme of many gifted females’ lives is one of declining

involvement with former achievement goals. The changes are most evident in academic

achievement testscores, course taking and other academic- related behaviours.

The implications of this result is that the Ebonyi State government should strengthen their

guidance and counselling units within school and across the state to enable the learners to get

cheaper and readily available counselling services.

(e). Influence of Parental Educational Status

A major and interesting revelation observed was that the pupils’ performances were,

as a result of parental educational status, highly contradictory in relation to the major subtests

and the entire instrument. On the numeric and spatial subscales and on the entire test pupils’

performances on these scales were found to differ significantly due to parental educational

status. This leaves parental education status a potent factor to be considered in the use of the

numeric and spatial subscales of the present instrument as Gift identification instrument(s). In

other words, parental educational status constitutes a serious threat to the interpretation and

nomination of mathematically gifted children using the “MAGII”. This finding, which also

constitutes a limitation to the study, has actually not deviated significantly from the realities

in the area of giftedness. The research finding conforms to the finding of Nokelainen (2006)

who in a study discovered parental influence and other self-attribution factors as being highly

facilitative to the development of mathematical giftedness and achievement. Environment

exerts a lot of influence on the education of a child. Armstrong (1995) stressed that an

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environment challenging in intellectual demands promotes positive attitude towards

education. Mcmahan (1992) provided evidence that some aspects of classroom learning

environment are positively related to students’ attitude towards the learning of Mathematics.

The result of the study has indicated that Parental educational status should be one of these

aspects of learning environmental variables that influence education.

On the contrary, parental educational status was found to have no significant influence

on the pupils’ performances on the subscales: quantitative, creativity thinking respectively

and on the entire scale. An additional revelation, which also constitutes a worthy criterion,

which favours the use of these subscales as Mathematics G. I. F T. identification instrument

(s), is that parental educational level is not significant. This implies that parental influences

and other self-attribution factors may not be factors to be considered in the use of the

subscales as Mathematics G. I. F. T. identification instrument.

This result, though not in line with the realities in the area of giftedness (Nokelachen,

2006) is highly expected. The only explanation to this finding is that Ebonyi State is one of

the educationally disadvantaged states of the federation. Most of the parents are just

beginning in education. Under this circumstance, it is may be possible that the envisaged and

the needed educational structures that should have made the expected differences in the

pupils’ performances within the various families have not been put in place.

(f). Interactive Effects of Gender and Parental Educational Status on pupils’

performances on the subscales and on the entire instrument

The finding recorded here was that the interactive effects between the proportions of

items that function differently and those that do not function differently as a result of gender

and parental educational status are not significant at the 5 percent level of significance. This

means that gender does not exert any differential effects across all the levels of parental

educational level. In other words, gender is most effective when pupils belong to one of the

levels of the parental educational level. This is highly expected as many parents attach

varying degrees of importance to education. Families thus exert different and varying levels

of parental influence, depending on the amount of resources available, on their children

education. Further, in Ebonyi state the political terrain favour the illiterates more than their

educated colleagues and although some of the parents may claim to possess more higher

certificates, these parents still suffer in the various offices under the bureaucratic bottle neck

of white collar job. At present, it is very difficult, if not impossible, to draw a sharp boundary

between the educated and illiterate families in terms of educational provisions. Onyilofor

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(2004) corroborated this view when he observed that the parental educational background

also affects the visually impaired children because it seems that illiterate parents ignorantly

deal badly with the usually impaired. The implication is that families in Ebonyi state probably

lack the necessary learning materials within their homes. They are thus encouraged to

develop more positive attitude towards the provision of enabling facilities, environment and

specific periods to supervise the academic work of their children.

(g). Pairwise Correlation Coefficients of the Subscales of the Entire Scale

The study yielded different correlation coefficients and values between the respective

pairs of the subscales and the entire test. Further revelation observed is that the correlation

coefficient between the numeric and creativity thinking subscale, and spatial and creativity

thinking subscales and vice versa respectively was not significant at the 0.05 level of

significance. This, in effect, means that the observed relationships between these pairs of

subscales and between the entire Test could be attributed to sampling error and thus may not

reflect the actual relationship existing in parent population. The finding that there was very

low inverse relationship between numeric and creativity-productive subscale is not

unexpected. First, the items in the numeric subscale are based on the content of the pupils’

school Mathematics curriculum whereas those of the creative-productive are items designed

to enable the pupils apply the Mathematics information (content) and thinking processes in an

integrated, inductive, and real-problem-oriented manner. There is a large computational

ability attached to the numeric. There are very minimal computational requirements of the

creativity and productive subscale and in the opinion of Ojerinder (2000) when there are

variations in the contents of tests, pupils’ performances and the correlation coefficients will

be affected. Jensen (1998) had this in mind when he said that in contrast to the robust

relationships between general ability and achievement; specific subtest profiles have been

unable to explain much of the variations in achievement measures as expected. An additional

discovery is that there are low correlation coefficients between the spatial and creative

thinking subscales. Again this is highly expected. This bears dialectics in relation to

intelligence and wisdom (Stemberge, 1995). Again, this was explained by Jensen’s (1998)

observation which stated that in contrast to the robust relationship between general ability and

achievement, specific subtest profile have been unable to explain much variation in

achievement measures is expected. The spatial ability subscale contains items that test the

pupils’ ability on a way of seeing things with the minds eye that is crucial for Mathematics.

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The creativity and productive thinking subscale contain items that test the pupils’ ability in

applying mathematical principles and thinking processes in an integrated inductive and real –

problem oriented manner.

In both cases, there are variations in the contents of the subscales, which is sufficient

to affect the correlation coefficient (Ojerinde, 2000).The different computational skills

needed to handle the variation in the content may have accounted for the inverse relationship

in the performances of the pupils in these scales. Further, subtest scatter is highly unrelated to

academic achievement (Hale and Saxe, 1983).

Other correlation coefficients between the various pairs of the subscales and between

the whole instrument were significant at the 0.05 levels of significance. This means that the

observed relationship may not have been as a result of sampling error. The observed

relationships between the subscales and between the subscales and the entire test are the

same, as they exist in the parent populations. This corroborates other findings in the area of

giftedness. Kline, Spyder, Guilmette, and Castellanos (1992) reported that subtest scatter had

no increment validity beyond general ability in predicting achievement. In summary the

various correlation coefficients have not only identified the specific areas the subscales and

the entire instrument can be put into more effective use but also areas of strengths and

weaknesses of the various subscales and the entire instrument. This corroborates Zeider’s

(2001) caution that even if subtest scatter is not used for diagnostic purposes, subtest scatter

might identify specific cognitive strengths and weaknesses. The implication is that Ebonyi

State Government should endeavour to develop an independent identification instruments

other than achievement tests being employed by teachers at the school and local government

levels.

(h). Correlation Coefficient between the Subscales and the Entire Scale and the

Teacher’s Nomination Scores

The result of the study revealed an inverse but less than average correlation between

the pupils’ performances on the respective subscales and between the entire test and the

teacher nomination scales. All the correlation values except the correlation coefficient

between the pupils’ performance on the spatial and teachers’ nomination scores were

significant. This implies that the pupils’ performances on the subscales and on the entire test

are inversely related to their performances on the teacher’s nomination scores and wear

significant semblance to the relationship that exist between in the parent populations. In

127

others words, pupils who achieved highly on the respective subscale and on the entire test

achieve very poorly in the teachers’ nomination scores. The implication is that the teacher

nomination instrument measures other constructs different from mathematical giftedness This

is not unexpected because the teacher’s nomination scores are obtained from classroom tests

and thus have high computational dimension. The instrument for the identification of

mathematical giftedness in Ebonyi Primary School System contains items meant to test the

aptitude of the learners rather than achievement. It is expected, therefore, that such factors as

variation in the content, test anxiety, reading difficulty and other factors could affect

performance. The finding is in accordance with Neisser, et al (1996) when they opined that it

is widely recognized that 1Q scores co-vary positively with academic achievement. Nwana

(1991) corroborated these views when in a study he obtained very small positive correlation

between the schools’ entrance examinations and school certificate examinations.

Another interesting finding is that the correlation coefficient between the pupils’

performance on the spatial subscales and the teacher’s nomination score is not significant at

the 0.05 level of significance. This implies that the small observed inverse relationship

between the pupils’ performances on the spatial subscale could be attributed to some chance

factors. In other words, it may be attributed to chance error. Normally, this is expected

because the specific skills needed to attend to both tests differ greatly. The teacher’s

nomination content contains items that require high computational ability, whereas the spatial

subscale contains test items that can only enable one to see things with his mind’s eye. The

computational ability required is less than that needed to handle classroom problems.

Hausman (2001) observed that spatial ability differs from mathematical ability in the

following words: spatial ability is separated from verbal or mathematical ability. The very

low correlation obtained was defended by Walkina (2003) when he cautions that even among

researchers who posit influences beyond general ability, academic achievement is not

generally assumed to be determined by cognitive subtests acting independently. Rather

achievement is presumed to be primarily determined by the higher-order general ability (g)

factor, followed by first-order ability factors. The educational implication is that the Ebonyi

State government should, as a matter of urgency, introduce into her Education System a gift

identification instrument quite different from the achievement tests being used for the

purpose at the primary and local government levels of identification. Further implication of

the finding is that the present identification procedure in which achievement tests are

throughout all the tiers of identification may not yield the deserved result for the state.

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(i). Differences between the Mean Scores of the Gifted Pupils’ on the subscales and

on the entire Instrument and Mean Teachers’ Nomination Scores is Significant at the 5

Percent Levels of Significance (i.e. P < 0.05)

An interesting finding is that the differences between the mean scores of the gifted

pupils on the subscales and on the entire instrument and the mean teachers’ nomination

scores is significant at the 0.05 levels of significance. These observed differences between the

pupils’ performances on the subscales and on the entire instrument and the teacher

nomination scores have not occurred due to mere chance. The observed mean difference is

not actually due to experimental manipulation. This is highly expected. This is expected

because teachers’ nomination scores are products of class works or standardized achievement

tests. This finding is in line with the view of the Senate Committee Report on the education

of gifted and talented children (2003) when it observed that high marks obtained at school

can be misleading however, as they may reflect perceptions of appropriate classroom

behaviour rather than the actual behaviour. Moreover, consistently low marks are not

necessarily indication of average or below average ability as gifted students who are

frustrated and bored may score poorly on class tests. Perhaps Tolan’s (1985: 16) opinion

addressed the same view when he said:

There is no rule that states that a child who is capable of scoring to the ninety percentile on group testing must be gifted, we must remember that achievement tests like the metropolitan. Achievement tests are “Grade level testing, Tests of this nature are definitely good for academically talented. At the same time, there is no rule that states that a child identified as gifted should achieve to a high standard in the classroom. This type of stereotyping can do serious and irreversible damage to both groups.

The above observation throws more light on the dangers of using identification procedures based totally on achievement tests. These tests are computational oriented in nature and a child who scores very highly on this type of tests can not be said to have satisfied all the required conditions to be classified as being gifted which has more attachment to the ability to reason rather than merely recording very high marks. However, as a new dimension to the understanding about the roles tests should play in factors such as problem – solving and insightful solutions, Stenberg (1982:57) concluded that:

Tests only work for some of the people some of the time – not for all of the people all of the time – and that some of the assumptions we make in our use of tests are; at best, correct for only a segment of the tested population

129

and at worst not correct for none of it. As a result we fail to identify many-gifted individuals for whom the assumptions underlying our use of tests are particularly inadequate. The problem then is not only that tests are of limited validity for everyone, but also that their validity varies across individuals. For some people, test scores may be quite informative, for others such scores may be worse than useless. Use of test scores cutoffs and formula results in a serious problem of under identification of gifted children

This may be the reason psychologists are admonished to ascertain what their tests can do. This result suggests that the judgement of whether one is gifted or not should not be based on classroom achievement or result of achievement tests as these achievement tests predict constructs different from what aptitude tests do. Educational Implication of the Study The findings of the study imply much educationally to all the primary schools teachers in Ebonyi State, educational administrators in charge of the identification of the pupils in Ebonyi State Primary Education System, the government and the National Examination Councils of Nigeria (NECO). The reliability coefficient of the instrument for identification of mathematical giftedness was found to have adequate reliability coefficients for the subscales as well as for the entire test. This means that the instrument has sufficient item variance to warrant its use as a mathematical giftedness identification instrument at the local government level of identification in Ebonyi State. The introduction of such instrument at this level of identification will not only sanitize the identification procedure in the state but also clear the barrage of problems associated with identification of giftedness at this level. As a result, the state government is urged to find ways of helping their serving teachers procure copies of this instrument or similar ones for use. The finding that the pupils recorded the best performances on the creativity thinking subscale is also advisory and rewarding one to the guidance counsellors, the teachers and educational planners within Ebonyi State since such information could be utilised as guidance and tools. Although Walkings and Guitting’ (2000) had observed that the incremental validity of subtests for forecasting guidance has been weak, it is believed that the findings with the aid of information gathered from other sections of the instrument could be used to plan for the pupils’ alternative training especially in situations where pupils identified as gifted are later discovered not to be. That most of the participants made very low achievements on the subscales and on

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the entire instrument is a regrettable revelation; yet it seems rewarding in that it tended to reveal the weakness of the instrument upon which the nomination was based as well as the weakness in the teachers’ training. The information affirms that most of the participants are either mere overachievers or children of people very close to the teachers, prominent politicians, and highly placed individual intentionally recommended by the teachers. Whatever the intention was the fact is that the instrument upon which the nomination was based was of a very psychometric quality. This exposes the fact the teachers need to be further trained especially on two broad areas, namely: test construction and Giftedness Education. The result that girls participated more and achieve more in some subtests is a welcomed development to educational planners and administrators within the state. The implication is that there is equally gender sensitisation to programmes and education this time in favour of the females in Ebonyi State. The implication is that teachers are advised to adopt gender equity approaches to Mathematics teaching in Ebonyi State. The result of the study, which revealed that parental educational level significantly influenced pupils’ performances on some subscales, is suggestive to the parents. The implication is that for more improved performance parents are urged and encouraged to identify with their children’s academic pursuit. The Government should ensure that more parental influences and enabling factors are put in place in overseeing the pupils’ home work, provision of necessary textbooks and writing materials and ensuring that the pupils are placed on regular study time table. The finding of the study also revealed that the pairwise correlation coefficient between the entire test and the subscales are found to be average, moderate or low. This implies that the items of the entire instrument exert an average, a moderate or a low functional relationship to those of these subscales. This result introduces economy to the identification procedure in Ebonyi the using this instrument. The implication is that some of these subscales, especially the spatial subscale can be separately or collectively employed in the identification of mathematical giftedness where it is not possible to procure/ use the entire instrument. The finding that there is an inverse pairwise relationship between the teacher nomination scores, subscales and entire scale is instructive and informative to educational planners and stakeholders in the gifted education sectors in Ebonyi State. This implies that the continuous assessment scores are predicting different concepts from what the instrument is doing. This implies that the government, educational planners and administrators should seek for a replacement for this continuous assessment if they should fill up their quota in the gifted and talented children academy, Suleja. The finding further revealed that there was significant a mean difference between the teacher’s nomination scores and the scores of the pupils on the subscale. This implies that the participants did considerably better in the continuous assessment than in the instrument. Although it is expected, the implication is that the participants experienced some difficulties

131

with the items of the instrument than with their class tests. Teachers are urged to introduce the use of printed question papers instead of the current practice of writing their examination questions on the board and subject their pupils to the same examination conditions as the one they conditions for the standard examinations. Recommendations The following are recommendations based on the findings: (1). Government should educate and train teachers on the behavioural characteristics of pupils who are gifted intellectually. This is important and necessary. The essence of this is to enable these teachers identify these children from their behavioural output rather waiting for possibly during classroom interactions or during assessment. This will lead to under identification or the provision of inadequate services when actually identified. (2). A third suggestion would be that there is a need to development and validate ‘giftedness’ monitoring instrument which could be used at the classrooms level of ‘giftedness’ identification procedure in Nigeria. The monitoring instrument advocated for should be based on likert-type rating scale to enable the teachers’ rates the degrees of the gifted characteristics and variables as they are being displayed. The essence of this is to enable the teacher to monitor the extent of the pupils’ giftedness constantly. (3). Teachers should adopt more gender inclusive strategies in their teaching in order to meet the general needs of the exceptional learners. Optionally, this strategy should incorporate school-wide and system –wide expertise and resources access, using all available school-based resources (teachers, classes, teachers, materials, pupils) at the pre-school through primary. (4). Government should sponsor independent resources to embark on further studies in order to learn more about identification and service delivery options for mathematically gifted pupils in particular and gifted pupils in general. Conclusion The success of any gifted and talented children education the world over has been the extent to which the identification programme has been effective. In Nigeria, experts’ opinions and results of findings have indicated ineffectiveness in the identification procedure. The non-use of appropriate instruments at the local government tier of identification has been greatly suspected of being responsible for the observed inefficiency. The present effort is, therefore, in response to and possibly the needed sealer to the observed inefficiency. The effort did produce standardized instrument that could be used at the local government levels in Ebonyi State to fill the gaps identified.

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In addition, the researcher investigated the influence of gender and parental educational status to the pupils’ performance on the instrument. Results of the study revealed that both gender and parental educational status influence Pupils’ Performances on the subscales and on the whole instrument. The study further revealed that the interactive effects of gender and parental educational level also significantly affected the pupils’ performance. Limitations of the Study There were serious limitations to the study. First, although the study has accomplished

the purpose it set out to achieve, its validity depends to a large extent on level of transparent

honesty and efficiency exhibited by the primary school teachers and the pupils. These

constitute a limitation to the present study because such deservedly high quality sincerity can

hardly be obtained in this context. Another limitation to the study is that the study involved a

small sample due to the educational backwardness of the state being studied. It is envisaged

that a higher number of participants would have made a significant change in the result

recorded in the study.

A third limitation is that the participants were nominated to participate in the study

based on their performances on a school based continuous assessment programme that has

very poor psychometric qualities. This constitutes a limitation because if instrument that had

very high psychometric qualities were used in the nomination, the result of study would have

been different and more efficient in that pupils of comparable ability would have been

nominated to participate. The level of the teachers’ training and knowledge of the concept of

giftedness constitute an additional limitation. Because of the shortfall in the Nigerian

teachers’ training and knowledge in the area, it was not possible to get the scores for teacher

ratings. Majority of the teachers who nominated participants for the study either complained

of lack of time for observation or inability to effectively rate the pupils as demanded. This

compelled the researcher to drop the teacher rating which ordinarily should have been

effective than the school -based continuous assessment. However, in spite of these

limitations, this study was considered to have been successful because the purpose for which

it was designed was achieved.

Suggestions for Further Study

This present study has revealed other area of research needs to be carried out in more

related aspects of identification procedures and the gifted and talented children education

133

programme in general. However, since it has been established that the efficiency of the Gifted

and Talented Children Education Programme depends on identification and since gifted and

talented is highly important in helping Nigeria achieve her goal of being self- reliant (Federal

Republic of Nigeria, F.R.N. 2004), the following areas are suggested for further research:

1. Similar investigation should be carried out in other parts of the country in order to

ascertain the applicability of the present findings to other parts of Nigeria.

2. Research work need to be carried out on the ‘development and validation of

monitoring G. I. F. T. instruments to be used for the identification of mathematical giftedness

at the school levels in Nigeria.

3. Research work needs also to be conducted on the development and validation

of G.I.F.T. readiness tests to be used at the gifted and talented children academy, Suleja, to

ascertain the readiness of the identified pupils for the gifted Education Programme.

Summary of the Study

The purpose of the study was to develop and validate an instrument for the identification of

mathematically precocious pupils within the Ebonyi State Primary School System. The study

thus employed an instrumentation research designs.

The primary purposes were to: develop an instrument for the identification of

mathematically precocious pupils within the Ebonyi State Primary School System; validate

an instrument for the identification of mathematically precocious pupils within the Ebonyi

State Primary School System; estimate the reliability of an instrument for the identification of

mathematically gifted children within the Ebonyi State Primary School System; determine

how the items of the instrument function as a result of gender; determine the significance of

the difference between the proportion of the items of the subscales and of the entire

instrument that functioned differently and those that do not function differently as a result of

gender; determine the characteristics of the distribution of pupils’ scores as a result of

gender; determine the extent to which the items of the instrument function differently as a

result of parental educational status ; determine the significance of the difference between the

proportion of the items of the subscales and of the entire scale that functioned differently and

the proportion of the items that do not function differently as a result of parental educational

status , determine the characteristics of the distribution of the pupils’ scores as a result of

parental educational status , determine the pairwise Interco relation coefficients between the

subscales and between the entire instrument for the identification of mathematically

134

precocious pupils.Within the Ebonyi State Primary School System, determine the pairwise

intercorrelation between the subscales and between the entire instrument and the teacher

nomination scores and finally to determine the interactive effects of gender and parental

education status on the pupils’ performances.

The study was wholly conducted in Ebonyi State. Only the pupils who were nominated by

their class teachers as being mathematically gifted were used. A total of five hundred and one

children were nominated by the teachers as being mathematically gifted in the forty –three

Primary School selected for the study. The major psychological constructs that form the bases

upon which the instruments for the identification of mathematical giftedness in the Ebonyi

state Primary Education System are: numeric ability, spatial ability, quantitative ability, and

creative ability. In order to realise the objectives of the study, the following research

questions were formulated as guides:

(1) What is the reliability index for the subscales and the entire Mathematics instrument

for the identification of mathematical giftedness within the Ebonyi State Primary School

System?

(2) To what extent do the items of the Instruments for the identification of mathematical

giftedness among pupils within the Ebonyi State Primary School System function differently

as a result of gender?

(3) What are the characteristics of the distribution of the pupils’ scores on the subscales

and on the entire instrument for the identification of mathematical giftedness among pupils

within the Ebonyi State Primary School System as a result of gender?

(4) To what extent do the items of the instrument for the identification of mathematical

giftedness within the Ebonyi State primary school function differently as a result of parental

educational status?

(5) What are the characteristics of the distribution of the pupils’ scores on the subscales

and on the entire instrument for the identification of mathematical giftedness within Ebonyi

State Primary School System function differently as a result of Parental Educational status?

(6) What are the magnitudes and directions of the pair wise Interco relation coefficients

among subscales of the instrument for the identification of pupils gifted in mathematics with

the Ebonyi State Primary School System?

(6) What are the magnitude and direction of the correlation coefficients between the

pupils’ performances on the subscales and on the `entire instrument?

(7) What are the magnitude and direction between teacher nomination scores and the

135

scores of the gifted pupils on the instrument?

In addition to the above research questions, the following Null hypothesises were tested at the

0.05 level of significance (i.e. p< 0.05):

H01: There is no significant difference between the proportion of items that function

differently and those that do not function differently due to gender at 5 percent significant

level (i.e. .p< 0. 05)

HO2: There is no significant difference in the characteristics of the distribution of the pupils’

scores as a result of gender at the 5 percent level of significance ( i. e p0.05 )

HO3: There is no significant difference between the proportion of items of the instrument that

function differently and those that do not function differently due to the parental Educational

status of the gifted and talented pupils within the Ebonyi State Primary School System, at 5

percent level of significance (i.e. p< 0. 05).

HO4: There is no significant difference in the characteristics of the distribution of pupils’

scores on the subscales and on the entire instrument as a result of parental Educational status

at the 5 percent level of significance (i.e. P 0.05)

HO5: The difference between the scores of the pupils on the subscales and on the entire scale

and the teacher nomination scores is not significant at the 0.5 levels of significance.

Ho6: The interactive effects between proportion of items that function differently and those

that do not function to gender and parental Educational status are not significant at 5 percent

level of significance (i.e. p< 0.05)

Ho7: The difference between the mean score of the gifted pupils on the instrument and mean

teachers nomination score is not significant at 5 percent level of significance (i.e. P<0.05).

The study was conducted in Ebonyi State of Nigeria. Ebonyi State of Nigeria is divided into

three distinct Education Zones, namely: Abakaliki , Afikpo and Onueke Education Zones

.There are a total of seven hundred and thirty – one Primary Schools in Ebonyi State in the

2005/2006 academic year. However, only forty-three Primary Schools were selected for the

study through the proportionate sampling technique. All the primary six pupils in the

2005/2006 academic year nominated by their teachers in these forty- three Primary schools as

being mathematically precocious participated in the study. Specifically, only five hundred

and one pupils who were nominated from these Primary Schools actually participated and this

number formed the sample for the study. The instrument for data collection was subjected to

both face and construct validation through the factor analysis procedures.

Out of a total of one hundred and twenty items the researcher started with ninety – one

136

survived both the face and construct validations. The sixty- three items that survived these

validation exercises were further subjected to concurrent validation using the 1999 version of

the National Examination Council of Nigeria (NECO) instrument, which is the only

standardised instrument of merit currently in use at the federal level of identification as a

standard. The instrument yielded measures of stability of 0.8, 0.71, 0.78, and 0.63 for the

subscales and 0.6 for the entire instrument. Data for the study were collected particularly

from the five hundred and one pupils that took part in the study.

The summary of the analysis of the data revealed the following findings for the study:

The reliability index of the subscales and the entire test is high enough to permit its

use as a Mathematics giftedness identification instrument in the Ebonyi State Primary school

system.

ii. The pupils recorded the best performance on the creativity-productive thinking subscale.

iii. Many participants recorded very low scores on the subscales and on the entire

instrument for the identification of mathematical giftedness in Ebonyi State.

iv. Girls participated more in the study than the boys.

v. Gender partitioned the entire items of the instrument into the proportion that functioned

differently as a result of gender and the proportion that did not function differently.

vi. On the numeric subscale and on the entire instrument the proportion of items that

functioned differently is significantly different from the proportion that did not function

differently at the 0.05 levels of significance due to gender.

vii. On the spatial, quantitative and creativity and productive thinking subscales the

proportion of items that functioned differently was not significantly different from the

proportion that did not function differently as a result of gender at the 0.05 levels of

significance.

viii. Pupils’ performances on the numeric subscale and on the entire instrument were not

significantly affected by gender.

ix. Pupils’ performances on the spatial, quantitative and creativity thinking subscales were

significantly affected by gender.

x) Parental educational status partitioned the entire items of the instrument into two disjoint

exclusive classes: proportion that functioned differently and proportion that did not function

differently as a result of parental education level at the 0.05 levels of significance.

xi) On the quantitative subscale the proportion of the items that functioned differently is not

significantly different from the proportion that did not function differently as a result of

137

parental educational status.

xii) On the numeric, spatial and creativity and productive thinking subscales and on the entire

instrument the proportion of items that functioned differently is significantly different from

the proportion that did not function differently as a result of parental education status.

xiii) Parental educational status was highly significant to pupils’ performances on the

numeric, spatial and on the entire instrument.

xiv)Parental educational status was not highly significant to pupils’ performances on

quantitative and creativity and productive thinking subscales.

xv. Pupils’ performances on the teacher nomination procedures were significantly better than

the pupils’ performances on the subscales and on the entire instrument.

There was a very low inverse relationship between the pupils’ performances on the numeric

and creativity and productive thinking subscales.

iv) There was a moderate positive relationship between the pupils’ performances on the

spatial and on the Numeric subscales.

V) There was a slightly above average relationship between the pupils’ performances on the

spatial and on the numeric subscales respectively and their performances on the entire

instrument.

vi) There was a considerably low positive relationship between the pupils’ performances on

the creativity and productive thinking and quantitative subscales, numeric and quantitative

subscales and creativity and productive thinking subscales respectively.

Vii) The interactive effects of gender and parental education status are not significant to the

pupils’ performances on the instrument.

Based on these findings of the study, the following recommendations were made:

(1) Ebonyi State Government is urged to increase her involvement in educating, training and

updating teachers’ knowledge about the behavioural characteristics of pupils who are gifted

intellectually and mathematically. The essence of this is to enable these teachers to be aware

of the gifted pupils in any school the teachers found themselves at any particular point in time

so as to fully understand the nature of their giftedness before confronting them in the

classrooms or during assessment. This will reduce under identification or the provision of

inadequate services when actually identified.

(2) Independent researchers within the Ebonyi State Education System should develop and

validate Mathematics giftedness monitoring instrument, which could be used at the classroom

level of identification in Nigeria in general, and Ebonyi State in particular. The monitoring

138

instrument be advocated for should be a rating scale which would enable the teachers rate the

degree of the pupils’ gifted characteristics and variables as they are displayed.

(3) Teachers should adopt more gender inclusive strategies in their teaching in order to meet

the general needs of the exceptionally gifted learners. Alternatively, this strategy should

incorporate school- wide and system – wide expertise and resources access, using all

available school- based resources (teachers, classes, materials, pupils, etc) at the pre- school

through primary stages.

(4.) Government should sponsor more independent researches on giftedness identification and

services delivery options for mathematically gifted pupils in particular and intellectual

precociousness in general at the school levels. The studies will enable the teachers and

stakeholders in the Gifted Children Education Programme in Ebonyi State to learn more

about identification and service delivery options available at each level.

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Indicate: i. parents’ Vocation/Educational levels ii.Father’s Vocation/Educational level………………………………………… iii.Mother’s Vocation/Educational level……………………………………….. iv. Others specifies …………………………………………….. APPENDIX V SECTION A Name of School……………………………………………………………… Name of Teacher…………………………………………………………….. Rank………………………………………………………………………….. Post Held:……………………………………………………………………. Section B Sir, I am developing a G.I.F.T. instrument that could be used to identify and nominate pupils who are mathematically gifted. You are required to enter one of the following five options (5 – Excellent; 4 – Much; 3 Moderate; 2 – Little; 1 – Very Little) in each of the cells to indicate the extent of the mathematically giftedness of the pupil(s) you are nominating.

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S/N Name of pupil Total 1 2 3 4 5 6 7 8 9 10

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11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 MATHEMATICS G.I.F.T IDENTIFICATION INSTRUMENT Candidate’s Name:……………………………………………………………………… School:……………………………………………………………………………………. Time Allowed: 1½ hr. Instructions:

1. There are three sections: A, B. and C in the paper. Answer all the questions in this section.

2. You should use pen or biro for the examination 3. Write your name, school and sex in spaces provided. 4. Circle the option that bears the correct answer to the question 5. Work as fast and as accurate as you can.

SECTION A NUMERIC MEASURE 1. Write in words 54, 019 A. Fifty-four thousand and nine B. Five thousand, four thousand and nineteen C. Fifty-four hundred and nineteen D. Fifty-four and Nineteen E. Five hundred and four hundred and nineteen

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2. What is the place value of 6 in 14,63” A. Hundredths B. Millionths C. Tenths D. Thousandths E. Units 3. A line that bisects a circle into two equal parts is called A. Arc B. Chord C. Circumference D. Diameter E. Radius 4. Write in figures, one million, four hundred. A. 1000400 B. 1400000 C. 1000040 D. 1004000 E. 1040000 5. Calculate the length of the unknown side marked X in the triangle below. A. 144cm A B. 25cm C. 18cm 5cm 13 cm D. 12cm E. 8cm C B x 6. Find e square root of 2 1/4 A. 2 ½ B 1 ½ C. 11/3 D 1¼ E. 2/3 7. Find the simple interest on N600 for 2 years at 5 percent per annum. A. N60 B. N6000 C. N15 D. N060 E. N6.00 8. Arrange the following numbers in ascending order of magnitude. 0.804, 0.408, 0.84 A. 0.084, 0.804, 0.804 B. 0.804, 0.84, 0.408, 0.084 C. 0.408, 0.804, 0.84, 0.084 D. 0.084,0.804, 0.408, 0.84 E. 0.084, 0.408, 0.804, 0.84 9. Simplify 92 ÷ 32 √144 + 1 122 A. 1.5 B. 6.0 C. 0.75 D. 1.75 E. 2.85 10. What is the sum of 70 and the square root of 169 A. 83 B. 232 C. 99 D. 2390 E. 750 11. What is the Lowest Common Multiple of 60, 45 and 25? A. 125 B. 750 C. 900 D. 1250 E. 67500 12. What is the value of M, + N, = 18, N = 15, P – Q P = 6 and Q = 3

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A. 11 B. 1 C. 33 D. 22 E. 10 13. Find the value of angle P, on the diagram below A. 350 B. 450 C. 850 D. 1750

E. 2100 14. Approximate 3540.27 to 4 significant figures A. 3550 B. 3540 C. 3510 D. 3500.3 E. 354 15. The area of a rectangular floor is 459m2. If its width is 18m, what is the sum of the

width and the length? A. 25.5cm B. 51.0cm C. 43.5cm D. 87cm E. 174cm 16. Simplify 1¼ + ¾ ÷ ⅛ A. 16 B. 32 C. 7 ¼ D. 1 E. 14 ¼ 17. Express 72 as a product of its prime factors in index notation A. 24 x 31 B. 22 x 32 C. 23 x 32 D. 22 x 33 E. 24 + 32 18. A man bought a tuber of yam at N15 and sold it for N18. Find the percentage profit of

the sale. A. 120% B. 83.3% C. 20.00% D. 16.6% E. 3.00% 19. The average age of boys is 15 years. If the average age of 5 of them is 14 years, how

old if the 6th boy? A. 90 years B 70 years C. 20 years D. 110 years E. 50 years 20. Insert the appropriate mathematical sign that will be in the box. 60038 9457 A. < B. > C. = D. ≤ E. ≥ 21. Circular fishpond has a radius of 14m. What are its circumference and diameter? A. 44m and 28m B. 88m and 28m C. 176m and 7m D. 616m and 7m

550 P

161

E. 1232m and 56m Use the shown figure to do question 22 22. What parts of the figure are combined to make the shape A. 3, 2, B. 6, 7 C. 5, 8 D. 4, 1 E. 4, 3 PART B Spatial Measure

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Study the following examples 23

A. B. C. D. E. 24. Attempt the following example. A is to ……………….as W is to M

A. A B. C. V D. D E. 25. 25. is as is to …………….. A. is B. C. D. E. 26. is to as is to A. B. C. D. E. 27. Pick the one that is different from the others in the following figures. A. B. C. D. E.

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28. A. B. C. D. E 29. In each of the following, select the correct figure to fill the blank square from the

given alternatives. ? A. B. C. D. E. Study carefully the figure (or pictures) below and choose from the alternative lettered A to E the picture that is most like the three pictures in the rectangle in each case. 30. A. B. C. D. E Study the following samples and then answer the questions which follow by selecting one of

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the given alternatives that best complete the figures sample. 31. is to as is to …………………. A. B. C. D. E. 32. is to as is to …………… A. B. C. D. E 32. 10 is to 20 as is to ____________________ A. B. C. D. E. 60 7 6 6 6 Study the following samples and then answer the questions which follow by selecting one of the given alternatives that completes the figure. Sample. 34. A. B. C. D. E.

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QUANTITATIVE ABILITY MEASURE Instruction: Sample problems are usually given before some of the questions. Study these carefully before attempting the problems. Sample: 3 4 5 25 3 27 3 6 4 100 4 20 4 2 6 5 2 35. 2 A A = …………………………… 3 A. B B. C. D. E. 4 8 16 2 0 2 72 3 36. A =……………………………………………….. A. B. C. D. E. 3 0 9 2 4 Sample: 4 9 10 2 8 3 27 4 64 37. 36 3 ? A. 128 B. 108 C. 98 D. 39 E. 198

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38. ? 5 125 A. 50 B. 120 C. 25 D. 625 E. 20 Sample: 39. 2! X 4! A. 6 B. 8 C. 12. D. 24 E. 48 40. 8! 7! A. 8 B.20 C. 25 D. 30 E. 36 41. 5! + 4! 3! A. 25 B. 20 C. 16 D. 9 E. 6 Example: A. 11 B. 5 C. 9 D. 6 E. 8 42. ? = …………………………………… 43.

2! = 2 x 1 3! = 3 x 2 x 1 4! = 4 x 3 x 2 x 1

4 5 3 6 7 2

8 7 6 9 10 5

4 7 6 5 ?

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A. 1 B. 4 C. 0 D. 5 E. 0.5 Example: 44. 32 5 4 36 5 3 A. 2 B. 7 C. 12 D. 15 E. 21 45. 42 5 3 A. 48 B. 16 C. 12 D. 6 E. 4 Example: 47 9 ? 1 4 A. 10 B. 12 C. 14 D.30 E. 16 48. ? 20 5 10 A.15 B.10 C. 10 D. 25 E. 30

1.5 2.5 3 ? 0.2

12 12

12

?

9 13 19 26 5.5 8

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Example: 49. 2 A. 12 B. 20 C. 23 D. 40 E. 60 50. 2 5 A. 6 B. 12 C. 18 D. 36 E. 48 Example: Aub = a + b A

51. 4 U 16 = ?

A. 20 B. 64 C. 4 D. 5 E. 11/5

52. (q,q)^ (r,s) = p/q x r/s

(3,3)^ (18, 12( = ?

A. 2/3 B. 3/2 C. 1 D. 21 E. 9

CREATIVE/PRODUCTIVE THINKING ABILITY MEASURE

The word “EDUCATION” is represented by 7 2 6 5 1 9 8 3 4

2 1 10

6 1

7

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53. Find the number, which represented “INDUCTION”

A. 3427659834 B. 384769834 C. 123456789

D. 7874769835 E. 246781234

54. Express 159834 in letters

A. ACTION b. CAUTION C. NATION D. TENDING

E. DATING.

C L U S T E R I N G

1 2 3 4 5 6 7 8 9 0

In the code, the shopkeeper must ensure the one and only one letter represents each digit.

For example, an article that cost him 7.25 would be marked R/LT. if he paid 64.09 for an

article he would mark it ES/EGN.

Use the code to find the correct answer to the following questions:

55. What is the cost price of an article marked U/CT?

A. N3.15 B. N3.95 C. N45.35 D. N6.15 E. N5.15

Given the code

A E F I L M N O S T U Y

+ ≠ √ ^ ÷ < ∆ * + X = ▼

56. Decode ≠ < = ÷ + X ≠

A. Evaluate B. Emanate C. Emerge D. Emulate E. Embrace

57. Write ELIMINATE in the code

A. ≠ ÷ ^ < ∆ B. ≠ ÷≠ < ≠ X ∆≠ C. ≠ ÷ ^ x +≠ ∆ D. ≠ ÷ <^ ^∆ +≠

E. ≠ ÷ x ^ ∆ + x < ≠

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58. Decode this message

< = + x + ≠ ≠ ▼ * =

A. I must eat him

B. I must see him

C. I must see you

D. I most lad you

E. O send sad you

59. In a certain code TCVU stands for the word RATS how would you write the word

SAT in this code?

A. UCV B. TCV C. CVC D. VUT E. VuT

60. Suppose the code LUMBERJACK stands for Lo246781cb and Lo246781cb for

Communiqué. What does the word JAMB stands for in the codes?

Study these examples

(a) (AVBVC) = A + B + C and A Λ B V C = A – B + C

(b) (2V4V5) = 2 + 4 + 5 = 11 and (6 V3) = 6 + 3 = 9

6Λ 3 6 – 3 3 = 3

Use the samples to work exercises 61 and 62

61. What is (13 Λ 4) + (6 V 5)?

A. 16 B. 14 C. 13 D. 19 E. 17

62. If 4324

87

x . What is X?

A. 3 B. 7 C. 5 D. 6 E. 8

Study the following sample and with it answer question 63

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Sample: (a) A B = A

AB

(b) 3 5 = 32

335

(c) 7 14 = 17

714

63. If x 9 = 2, what is x?

A. 2 B. 3 C. 13 D. 11 E. 12

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APPENDIX VI: Factor and item loadings on each item/ subscale of MAGII Var item Factor 1 Factor 2 Factor 3 Factor 4 Cum Var001 22 0.047 .590 .308 -.282 .354 Var022 46 -.189 .330 .482 -0.083 .384 Var003 61 -.248 -.221 .292 .537 .485 Var004 23 .227 .386 -.460 0.042 .414 Var005 64 0.002 -.253 .119 -.118 0.091 Var006 44 -.248 -.221 .292 .537 .485 Var007 27 -.163 .708 -.0.097 .270 .610 Vare008 45 .235 -.0.055 .558 -.314 .469 Var009 60 .235 -.0.055 .558 -.314 .355 Var010 1 .575 -.107 0.068 -.0.020 .511 Var012 12 -.187 -.301 -.330 -.0.057 .238 Var013 66 .313 .248 .476 .465 .602 Var014 3 .483 .231 -.390 .323 602 Var015 67 -.156 .521 -0.087 .363 .435 Var016 47 0.083 -.196 -0.019 .555 .354 Var017 68 0.066 0.084 -.325 -.249 .179 Var018 28 -.182 .561 .180 -.0.058 .393 Var019 24 0.035 .535 .300 -.297 .462 Var020 62 .173 2.80 -.0.011 .522 .381 Var021 63 0.085 .288 .211 .501 .386 Var022 4 .434 .338 -0.049 0.070 .310 Var023 5 .674 -0.061 .161 .221 .533 Var024 6 .401 -.217 -.172 .103 .248 Var025 69 -.167 0.084 0.012 .331 .145 Var026 42 .158 0.062 .464 -.218 .255 Var027 43 .173 .280 -0.011 .522 .381 Var028 41 0.080 -.138 .546 -.453 .528 Var029 7 .424 -.547 -.0.029 -.188 .515 Var030 59 -.189 .330 .482 -0.083 384 Var031 58 .106 .609 .206 0.045 .573 Var032 8 .427 .307 ,128 .213 .338 Var033 57 0.035 .532 .300 -.297 .462 Var034 40 -.166 -.014 .552 -.286 -.414 Var035 9 .714 -.195 -0.080 0.076 .561 Var036 10 .692 -0.070 .122 .285 .585

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Var037 70 -.685 0.057 0.025 .127 .490 Var038 71 -.215 .379 .369 .129 .343 Var039 56 -.227 .386 -.60 0.042 .414 Var040 11 .559 -.271 .339 0.074 .506 Var041 48 0.084 .288 .211 .501 .386 Var042 38 -.296 -.171 .406 -.157 .307 Var043 25 .016 .609 -.303 .253 .537 Var044 51 0.093 0.016 -.289 .690 .566 Var045 12 .659 -0.017 0.032 -0.001 .435 Var046 55 0.047 .598 .308 -.282 .535 Var047 13 .371 -.458 -.0.27 -.259 .416 Var048 14 .690 .143 -.710 -.155 .634 Var049 39 .262 -0.037 .521 -.277 .416 Var050 72 .462 .519 .129 -.170 .246 Var051 73 -480 -0.039 -0.097 .177 .246 Var052 15 .379 .111 -.149 -0.011 .178 Var053 74 -.227 -.216 -.045 .224 .322 Var054 75 -.399 0.011 -.461 0.083 .379 Var055 20 .464 .199 0.023 0.013 .256 Var056 16 .415 -.455 .326 0.021 .486 Var057 49 .175 -.194 -.341 .413 .355 Var058 26 0.059 .413 -0.080 -0.017 .192 Var059 17 .501 -0.008 -0.017 -.158 .277 Var060 18 .611 -.266 -.0.000 -0.082 .450 Var061 21 .398 0.079 -.102 .107 .187 Var062 29 -.219 .368 -.162 .149 .232 Var063 76 .206 .318 0.090 0.057 .155 Var064 32 2.73 4.55 .154 .250 .352 Var065 77 -.472 .145 -.214 .250 .352 Var066 78 -.147 0.056 0.074 0.097 .331 Var067 50 0.028 -.205 -.162 .421 .246 Var068 19 .431 .330 .165 -0.097 .331 Var069 79 -.203 -.242 .227 .207 .194 Var070 37 -.168 -.359 .684 .252 .695 Var071 30 .131 .428 0.093 -.129 .225 Var072 80 -.109 0.081 -.368 0.015 .154 Var073 31 .253 .468 -.129 0.004 .315

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Var074 36 -.273 .175 .710 -0.042 .611 Var075 33 .125 .368 -0.043 -0.049 .155 Var076 81 -.417 0.037 .203 -.253 .281 Var077 34 -.206 .614 0.038 0.034 .270 Var078 72 .193 -.116 -.167 -.553 .385 Var079 35 -.124 -.131 .410 -.422 .379 Var080 83 .189 .456 0.078 .529 .529 Var081 84 -.118 -.276 -.544 -.214 .434 Var082 85 .31 -.281 0.025 .125 .194 Var083 52 -.166 -0.095 .331 .442 .342 Var084 53 -.156 .256 -0.070 .360 .226 Var085 86 .331 .182 .349 .163 .291 Var086 87 -.229 0.063 0.092 .311 .161 Var087 88 .130 -.113 -.125 -.156 0.070 Var088 54 0.073 -.166 0.053 .504 .290 Var089 89 0.035 -.112 .335 0.079 .132 Var090 90 .186 0.056 -.102 -.243 .107 Var091 91 .152 -.150 -.261 .195 .157 Var092 92 -.227 .300 .159 -.510 .427 Var093 93 .2334 -.625 -.128 .173 .491