STATEMENT OF THE PROBLEM: ITS OBJECTIVES,

HYPOTHESIS AND VARIABLES.

Based on the observations in the earlier chapter, tlie researcher is in a position to

state the probleli~ with its significance, objectives, hypotheses, variables and operational

definitions of ternis and explanation of concepts.

3.1. SIGNIFICANCE OF THE STUDY

The development of a country is primarily determined by the quality of its human

resources. India needs today, effective and productive citizens with scientific and

constructive thinking and positive attitudes. This need can be met by well-planned

educational curricula, including a systenlatic mathematics programme at the school level.

There is a specific mention in the National Policy on Education 1986 (NPE) about

mathematics education in the following words: "Mathematics should be visualised as the

vehicle to train a child to think, reason, analyse and articulate logically. Apart from being

a specific subject, it should be treated as a concomitant to any s~lbject involving analysis

and reasoning."

The teaching of mathematics should be rewarding experience. Teachers must be

trained to generate a healthy intellectual envitonmeiit and encourage students to

participate and express their views through open discussions on creative problems of

mathematics.

Research in psychology has shown that 'almost any subject can be taught in some

intellectually honest form to any child at any stage of development, if it is properly

taught' (Bruner). The limitations are set not so much by the capacity of children to learn,

as by the capacity of teachers to communicate.

"No system of education, no methodology, no text book can rise above the level

of its teachers. If a country wants to have quality education it I I ~ L L S ~ llavc quality

teachers."

---- V.S. Matthews

Whether the students learn or not will depend upon many factors, probably the

chief of which are

1. his motivation and readiness to learn

2. his maturity level in relation to the task to be learned

3. his relation to the teacher

4. his ability to learn through words

5. the degree of his freedom from fear and

6 , the teachers skill in communication.

If these conditions are reasonably favourable, the student can learn much that is

significant.

But the present state of teaching mathematics in the majority of our schools is far

from satisfactory. The rate of failures in mathematics is considerably higher than in any

other subject. Many pupils find mathematics a difficult subject. For most of them

mathematics has been a meaningless group of symbols and problems or at best,

combinations to be memorised.

Moreover, many changes have been carried out in the mathematics curriculum.

There are certain new topics, included in the present curriculum, but the teachers are not

familiiir with them. Completion of syllabus has becoille a subject of concern for the

teachers and students. Hence, the teaching community generally feels that it is time

cotisuniing and also bmdensame for them to adopt new strategies to teach mathematics

in tune with the changing trends and demands.

Most of the teachers very frequently air their feelings as follows:

"Mathematics is a difXcult subject for students"

"Teaching Geometry is very difficult"

"Mathematics can't be taught meaningfully"

"Mathematics is a dry subject" etc.

This attitude of the teachers' lead to the development of negative attitude in the

students and they voice it by saying:

" Mathematics is difficult to learn"

"I am afraid of mathematics"

"I am afraid of Algebra"

"I dislike mathematics"

"Geometry is very difficult"

"How to get through the mathematics examination?" etc.

These attitudes and circumstances raise certain pertinent questions-How to make

teaching and learning mathematics easy and more meaningful? What are the main

reasons for these difficulties, problems, and for such attitudes in the students and

teachers? What exactly is needed now to overcome these difficulties, problems and to

improve the present situation?

It is against this backdrop that a comprehensive and constructive research work is

felt necessaty relating to mathematics education so as to get a better picture of the

sit~iation and to identify means and ways to improve the teaching- leami~~g process.

3.2. STATEMENT OF THE PROBLEM

Based on the above observations, the problem for the present investigation is as

follows:

"An Investigation into the Problems relating to Teaching-Learning Mathematics

at secondary level".

3.3. OBJECTIVES OF THE STUDY

The main objectives of the study are:

1. To identify the difficult areas in secondary level mathematics as perceived by the

pupils and teachers.

2. To identify the problems faced by the pupils in learning mathematics and by the

teachers in teaching the subject.

3. To study the attitudes of pupils towards learning mathematics and of teachers

towards teaching it.

4. To study the variations in the problems and attitudes of pupils of different sub

groups depending upon their personal and demographic variables.

5. To study the variations in the problems and attitudes of teachers of different sub

groups depending upon their personal and demographic variables.

6. To suggest the suitable strategies for the improvement of teaching - learning

mathematics at the secondary level.

3.4. HYPOTHESES

To realise the objectives stated above, the following descriptive and statistical

hypotheses were forn~ulated in null form for the purpose of testing.

1. The pupils in general do not feel that studying n~atliematics at the secondary level

is an easy task.

2. The teachers in general do not feel that teaching of mathematics at the Secondary

level is an easy and pleasant job.

3. There would not be any significant problems faced by students in learning

mathematics.

4. There would not be any significant problems faced by teachers in teaching

mathematics.

5. Pupils in general do not possess positive attitudes towards learning mathematics.

6 . Teachers in general do not possess positive attitudes towards teaching

mathematics.

7. Personal and demographic variables of pupils would not significantly influence

the intensity of problems faced by them in learning mathematics. (This major

hypothesis will be divided into minor hypotheses separately for each independent

variable for testing)

8. Personal and demographic variables of teachers do not significantly influence the

intensity of problems faced by them in teaching mathematics. (This major

hypothesis will be divided into minor hypotheses separately for each independent

' variable for testing)

9. Personal and demographic variables of students do not signiticantly influence

their attitudes toward learning matheniatics. (Tl~is major llypothesis will be

divided into minor hypotheses separately for each independent variable for

testing)

10. TIie personal and demographic variables of teachers do not significantly influence

their attitudes toward teaching mathematics. (This major hypothesis will be

divided into nlinor hypotheses separately for each independent variable for

testing)

3.5. VARIABLES STUDIED

As the present study envisages an investigation into the problems relating to

teaching-learning mathematics at the secondary level on the basis of the difficulties (in

content, teaching and learning), problems, and attitudes of students and teachers, the

dependent variables are as follows:

Dependent Variables

1. Difficulty level of different chapters (in content, teaching and learning) as

perceived by students and teachers in secondary level mathematics.

2. Problems of teachers and students in teaching and learning mathematics

respectively.

3. Attitudes of students and teachers towards mathematics education.

Independent Variables

The independent variables considered in the iilvestigation are two kinds, namely,

student related personal and demographic variables and teacher related personal and

demographic variables. The student related independent variables are class. sex, age.

locality, management of school, father's occupation, family literacy index, and annual

inconie of the family etc. The teacher related independent variables are sex, age,

educational qualifications) general and ii) professional, experience, locality, and

management of the school etc. A brief description of these variables is given as follows:

i) Variables related to Stude~lts

1) Class:

Students studying VIII, IX, and X classes are considered in the study to tind the

differences among the classes.

2) Sex:

Male and female students (boys and girls) are considered as sub-samples to

carry on the differential analysis.

3) Age:

The chronological age of the students as reported by them through the personal

data sheet is considered, to divide the sample into three subgroups to study the

variations in their problems and attitudes toward learning mathematics.

4) Locality:

The entire sample of the subjects is classified inta three groups the urban, semi-

urban, and rural, depending upon their residential status, i.e., those who reside in the

municipal towns and cities as urban, those who reside within the area of 20 krn from

town as semi- urban and those who reside in panchayat area as rural groups.

5) Management:

The scl~ools included in the study arc categorised into four types viz., government

schools, Zilla parishad schools, Municipal schools, and private schools to find the

variations in the problems and attitudes of their learners.

6 ) Father's occupation:

The occupational status of the parents may have its bearing oil the problems and

attitudes of students towards mathematics education. However, the occupation of father

alone is considered in this investigation. Based on the occupations the sample is divided

into three sub groups.

7) Family literacy index:

The educational level of the family is estimated by collecting information about

the number of years of study by all individual members of the family and dividing the

total by number of persons in the family which gives the family literacy index. Thus, the

family literacy index reflects the educational status of the family and it may have its

influence on the problems and attitudes of students in leatning mathematics.

8) Family Income:

The annual income of the family as reported by the student is considered for

making three sub groups of the sample of subjects. The economic status of the family

may have its influence on the problems and attitudes of students in learning

.mathematics.

(ii) Variables Related To Teachers:

The nlale and female teachers of matherilatics of the seconda~y school are

included in the study and there may exist difference between them in teaching the

subject.

2) Age:

The age of the teachers may influence their problems in teaching and their attitude

towards teaching mathematics. Therefore, the chronological age of the teachers as

reported by them through personal data sheet is considered as a variable for the study.

The sample is divided into four sub groups.

3) General Qualification:

The general qualification of the teachers of mathematics may influence the

problems in the field. Therefore, the general education possessed by them is considered

as one of the personal and demographic variables in the study. The sample is divided

into three sub groups based on the experience.

4) Professional Qualification:

The Professional qualification of the teachers of mathematics may exercise a great

influence on their problems in mathematics education. Therefore, it is taken as one of the

personal and demographic variables in the study. The sample is divided into three sub

groups based on the experience.

5 ) Teaching Experience:

The experience in years (length of sellrice) in the field of teaching mathe~ilatics

tnay intluence nlore the problems they face in teaching mathematics and their attitudes

towards mathematics education. Therefore, teacher's service is included as a variable in

the study. The sample is divided into four sub groups based on the experience.

6) Locality:

Mathematics teachers working in urban, semi-urban and rural areas may have

differences in the problems they face in teaching mathematics and in their attitudes

towards mathematics education. Therefore, all such teachers are regarded as criterion

groups for the investigation.

7) Management:

For the present study as in the case of students, teachers are classified into four

categories: Teachers of government schools, of zilla parishad schools, of municipal

schools and of private schools.

3.6. OPERATIONAL DEFINITIONS OF TERMS AND EXPLANATION OF CONCEPTS

The following definitions and descriptions are operationalised for the purpose of

measuring the variables in study.

1. Mathematics:

"Mathematics is the science of number and space"

"Mathematics is the science of measurement, quantity and magnitude".

"Mathematics is the science which draws necessary conclusionsJ'

. , "Mathematics is a way to settle in the mind a habit of reasoning."

2. Mathematics Educatioa:

The study of how one studies Mathematics is often called Mathematics Education.

Usually a person sludying ~nathe~natics is at least partly interested in tlle question of how

allyone would ever think of that in the first place.

A group of pupils or students scheduled to report regularly at a particular time to a

particular teacher (Good, 1973)

4. Secondary School or High School:

Schools with classes VI to X are called high schools or secondary schools in the

state of Andhra Pradesh in India. There will be public examination at the end of VII class

and X class in these Schools.

The ideas, meanings, concepts, explanations, etc., presented in the form of

lessons/chapters in the textbook.

B. 0. Smith(1963): Teaching is a system of actions involving an agent, an end in

view, and a situation including two sets of factors-those over which the agent has no

control (class size, size of classl.oom, physical characteristics of pupils etc.) and those that

he can modify (ways of asking questions, instructions and way of structuring information

or ideas gleaned.)

Yoakln and Simpson: Teaching is a means whereby society trains the youlig in a

sclected environment as quickly as possible to adjust themselves to the wol.ld in which

they live.

Learning:

The dictionary of C. V. Good (1973) defines it as "Change in sesponse 01-

behaviour(such as innovation, elimination or modification of responses, involving some

degree of performance)caused partly or wholly by experience, such experience being in

the main conscious, but sometimes including significant unconscious components, as is

common in motor learning or in reaction to unrecognised or subliminal stimuli; includes

behaviour changes in the emotional sphere, but more commonly refers to the acquisition

of symbolic knowledge or motor skills, does not include psychological changes, such as

fatigue or temporary sensory resistance or non-functioning after conditioned stimulus."

Gates and others defme it as "the progressive change in behaviour which is

associated on the one hand with successive presentation of a situation, and on the other,

with repeated efforts of the individual to react to it effectively."

Teaching - Learning Process:

Teaching - Learning process is a ineans by which the teacher, the learner, the

curriculum and other variables are organised in a systematic manner to attain pre-

determined goals and objectives.

Difficulty Level:

An approximation is niade in order to tit the content of reading materials into the

reading ability of the child by different testing procedures. The difficulty level of cliaplers

included in the textbooks of rnathen~atics for VIII, IX and X classes is considered in this

study.

Content Difficulty:

Some of the topics included in the prescribed textbook would be above the ability

levels of students studying that particular class. Such topics are treated as difficult to the

students content-wise. Teachers also find difficult in handling the contents, which are

newly introduced and with which they are not aware of.

Teaching Difficulty:

Teachers may find difficulty in transmitting the difficult and some of the newly

introduced lessons effectively and meaninghlly to the students. It has been treated as

teaching difficulty.

Learning Difficulty:

Students find difliculty in understanding some of the contents given in the

textbook, even if the teacher presents them effectively. It has been taken as learning

difliculty.

Any significant, perplexirig and cllallengilig situation, real or al.tificial, tlie

sol~~tiorl of which requires reflective thinking.

The tern1 'problems' refers to those difficulties of the secotldary school teachers

in teaching and of tlie pupils of VIII, IX, X classes in learning mathematics syllabus.

14. Attitudes:

Guilford (1954) defined attitude as " A personal disposition common to

indivisual but possessed to different degrees which implies to react to object situations

or positions in ways that can be called favourable or unfavourable."

According to Bogardus (1931) "Attitude is a tendency to act toward or against

something in the environment which becomes thereby, a positive or a negative value."