English SEM/KENYA Paris, April 1984

UNITED NATIONS EDUCATIONAL

SCIENTIFIC AND CULTURAL ORGANIZATION

STATISTICAL ANALYSIS OF DEMOGRAPHIC

AND EDUCATION DATA IN

THE REPUBLIC OF KENYA

Document prepared for the National Training Seminar on Education Statistics in

the Republic of Kenya

Nairobi, 6 August - 17 August 1984

Division of Statistics on Education Office of Statistics Unesco

ST-84/JS/10

1 3 JU'iL 1984

PREFACE

Enrolment projections constitute the numerical basis for planning the future supply of educated labour as well as the future needs for teachers, classrooms and other facilities.

Wnile the need for enrolment projections is well recognised, two factors often counteract developing countries' efforts in this area. Firstly, the national services responsiDle for preparing such projections frequently do not have personnel sufficiently qualified in the statistical methods required. Secondly, to apply sound projection methods requires that a minimum of reliable data on education and population be available, Unfortunately, both the quantity and the quality of the statistics available in this field leave much to be desired in many developing countries.

Tne Unesco Office of Statistics has, since 1972, been engaged in activities relating to education projections with special reference to developing countries. These activities have revealed the need for training in simple methods of quantitative analysis of the relationship between demographic growth and its implications for school enrolment.

Tne purpose of the present document is to serve as a support for a training seminar in the Republic of Kenya. Although self-contained, this document should be read with this in mind since several topics which have only been touched upon here will be dealt with in further detail during the presentation of the seminar or in the course of the practical exercises.

Tnis seminar has been prepared by the Unesco Office of Statistics with the financial support of the Swedish International Development Agency (SIDA) and with the collaboration of the Ministry of Education, Science and Technology of the Republic of Kenya. We should like to express our gratitude to the national authorities for their help in supplying the statistical information required for preparing this document.

Division of Statistics on Education Office of Statistics

Unesco

Paris, April 1984

TABLE OF CONTENTS

Page

INTRODUCTION 6

PART I: POPULATION AND EDUCATION IN KENYA 7

SECTION 1: POPULATION; BASIC CONCEPTS OF DEMOGRAPHY 7

1.1.1 The Subject-Hatter of Demography 7 1.1.2 The Size of the Population 7 1.1.3 The Rate of Population Growth 8 1.1.4 Births 11 1.1.5 Deaths 13 1.1.6 Crude Rate of Natural Increase 14 1.1.7 Life Tables 14 1.1.8 Migration 15 1.1.9 The Importance to Educational Planners of Population

Projections 19

SECTION 2: POPULATION FACTORS IN EDUCATIONAL PLANNING ... 21

1.2.1 Introduction 21 1.2.2 Quality of Demographic Data 22 1.2.3 Some Examp4.es of Interaction between Population and

Education 23 1.2.4 Implications of Alternative Rates of Growth in the

Population 24 1.2.5 The Burden Imposed by the School Population 25 1.2.6 The Geographical Distribution of the Population .... 28 1.2.7 The Distribution of the Population by Sex and Age .. 31 1.2.8 Literacy Rates and Educational Attainment 36 1.2.y Concluding Remarks on Part I 42

PART II: METHODS OF ANALYZING AND PROJECTING SCHOOL ENROLMENT 43

SECTION 1 : ENROLMENT RATIOS 43

11.1.1 Introduction 43 11.1.2 Definition of Enrolment Ratios 43 11.1.3 Enrolment Ratios for Kenya 48

4

SECTION 2: EDUCATION FLOW MODELS 54

11.2.1 Introduction 54 11.2.2 Characteristics of Educational Flow Models 55 11.2.3 Distinction between Enrolment Projections, Forecasts

and Targets 56 11.2.4 The Advantages of Mathematical Models 57 11.2.5 The Flow of Pupils Through a Cycle of Education as

analyzed by the Grade Transition Model 57 11.2.6 Calculation of Promotion, Repetition and Dropout

Rates 62 11.2.7 Some Aspects of Migration and Transfers between

Schools 65

SECTION 3: USE OF FLOW MODELS FOR RECONSTRUCTING THE SCHOOL HISTORY OF A COHORT. 71

11.3.1 Introduction 71 11.3.2 Cohort Reconstruction 72 11.3.3 Discussion of the Assumptions behind the Cohort

Reconstruction 75 11.3.4 Cohort Flow Indicators derived from Cohort

Reconstruction 77 11.3.5 Apparent Cohort Method 86

SECTION 4: USE OF FLOW MODELS FOR PROJECTING ENROLMENT BY GRADE 89

11.4.1 Introduction 89 11.4.2 The Role of Education Projections in

Educational Planning 89 11.4.3 Preparing an Enrolment Projection 89 11.4.4 The Use of Sprague Multipliers for Estimating the

Distribution of Population by Single Years of Age. 91 11.4.5 Methods of Projecting New Entrants 93 11.4.6 Projecting New Entrants for Kenya 96 11.4.7 Some factors Affecting the Development of

New Entrants 102 11.4.8 Some Special Problems Encountered in Projecting

New Entrants to Secondary Education 103 11.4.9 Projecting Enrolment by Grade Using the Grade

Transition Model 106 11.4.10 Some Effects of Capacity Limits on Transition

Rates 109 11.4.11 Examples of Changes in Educational Policy Which

May Affect the Transition Rates Ill 11.4.12 An Example of How the Grade Transition Model can

be Used to Examine Effects of Policy Changes: Introduction of Automatic Promotion 115

11.4.13 Projecting Enrolment by Grade for Kenya 117 11.4.14 Projecting Enrolment by Grade Using the Grade

Ratio Model 123 11.4.15 Concluding Remarks on Part II 125

5

PART III: THE PROJECTION OF TEACHER SUPPLY AND DEMAND 128

SECTION 1: CHARACTERISTICS OF THE TEACHING STOCK *.. 128

111.1.1 Introduction 128 111.1.2 Description of the Teaching Stock in Kenya 135

SECTION 1; PROJECTION OF TEACHER REQUIREMENTS 135

111.2.1 Introduction 135 111.2.2 Methods Based on the Number of Pupils and the

Pupil-Teacher Ratio 135 111.2.3 Method Based on the Number of Pupils per Class,

Hours Taught by Teachers and Hours Pupils are in Contact with Teachers 136

111.2.4 Projecting the Demand for New Teachers 138

PART IV: ANALYSIS OF EDUCATIONAL EXPENDITURES AND OF EDUCATIONAL COSTS 141

SECTION 1: ASSESSMENT OF NATIONAL EDUCATIONAL EXPENDITURE 141

IV.1.1 Introduction 141 IV.1.2 Definitional Problems 141 IV.1.3 Sources of Educational Finance 142 IV.1.4 Public Expenditures on Education in Kenya 143 IV.1.5 Alternative Ways of Disaggregating Expenditures ... 145

SECTION 2: THE ANALYSIS OF EDUCATIONAL COSTS 149

IV.2.1 Distinction Between "Costs" and "Expenditures" .... 149 IV.2.2 Purpose of Cost Analysis 149 IV.2.3 The Concepts of "Joints Cost" and "Opportunity

Costs" 150 IV.2.4 Costing Educational Plans 152 IV.2.5 Concluding Remarks on Part IV 153

ANNEX I. The Education System in Kenya (1983) 154 ANNEX II. Map of Kenya with provincial Boundaries 155 ANNEX III.Selected Enrolment Statistics for Kenya 156

6

INTRODUCTION

Since the Second World War, the majority of the developing countries of the world have experienced two interrelated phenomena with profound social and economic implications. Populations have increased at an unprecedentedly rapid rate and the demand for and expectation of education has developed at a pace with no historical parallel. The demographic explosion, due above all to improved public health measures and better access to medical care, has produced a continuous underlying expansionary pressure on educational systems. The explosion in expectations for better education has added to this dynamic social force. This demand has come from all sections of society. It has been a demand expressed by governments with a view to the fulfilment of their plans for economic development and growth. It has also been a more diffuse social demand: the expression of a growing desire for greater personal self-fulfilment and the realization of individual economic potential.

These two great social forces have raised critical problems for all governments. The problems have involved difficult issues of choice between alternatives. The choices have included the pace at which to expand the volume of resources being channelled to the education sector: how to distribute resources between the various levels of education; how to distribute limited resources according to such criteria as sex, age and geographical region; and how to raise the revenue to cover the expanding costs. For all these and many other reasons which will readily spring to the reader's mind, there has been the need to take a view of future developments in the underlying processes affecting the development of education systems.

In short: educational systems must be planned. They must be planned to serve the major economic and social objectives of society: efficient economic development, the pursuit of social justice,and a greater access to knowledge for its own sake. In this planning process an understanding of the interaction between population and social and economic aspects of development is essential. This need is often recognized in theory, but in practice both planning and administration tend to be compartmentalized with resulting incongruities and lack of co-ordination between different sectors. Educational planners, for example, do not always have access to demographic expertise to enable them to appreciate the policy issues posed by rapid population growth and migration, and to take account of the implications of changes in the size, structure and geographical distribution of the population of school age.

With these considerations in mind, the purpose of this paper is to examine the use of demographic and educational data for planning the development of education in Kenya mainly but not exclusively at the primary level.

The first part of the paper explains the basic concepts of demography and their relationships to educational planning. The second part, and the heart of the paper, explains and develops in the context of Kenya the basic educational flow model. There follows, in Part III, an analysis of the planning of the supply of teachers and finally, in Part IV, the financing of the educational system is examined. In reading this paper it should be borne in mind that it has been prepared as a support for the teaching at a national training seminar, where other papers will also be presented, prepared by Unesco or by national specialists. Although some sections of the present paper are self-contained, others are heavily marked by this fact. This is particularly true for those sections containing practical exercises for which some of the required statistical material will be distributed to the participants only during the seminar.

7

PART I; POPULATION AND EDUCATION IN KENYA

SECTION 1; POPULATION: BASIC CONCEPTS OF DEMOGRAPHY

I.1.1 The Subject-Matter of Demography

Demography is the scientific study of certain characteristics of human populations, particularly with respect to their magnitude, their change over time, and their structures according to sex, age, occupation, geographical location and other characteristics. Virtually all quantitative analyses in educational planning depend on population information in one form or another. For this reason all educational planners need an understanding of the basic concepts of demography - including an appreciation of their limitations. We shall, therefore, review some of these concepts in this section. However, as the main objective of this seminar is to provide training in education statistics methods, this review will be partial and we refer the readers to specialised literature on demography for further study of this topic.

Human populations undergo continuous change. The changes in the set of individuals which make up the population may be divided into three, usually termed by demographers the "vital processes":

(a) births (b) deaths (c) migration

Before we examine how these vital processes may be measured, let us look at a fundamental statistic: the size of the population.

1.1.2 The Size of the Population

The main sources of information on population size -that is the state of a population at a given time - are censuses, registration systems, and demographic research reports of government and other agencies. Censuses involve the complete enumeration of all the inhabitants of a defined geographical area. In industrialized countries these have had a long and valuable history. In the United Kingdom, for example, censuses of the population have been taken every tenth year since 1801. They are, however, expensive to carry out and demand large numbers of trained personnel for their satisfactory completion. Consequently, several developing countries have yet to implement scientific population censuses. This is not the case for Kenya where four censuses have so far been undertaken. Two of these were conducted before independence (in 1948 and 1962) while the two others have been carried out in the post-independence period, the first in 1969 and the second in August 1979. The total population of Kenya recorded in the last census was 15.327.061. (1)

(1) See Kenya Population Census, 1979, Vol. 1, Central Bureau of Statistics, Nairobi, June 1981, Table 1.

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1.1.3 The Rate of Population Growth

The average annual rate of growth is an important basic tool in demography. It should not be confused with the total percentage growth of population over a period of time. To clarify the distinction between these two concepts, let us consider the increase in the total population of Kenya between the 1969 and 1979 censuses. The former census recorded a total population of 10.942.705 as compared to 15,327,061 in the latter, i.e. an increase of 4.384.356 during this ten year period. The total percentage growth during this period is calculated by means of the following formula:

(1) Percentage growth over the period = 100 n

where P = Population in the initial year "o" (here 1969) o

where P = Population in the final year "n" (here 1979). n

Hence the percentage growth over the period 1969-1979 is:

100 15,327,061

10,942,705

= 40.1 %

The average annual rate of growth is calculated by formula 2 shown below. This is in fact the standard formula for reckoning compound growth where annual percentage increases are reckoned on the base of both the original figure in Year 1 and the compounded successive annual increments. It contrasts with the simple rate of growth formula which adds a constant amount each year to the original. The difference between a compound rate of growth and a simple rate of growth can readily be illustrated by considering how a sum of 1,000 dollars would grow in the face of 10% rates of interest.

Simple

Year Accrued Capital Sum

Year 1

Year 2

Year 3

Year 4

Year 5

1 000

1 100

1 200

1 300

1 400

Interest

Annual Interest (10 % of original

capital)

100

100

100

100

100

Compound Interest

Accrued Capital Sum

1 000

1 100

1 200

1 331

1 464.41

Annual Interest (10% of accrued capital)

100

110

121

133.1

146.41

9

Population growth is similarly of the compound variety and it is quite easy to see therefore that one cannot simply divide the total percentage increase above (40.1 % ) by the number of years (10) to arrive at the average annual rate of increase. Instead the formula one uses to arrive at the average annual rate of increase is:

(2) P = P (1+r) n

n o

"r" being the rate we want to calculate.

To calculate r from this formula we have to take logarithms, and re-express the formula as:

log P = log P + n n o

log (1+r)

Tnis in turn can be re-arranged as:

3 •

log P - log P = n n o

log P - log P n o

log(l+r)|f or log (1+r) = i In the example under discussion we have:

P = 15r327,061 n

P = 10,942,705 o

n = 10

(1) Thus, talcing logarithms we get:

log 15,327,061 - log 10,942,705 log (1 + r) = ••

10

7.1855 - 7.0391 = = 0.0146

10

Taking the antilog of 0.0146 we obtain:

1 + r = 1.0342

or that r - 0.0342 or 3.42 %.

(1) Logarithms to the base 10 have been employed here: Logarithms to the base "e" (the exponential constant, e = 2.7183) could also be used.

10

Hie rate of growth of the total population describes population change but does not explain it. For an understanding of the underlying factors giving rise to this change, the vital processes must be analysed: births, deaths and migration.

EXERCISE I

The following data and projections are available for the population of Kenya and total Africa for the period 1960 - 2000 (figures in thousands)

I Year

1960 1970 1980 1990 2000

Kenya (a)

• • • 11,247 16,667 24,872 37,505

Kenya (b)(c)

8,189 11,253 16,466 24,831 37,138

Total Africa (c)

275,246 354,663 469,982 635,350 852,885

I

I (Sources: (a) Kenya Statistical Digest, September 1972, vol. X, No 3, | I Central Bureau of Statistics, Populations Projections for Kenya, i

1980-2000, Central Bureau of Statistics, Nairobi, March 1983.

(b) It will be seen that the estimates for Kenya (a) (from Kenya's Central Bureau of Statistics) do not differ significantly from the UN estimates population for Kenya (b). In a number of tables to follow, the UN estimates will be used.

I (c) World Population Prospects as Assessed in 1980, New York 1981. (The projections refer to the "Medium Variant")

Employing these figures please calculate:

(1) The total percentage growth during each of the four ten-year periods covered for Kenya and total Africa;

(ii) The average annual rates of growth for the same periods.

Compare the results.

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1.1.4 Births

Crude Birth Rate

The crude birth rate of an area is defined as the number of live births occuring in that area in a given time period, usually a year, divided by the population of the area as estimated at the middle of the particular time period. The rate is most often expressed in terms of "per 1,000 of population".

Number of live births in a year (3) Crude birth rate = - -• ; x 1,000

Mid-year total population

Column 2 of Table 1.1 gives estimates of the crude birth rate for Kenya as well as for selected regions and countries. The table shows that the crude birth rate for Kenya exceeds by a substantial margin the average rate for all African countries covered and Europe.

The crude birth rate is an elementary statistic which requires only global information for its calculation. It is not calculated with any reference to the structure of the population according to age or sex, even though it is the proportion of women of child-bearing age in the population that largely determines present and future population changes. Therefore, a more refined measure of "fertility" is desirable.

Fertility Rates

Fertility measures the rate at which a population augments itself by births, relating births to the number of females "at risk", that is, of child-bearing age. Three fertility rates may be distinguished here, the general fertility rate, the age-specific fertility rate, and the total fertility rate.

(a) The general fertility rate

(4) the general fertility rate =

Number of live births in a year = x 1,000

Mid-year population of women of child-bearing age

Often "child-bearing age" is taken to be 15 - 49 years.

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Table 1.1

: Region : or : Country

: Annual growth of population, crude birth and death rates and rate of natural increase. Kenya and selected countries and regions, 1980-1985.

» •

: Annual rate : :of population: : growth (%) : : 1980-1985 : » •

Crude birth rate (per 1000) 1980-1985 •

: Crude : death rate (per 1000) 1980-1985

: Rate of : : natural increase : : (per 1000) :

1980-1985 :

(1) (2) (3) (4)

Europe 0.34 14.1 10.7 3.4 Africa 3.00 45.6 13.9 31.7 Eastern Africa 3.09 47.9 15.2 32.7 Kenya 4.10 53.5 11.0 42.5 Tanzania 3.21 46.2 12.5 33.7 Uganda 3.18 44.6 12.8 31.8 Zambia 3.25 49.0 15.5 33.5

Source: World Population Prospects as Assessed in 1980, United Nations, York 1981, Table A-2.

(b) The age-specific fertily rate

The rate discussed under point (a) above was called a "general" rate because it attibutes all births to all women within these age-limits. Clearly, however, fertility is not constant over all years of child-bearing potential. A more disaggregated measure of fertility is the age-specific fertily rate:

(5) the age-specific fertility rate =

Number of live births born to women in a specified age-group in a year

Mid-year population of women in the specified age-group x 1,000

In calculating the age-specific fertility rate, potential mothers may be grouped by single year of age or by age-groups of, e.g., five years. It needs hardly be added that the age of women is not the only factor affecting fertility. Fertility, depends on numerous other influences - social and cultural as well as physical- including the availability and use of techniques of birth control, age at marriage, duration of marriage, average time between births, and so on.

13

For Kenya, the following rates have been estimated by five-year age-groups for the period 1977-1978: (1)

Age-groups; 15-19 20-24 25-29 30-34 35-39 40-44 45-49

Rates : 177.4 377.4 386.1 322.6 233.2 107.1 13.9

(c) The total fertility rate

Another very useful summary indicator of fertility is the total fertility rate defined as the average number of children a woman will have if she experiences a given set of age-specific fertility rates throughout her lifetime. It is derived from the actual or assumed age-specific fertility rates. This is a good index to measure fertility changes as it is independent of the age and sex distribution of the population. The source quoted for the age-specific fertility rates shown above gives a total fertility rate of 8.1 for Kenya for 1977-J.978.

* * * * * *

It is important to note that fertility rate calculations are based on the number of births occurring in a single year. Obviously, these rates may change quite considerapiv over time.

The second vital process governing the changes over time of a population is death. We shall below define the main measures used in demography for analyzing this aspect.

1.1.5 Deaths

The crude death rate of an area is defined analogously to the crude birth rate. It is the number of deaths occurring in that area in a given period, usually a year, divided by the population of the area as estimated at the middle of the time period:

Number of deaths in a year (6) crude death rate = x 1000

Mid-year total population

Column (3) of Table 1.1 gives crude death rates for Kenya and for selected countries and regions. We note the death rate for Kenya is considerably below the average rate for Africa, and especially, the African Countries covered. Deaths result, of course, from a multitude of causes (some of which can and some of which cannot in principle be influenced by public policies). The different age-groups in the population experience different rates of mortality from specified causes. For this reason, the crude death rate is only a relatively clumsy tool for the social planner. To further investigate the mortality experienced by a population, death rates according to age may (data permitting; be usefully calculated.

(1) Social Perspectives Vol. 5, No 2, Central Bureau of Statistics, January 1981, p. 8.

14

The age-specific death rate is defined as follows:

(7) age-specific death rate Number of deaths in a year in a specified age-group

= - • • x 1000 Mid-year population in the specified age-group

One commonly-calculated age-specific death rate is the infant-mortality rate:

(8) infant mortality rate

Number of deaths below age 1 in a year - x 1000

Number of live births in the year

Because of the susceptiDility of small babies to infection and their vulnerability to accidents, this rate is generally much higher than other age-specific death rates (until a great age is reached). It, and the other age-specific rates up to the year of entry into the school system, are of obvious importance to the educational planner in projecting future school intake.

1.1.6 Crude Rate of Natural Increase

Another basic demographic relation which may now be introduced is the crude rate of natural increase. This measures the change in population size due to births and deaths as a percentage of total population. (Note that it takes no account of net migration: the difference between emigration and immigration). It is defined as follows:

Number of births in a year minus number of deaths in a year

(9; Crude rate of natural increase = Mid-year population in the year

Table 1.1 shows data for the crude rate of natural increase for selected countries and regions. We note that, due to a comparatively low crude death rate, and a very high crude birth rate, the rate of natural increase in Kenya is considerately higher than in the other Eastern African countries/regions shown in the table, including Kenya.

1.1.7 Life Tables

The life table is an analytical tool of great importance in demographic analysis. It presents the life history of a hypothetical cohort of individuals from birth (though it could commence at any age) to their eventual death.

15

A cohort is a set of individuals possessing some common characteristics. In this case, the characteristic is a common year of birth. In later sections of this paper, we shall consider cohorts of individuals flowing througn the educational system and in that analysis cohorts may be distinguished by their age or by their common school grade in the initial year of the flow analysis.

A cohort of individuals born in a particular year is gradually diminished year by year by death until all members have died. A life table may be a "longitudinal" or "generation- life table based on the observation through time of the mortality experienced by a real cohort of individuals. Such tables are, however, of relatively little value compared with life tables constructed by applying current mortality rates by age to a theoretical cohort of, say, 1,000 persons. The construction of such tables ("current or period" tables) requires a considerable amount of information, and they are not available for all countries. However, if such tables can be drawn up, valuame indices may be estimated from them. These include:

(a) probabilities of death and survival for individuals at particular ages or periods.

(b) life expectancies at particular ages: the average number or years that persons at particular ages can be expected to live, i.e. will live on average if current mortality rates continue into the future.

Life expectancy at birth is a widely used indicator in comparative studies. Low life expectancy at birth is usually associated with high infant and chilanood mortality rates. Even where a country's life expectancy at birth is low by international standards, it is often the case that life expectancy at age 10 is significantly higher and indeed comparable with countries at relatively advanced levels of socio-economic development. This is because of the very high rates of infant and early chilhood mortality. Once an indiviaual has survived this particularly risky period of his life he may expect to survive for a number of years comparable with his surviving contemporaries in other countries having much lower rates of childhood mortality.

According to UN estimates, the life expectancy at birth for the period 1980-1985 in Kenya is 53.7 years for males and 58.2 for females. The corresponding average figures for Africa are, respectively, 49.3 and 52.4, while the averages for Europe are 75.8 years for females and 69.7 for males.

1.1.8 Migration

The third major component explaining population change together with birth and death is, of course, migration. Clearly, in analyzing past changes in the total population of a country, as well as in projecting future changes, rates of emigration and immigration may play an important role.

16

However, not only international migration is of concern to the educational planner; internal migration is often as important and sometimes more important. For example, the level and direction of internal migration may be decisive in determining where new schools should be established. On the other hand, the location of schools may affect both the level and direction of internal migration.

It is not possible in a general background paper such as this to discuss these very important and complex processes at any length. Furthermore, the statistical data required for studying migration processes can unfortunately rarely obtained even in highly industrialized countries having relatively comprehensive systems of data collection. We shall, therefore, limit ourselves to highlighting some general problems in this area. Those wishing to study this subject further are referred to the considerable amount of work which has been carried out in this area in recent years. (1)

Planning to take into account the effects of migration can start only when policy makers become concerned about its implications and consequences. To understand these implications and consequences necessitates a considerable amount of statistical information. We may, for example, wish to answer the following type of questions:

(i) What are the origins and destinations of migrants (e.g. country, region, state, province, rural-urban area)?

(ii) How many people moved during specific time period from and to specific areas?

(iii) What are the significant economic, social, cultural and physical destinations of these migration movements?

(iv) Under what circumstances are the decisions to move made?

(1) See for example:

- Methods of Measuring Internal Migration, Population Studies No 47, united Nations, New York 1970.

- Methods of Projecting Urban and Rural Population, Population Studies No 55, United Nations, New York 1974.

- Trends and Characteristics of International Migration since 1950, Demographic Studies No 64, United Nations, New York, 1979.

- Planning of Internal Migration: A Review of Issues and Policies in Developing countries, ISP-RD-4, U.S. Department of Commerce, Bureau ot the Census, Washington, 1977.

17

(v) If none of the above relevant factors changer how many migrants can be expected between different areas in the future?

(vi) If there are changes in any of the significant differences between origin and destination or between migrants and non-migrants, how does this affect future migration?

In collecting information on these aspects we first need to define the type of migration that is to be estimated. A critical distinction is whether the migrant has crossed a national border. If so, it is international migration; if not it is internal migration.

(a) International Migration

To understand the impact of international migration on the population of the sending and receiving countries, it is essential to study the sex and age characteristics of migrants. It has been found that migration for economic motives is highly selective with respect to sex and age. Generally, migrants have included a larger number of males than females and have been over-represented in the young working age and under-represented in the ages of childhood and old age compared to the total population.

Because of these atypical characteristics, migrants often have an effect on the laoour force disproportionate to their numbers. Moreover, their demand for various social services, such as those associated with education, reflects their special composition by sex and age. Being concentrated in the young working ages, they also have the potential of adding significantly to the natural increase of the population they join. The particular sex-age distrioution of migrants may complement that of the receiving country in offsetting labour force shortages caused by period of low birth rates in the past.

Conversely, the departure of persons in the peak reproductive ages may contrioute to a reduction in the crude birth rate of the country of emigration. If the emigrants are predominantly men, marriage and fertility rates of the non-migrating female population are likely to be affected. The country of emigration, through the loss of a disproportionate number of young people, may be deprived of part of the most dynamic and best qualified element of its labour force. This brain drain may have serious implications, particularly for some of the less populous countries for which the number of emigrants may form a substantial part of their highly skilled work force.

(b) Internal Migration

With regard to internal migration, migrants may move between different regions, provinces, or urban and rural locations. A commonly used classification is the urban or rural character of the origin and destination. By this typology, migrants may move from rural to rural, from rural to urban, from urban to urban and from urban to rural locations. A majority of the research studies carried out on internal migration in countries of the Third World focuses on rural-urban migration, probably because the problem of rural stagnation and urban explosion are so widespread among developing nations.

18

In Kenya, the level of urbanisation is still quite low by African standards. For 1980, the UN has estimated that about 14 % of the population lived in urban areas as compared to 16 % for the region of Eastern Africa and 29 % for Africa as a whole. (1) The reader should note that the definitions of urban and rural areas differ somewhat between countries. According to the UN document quoted as source for the above estimate, in Kenya the term "urban area" includes "towns with 2,000 or more inhabitants".

One characteristic which may affect migration estimates is the permanency of migration. For example, the policy maker may be concerned with all migrants going between certain origins and destinations, or he may be concerned only with the "permanent" migrants who take up a new place of residence after moving. In such a case, "seasonal" migrants who move temporarily are not included in the estimates. Estimates of permanent migrants may be further subdivided if one includes only persons who have moved before, e.g. for stepwise or cyclical migration. Separate estimates are generally made for seasonal and permanent migrants, because this distinction is more relevant to planning decisions than the differences between stepwise and permanent migrants.

Another important element in classifying migrants is delineation of the time period within which migrants are estimated. This may be in months, years, or even decades, with subdivisions of the time period if needed. Unless estimates are made relative to a specific time interval it is difficult to connect the estimated number of migrants with relevant causes or impacts.

Choosing which type of migration to estimate depends very largely upon the geographical scope of the area involved and the level of detail required for planning purposes. For example, an educational planner concerned only with the capital city needs detailed estimates of the migration going to and from the city. On the other hand, an educational planner working in a rural area may need to know about seasonal migration into and out of the area covered by the schools for which he is responsible.

When the type of migration bo be estimated has been decided upon the next step is identification of who migrates. Without knowledge of specific migrant characteristics, preparation of migration policies is severely handicapped, if not impossiule. The characteristics most relevant to defining the migrant population are age, sex, marital status, educational attainment, occupation, employment status and income prior to moving. The age-structure of the migrants, is of course, of particular importance for educational planning.

Orten an important part of estimating past, present and future migration is the identification of significant differences between the origin and destination. Differences that have been most useful in predicting migration are economic, social, cultural and physical, in that order of importance. Examples of factors which differ for origin and destination areas are income levels and distriDUtion, employment opportunities for different occupations, educational opportunities and levels of living. Identification of these types of differences may both amplify understanding as to why certain persons move and suggest potential mechanisms for migration policies.

(1) See "Estimates and Projections of Urban, Rural and City Populations, 1950-2025: The 1980 Assessment", ST/ESA/SER.R/45, United Nations, New YorK, 1982, p. 28.

19

Finally, information on the factors causing migration is very important For example, are parents migrating in order to live in a place where they can more easily obtain education for their children?

Projections of future internal migration are usually based on the estimates of past and present migration and assumptions concerning future levels. One assumption is that migration will continue as in the past. Thus, analysis of a set of estimates for different time peiods may show a trend whicn can be used to project future migrations. In addition, the analyst can fit the observed trend to a straight line or a curve. Trend analysis is the most simpie method for projecting migration and is often used.

In Kenya, the Government has been conducting a very active, rural development policy. It is strongly believed that other than the search for employment which influences the rural-urban migration, there is also the urban attractions by various facilities found largely in the urban areas. Basic needs sucn as education, health services, water and electricity are now being actively expanded in the rural areas. The current 1984/1988 Development Plan emphazises the Government's Commitment to the development of rural areas by focusing planning at the district level. It is hoped that this re-orientation of development will facilitate rural development, create more attractions and possibly employment opportunities in the rural areas, thereby slowing down the rate of rural- urban migration.

* * * * * *

We shall not go further here in discussing the implications of international and internal migration for educational planning. We shall however, return to some aspects of this topic in later sections of this document particularly with regard to the effect of migration on tansfer of pupils between schools.

1.1.9 The Importance to Educational Planners of Populations Projections

Population projections are based on specific assumptions about future changes in the many influences on births, deaths and migration summarised under the three "vital processes" discussed above. Estimates of the size of future cnanges in these influences inevitably rest on evidence derived from analysis of past and current trends. These assumptions about future change are then applied to the present population structure. Population projections thus show the prospects for the future size and structure of the population, given the present size and structure and current trends.

Obviously, any set of assumptions covering a lengthy period into the future is liable, in the event, to be demonstrated as "false". Changes in technology, social behaviour and values will all have their interdependent influences. Population projections do not therefore - indeed cannot - reflect the impact upon population changes of radical new developments or influences in society. They have the objective of making explicit how the present population will develop over time, assuming the continuation of observed trends in the present structure.

Tne orthodox method of population projection is to postulate various patterns of change in the components of population growth. That is to say,

20

assumptions are made about future rates of fertility, mortality and migration. Commencing with the current age and sex distribution of the population, future population estimates are made by applying, where available, age- and sex-specific fertility, mortality and migration rates to each population sub-group. New assumptions about rates may be introduced at any stage of the projection period. In general, a number of plausible assumptions about rates will be made in order to present a set of alternative projections. Such alternative projections permit sensitivity apaiysps to be made. The projected population may be more or less "sensitive" to variation in the assumptions about particular vital rates. To the extent that projection varies little with (i.e. is less sensitive to) changes in a particular assumed rate, less attention need be given to the "correctness" of that assumption. Where, however, a projection is very sensitive to a particular assumed rate, the assumption requires closer scrutiny, and if possible, the development of a better information base on which to ground it.

Educational planning is concerned with decisions about the future nature and shape of the education system and with the means to realise desired educational changes. Always in the forefront of the planner's preoccupations is the time dimension. This is, in part, a matter of setting and meeting target dates for the achievement of objectives and of taking into account the lead-and lag-times which limit the possibility of effecting speedy change. In part it is a matter of the main participants in formal education being transients who progress - generally at a more or less standard age and at a standard pace - through the grades, stages and cycles of the education system.

The world of the educational planner comprises two kinds of phenomena: the factors he can manipulate and control on the one hand; and the given constraints to which he, in turn, has to adapt, on the other. Of the latter category by far the most fundamental for the educational planner are the size, structure and growth of population. For once a country has decided that some specified proportion of a certain age-group is to be accommodated in school, the providers of education are in a sense at the mercy of parents. It is parents who determine the number of births and consequently the number of children who must be catered for by school provision. True, the educational policy makers and planners may have a little discretion in defining what "school-age" means in any particular society; but they have virtually no influence over changes in the size of the population falling within any category they prescribe.

Many of the inputs to the education system, such as buildings and teachers, are directly related through such norms as laid-down pupil-teacher ratios to the number of children. Although they cannot be quickly brought into existence, buildings and trained teachers have a life in the education system which exceeds the duration of individual pupils' schooling. To a great extent, therefore, the work of the educational planner is dominated by his concern with the problem of phasing, and in particular with attempting to maintain dynamic balance between independently determined population change and determinable resource provision. His ideal will be to ensure, as far as possible, that at no time and in no place will there be either insufficiency or excess of provision, as defined by standards and norms providing in the society in question. Such considerations will have a dominant place in educational planing, in any kind of system, whether it be a system oriented to satisfaying 'demands' for education expressed by the population itself, or one geared to fulfilling 'needs' of the society and economy as identified by social planners.

21

Population projections thus provide an essential foundation on which the work of the educational planner rests. They help to define the future goals of the education system in quantitative terms for successive periods of time. They thus establish rather specifically the required evolutionary trend of educational provision and, because such trends are often irregular - implying that short-term requirements may diverge from those in the longer term - they highlignt the challenge of optimisation over time.

Projections of the school age population are necessary in educational planning as a basis for projecting entrants to the school system, as well as for projecting the enrolment ratios corresponding to a given development of enrolment. It is very important to try out alternative population projections as future population development is always uncertain and as it may have strong implications for the projections for the educational system. The population projections are particularly uncertain for yet unborn cohorts (which will suppiy new entrants six and more years ahead). However, population projections for even shorter periods are subject to uncertainty, in particular because of migration. This applies particularly to projections for different regions within a country. We shall return to the problem of making population projections by single years when discussing the use of Sprague Multipliers in Part II of this document. We shall, in Section 1.2.4 also illustrate the implications of different rates of population growth on the future development of the population of school age.

EXERCISE II I

On the basis of the growth rates given in the first column of Table I.I of : this document, use formula (2) to calculate the number of years it would take : for the populations of the countries listed in the table to double if these : growth rates were to remain constant in the future. :

SECTION 2 : POPUIATION FACTORS IN EDUCATIONAL PLANNING

1.2.1 Introduction

The development of enrolment in the educational system and demographic factors are inter-related in many ways. After having underlined in Section 1.2.2 the importance of accurate population statistics for educational planning, Section 1.2.3 gives some examples of this inter-action. Section 1.2.4 illustrates the effects on education requirements of different rates of growth of the population of admission age to primary schools in selected countries and major regions of the world. Apart from causing high population growth, the high levels of fertility and declining mortality common to most developing countries imply that a comparatively large share of these countries1 populations belongs to the school age-groups. The effect of this factor on the "burden" of the educational system on the population of working age is illustrated in Section 1.2.5. This is followed in Section 1.2.6 by a discussion of the relationship between the geographical distribution of the population and the location of schools, and in Section 1.2.7 by a discussion of the distribution of the population by age and sex.

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In Section 1.2.8 our attention turns from the effects of population on education to the inverse relationship, viz., the impact of education on population. In that section we shall discuss aspects related to literacy and educational attainment while Section 1.2.9 briefly lists some other impacts of education on fertility, mortality and migration.

Apart from the links between population and education discussed in this Section, other interrelationships are dealt with in later sections of this document. For example, an important feature in many developing countries is that late entry to the school system and extensive repetition lead to a very wide age-range in each grade. In addition to the purely pedagogical problems that wide age-span within a class might present to the teacher, this phenomenon faces the educational statisticians and planners with special analytical problems. As we shall see later, this creates problems when projecting new entrants in a school system where there are many late entrants and in a situation where the proportion of entrants who are over-aged is being gradually reduced. Furthermore, in Part II of this paper, we shall discuss the use of enrolment ratios as measures of school participation in countries where the enrolment in a particular educational grade or level includes a large number of pupils outside the age-range which, according to national regulations, should be enrolled in this grade or level.

1.2.2 Quality of Demographic Data

The efficient administration of an educational system depends to a considerable extent on the availability of appropriate statistics such as those which have been discussed in Section 1. In Kenya as in most developing countries, certain key data are not fully available But almost as important as the question of availability is that of quality. Amongst the characteristics of high-quality statistics are completeness of reporting on the phenomenon being described; clear definition of categories which must be collectively comphehensive, but at the same time individually mutually exclusive; computational accuracy; consistency between tabular presentation; clear presentation of the results, with adequate explanation of the assumptions and procedures used. Several factors may tend to work against the availability of high-quality statistics.

One such factor may be that only limited financial provision may be made for statistical work in the public sector. Secondly, there is often an acute shortage of qualified statisticians at all levels. Despite these two factors there is frequently a rapidly growing demand for statistical information for planning and other purposes. This inevitably causes statistitians to compromise from time to time on quality in order to facilitate speedy analysis. Further compounding the problems of quality may be poor communications and the low educational level of some of those from whom the information must initially be obtained. For all these reaons, progress in quality improvement may often be slow. Thus, the emphasis must be on statistical material that is simple and good, rather than on more complicated (however seemingly desirable) information.

23

Many developing countries will probably not be able to match, in a short space of time, the costly and complex data-gathering and analysis systems which exist in developed countries. Regular censuses and sample surveys are the essential tools for a satisfactory data framework. Bur these can only be developed slowly with the gradual (and costly) building of the necessary administrative machinery and personnel - and indeed changed attitudes of the general public towards the provision of data. At an early stage of this process, efficient systems of birth, death, marriage and divorce registration shouia ideally be implemented.

The educational planner, however, is obliged to work with the data at his disposal, whilst simultaneously developing better information for the future. Given that data are often of a questionaole quality, the statistician and planner must accept and make explicit allowance for margins of error in estimations of present circumstances and projections of the future. He or she must be aware of the methods employed in the collection of statistics, and must have a thorougn understanding of the techniques used in their analysis. With these caveats in mind, we now turn to illustrating with practical examp±es the importance of reliable demographic data for analyzing various links between population and education.

1.2.3 Some Examples of Interaction between Population and Education (1)

An educational planner or statistician may be asked to answer one or more of the following types of questions about effects of alternative future growth patterns of the population;

a) If a given target for future enrolment ratios is to be attained, how much must enrolment increase under alternative assumptions about future population growth? How much must enrolment increase to keep enrolment ratios constant." What is the required increase in educational costs in order to keep enrolment ratios constant?

b) Given that a fixed proportion of the 7-year old children are going to enter school, and that the transition rates of the school system are known, how much will future enrolment be affected by alternative population trends? How much will educational costs be affected? How much will teacher needs be influenced? The effects on future enrolment can be assessed using the models presented in Part II of this paper.

(1) For a further discussion of this aspect, see for example G. Jones: Population Growth and Educational Planning in Developing Nations, John Wiley and Sons, New York 1975.

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c) Suppose that the development of total enrolment is restricted, e.g. due to government plans for the use of resources in education. What will be the implications for the development of enrolment ratios, of alternative patterns of population growth?

d) What will be the future "burden" of the educational system on the rest of society, expressed by the ratio between the number of pupils and the size ot the labour force ("dependency ratio") Such measures can be computed if separate projections for labour force participation rates are available.

e) What are the consequences of the demographic development for the requirements for teacher training? In particular, what is the development over time of the requirements for new teachers, if the school-age population fluctuates over time, due to "baby booms" and intervening periods of low fertility? Such problems have mainly arisen in developed countries up till now.

f) To what extent will rapid population growth imply lower quality of education (larger classes, lower teacher/pupil ratios, less teaching material per pupil,etc)? To what extent will such factors influence drop-out rates, absenteeism and various measures of school achievement? The answers to such questions depend on the particular circumstances in each country, e.g. whether a scarcity of resources for education is met by reducing the quantity and/or quality of education provided.

We shall not show here in detail how answers can be obtained to all these types of questions. In most cases, the approach is rather self-evident, using alternative population projections in combination with the enrolment projections. However, in the following two sections we shall illustrate some aspects of questions (a) and (b) above by some data.

1.2.4. Implications of Alternative Rates of Growth in the Population

Tne distrioution of the population according to age and sex permits the measurement of the relative size of the school age population. This is a basic statistic in any educational planning process.

Tne actually enrolled population depends on a number of (interdependent) factors. Clearly the ultimate constraint is the population of school age. In many developed countries this constraint is operative as primary level enrolment approaches 100% of the relevant age group. In seme developing nations a much lower percentage may attend primary school. Within this constraint an influence on the enrolled population is the demand for education as expressed in the first instance by pupils and their parents. The extent to which this "social" demand is met may sometimes be measured by the proportion of indiviaual demands for enrolment which can be matched by the supply of school places. This can never be a wholly satisfactory measure of social demand. Expressed demand will, invevitably, depend to seme degree on the known supply of places. Further, social demand is expressed by the public authorities, responding to their perceptions of the demand of society.

25

Tne demand for education may be seen as both a "derived" demand and a direct demand. It is a derived demand in that it stems from a higher level demand for those things which education itself provides, such as higher incomes and social mobility. It is a direct demand insofar as education is wanted for its own sake. Governments have difficult choices to make concerning how far they wish, and are able within resource constraints, to satisfy these different elements. They will ultimately choose according to the relative priorities they attach to their major political objectives: for example immediate satisfaction of expressed popular desires, of following their own conception of the just society. Frequently these objectives conflict. For example, a greater degree of equality of educational opportunity between geographical areas, social classes or the sexes may be costly to achieve and might involve delaying the attainment of other social and economic objectives.

Tne high rates of growth of the school-age population in most developing countries are caused by rapidly declining child mortality and continued high birth rates. To illustrate the implications of this factor for the educational system, we shall show below (for selected countries and regions) United Nations projections for the increase in total population between the years 1981 and 2000. The figures are given in Table 1.2 and refer to three alternative projections prepared by the UN in 1980: the mejjjjum, highland low variants". Distinctions among these variants "aïe mostly due to the differences in assumed future fertility rates; however, different assumptions are also adopted on future mortality and migration rates when such differentiations seem appropriate. In general, the medium variant represents future demographic trends which seem more likely to occur in view of observed past demographic trends, expected attitudes towards population issues, ongoing government policies and prevailing public attitudes towards population issues. On the other hand, the high and low variants respectively indicate the plausible, but not exhaustive, range of future deviations from the medium variant projections, since future fertility, mortality and migration rates could take alternative courses under various conditions. As usual in United Nations projections, no catastrophes such as wars, famine and epidemics which would inevitably affect demographic trends are assumed in formulating those future assumptions. (1)

Tne figures shown in Table 1.2 illustrate well the implications of the existing differences in fertility, mortality and migration between different countries and regions. For example, while according to the medium variant the population would increase by 76% during this 19-year period in Africa, the increase in Europe would be of only 5%. We also note the considerable differences between key countries in Eastern Africa as well as between the different population variants. Obviously, these differences will have considerable implications for the resources required for the education sector in the countries concerned.

1.2.5 The Burden Imposed bv the School Population

Tne dependency lâtifi and the ratio of the school population to the economically active population are two indicators of the "burden" imposed on society by the education system.

(1) World Population Prospects as assessed in 1980

ST/ESA/SER.A/78, United Nations, New York, 1981.

26

Table 1.2 Projected Percentage Change Between 1981 and 2000

in the PopttLatioon, by Three Population Variant?. Both Sexes.

: : Low Variant : Medium Variant : High Variant :

* Kenya 82 ÏÏ7 124 Mozambique. 58 74 77 Uganda 70 86 91 Zimbabwe 64 92 100 Eastern Africa 57 82 88 Africa 56 76 82 Europe 3 5 8

£Qlir££.: Demographic Indicators of Countries. Estimates and Projections as asseaspd in 1980. ST/ESA/SER.A/82, United Nations, New York, 1982.

Tne dependency ratio may be defined in several ways. One commonly used definition is to relate the populations under 15 and above 64 years, i.e.:

(Population aged under 15) + (population aged over 64) (10) Dependency ratio = - - - x 100

Population aged 15-64

We may also calculate separate dependency ratios for the child population (e.g. the population aged below 15 years), and for the aged population (e.g. the population aged 65 years and above). The former ratio is, of course, the more relevant one for educational planners. As an example, we mention that in 1980 the ratio between the population under 15 years and that aged 15-64 years was 1.07 for Kenya. In other words, in 1979, Kenya had 1070 children aged less than 15 years per 1,000 persons of working age. This compared to a figure of 345 for Europe for the same year in 1980.

Tne economically active and inactive population are not easy to measure satisfactorily. Not all countries adopt the United Nations proposed broad definition which would describe the active population as all those of either sex who make their labour available for the production of goods and services.

Tne activity rate may be defined as follows:

active population (11) Activity rate = - - x 100

total population

Activity rates may be calculated on an age-specific basis and separately for males and females. There is room for vigorous debate on the correct age to use, on what constitutes "economic activity" and on the definition of unemployed. Moreover, allowances have to be made for differences in economic structure between countries.

27

One measure of the "burden" on the population of working age of providing education to the population of school-age children is obtained by calculanting the rate between these two populations. Actually in many countries this would only be a measure of the potential burden since not all their school-age children are in fact enrolled in school. A measure of the actual burden is provided by the ratio betweeen the actual enrolment and the population of working age. Table 1.3 shows estimates of these two ratios for 1980 for selected countries and regions. The third column shows the age-specific enrolment ratio (this concept is explained in Part II) for the age-group 6-11 years.

Table 1.3 Ratios between the Population of School and Working Age, and Age-Specific Enrolment Ratios for the Age-Group 6-11 Years,

Selected Countries and Regions.

: : Enrolment in : Age-Specific : Countries and i Population 6-11 i Primary Education i Enrolment Ratio t

Regions : Population 15-64 : Population 15-64 : (Age-Group 6-11) : : (%)

0.25 0.50 0.23 0.38 0.35 0.45

63 86 48 77 69

100

(1) (2) (3)

Africa ('80) 0.32 Kenya ('81) 0.40 Mozambique ('81) 0.31 Tanzania ('80) 0.33 Zambia ('81) 0.34 Zimbabwe ('82) 0.35 Developed Countries ('80) 0.15 0.16 93

Source : UN Population Divison for population data and Unesco Office of Statistics for enrolment data.

In order to have comparable figures this ratio has been used for all countries and regions included in the table.

In examining the first column of Table 1.3 we note first of all the considerarue difference between developing and developed countries with regard to the relative size of their school-age populations. Measured in this way, the burden of the population of working age in Africa of enrolling all children of primary school age (here the age-group 6-11 years) was, in 1980, double that of the developed countries. This is purely an effect of the young age-structure of the developing countries* populations.

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The second column of Table 1.3 shows, the actual burden on the population of working age of providing primary education. We note that while for each 100 persons aged 15-64 there were about 16 primary school pupils in the developed countries, the corresponding figure for Africa was 25. Thus, in spite of Africa's lower enrolment ratio - see the third column of the table - the burden on the African working population, measured in this ways, was higher than in the developed countries. The reason once again is the developing countries' "young" age-structure. We note the extremely high "burden" for Kenya, explained by this country's very young age-structure and its comparatively high level of primary school enrolment.

1.2.6 The Geographical Distribution of the Population

The geographical distribution of the population is obviously of vital importance to the educational planner. The population density of an area is an initial, crude indicator of the distribution of the population throughout the nation. It is defined as:

Mid-year population residing in a given area (12)

Surface of this area

Kenya has an area of 582,646 square kilometers. In 1980 the population was estimated at 16,667,015 which gives a population density of 29 inhabitants per square kilometer. This is somewhat higher than the UN estimates of the average density for Africa in that year (15.6). It is also higher than the population density of Zambia (8), Tanzania (19), but lower than that of Uganda (56).

However, average measures of population density of the above type, covering the whole nation, are too crude to be of much use for planners as they mask the fact that some areas are much more densely populated than others. Table 1.4 illustrates this aspect as regards the differences in population density between Provinces in Kenya. The table shows that the density ranges from 3 persons per square km in North Eastern Province to 1311 in Nairobi. And within Provinces there are often considerable differences in population density between districts. For example, in Rift Valley Province, the population density of Kerich was 161 in 1979 as compared to 4 persons per square km in the District of Samburu.

However, even densities by Province or District are measures too crude for educational planners. To plan the location of new schools one needs ideally to know population densities and probable catchment areas of the new schools. In the many densely populated areas, there may be problems of finding school

29

sites, but the educational planner normally has no fear that schools may not reach the optimum size for lack of pupils. In rural areas, with many small and relatively isolated communities, the viability of planned new schools may be an important issue. (1)

One may use as a guiding principle in school location the objective that, where possiDle, pupils should be able to reach the school on foot. The maximum distance a child may be expected to walK depends, of course,on factors such as age, whether or not there is a road, the nature of the walk (e.g. flat or hilly), climate, etc. Depending on these factors, the time the child will spend reaching school will vary. In fact, it is not generally the distance children have to travel, but the time it takes to make the journey that should be the guiding principle for determining the catchment area of schools.

(1) Those readers with a particular interest in questions of population distribution in relation to school location are advised to consult the recent series of studies on this subject by th International Institute for Educational Planning (HEP), Paris. For example, see J. Hallak, Planning the Location of Schools, HEP, Unesco, Paris 1977. The HEP has also prepared a series of very useful studies on regional disparities in the provision of education, see for example : Gabriel Carron and Ta Ngoc Cna+u: Reduction of Regional Disparities : The Role of Educational Planning, the Unesco Press, Paris, 1981. The authors of this study have also edited two comprehensive studies on the same theme: Regional Disparities in Educational Development : A Controversial Issue, Unesco -HEP, Paris 1980, and Regional Disparities in Educational Development; Diagnosis and Policies for Reduction. Unesco - HEP, Paris, 1980.

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Table 1.4 : Population Density by Region. Kenya 1980

Province : Population : Area : Density of : : ('000 km2) : Population/km2

Nairobi Central Coast Eastern North Eastern Nyanza Rift Valley Western

Total

869,919 2,511,452 1,439,530 2,916,478 402,925

3,057.581 3,482,672 1,959,558

16,667,015

684 13,176 83,603 159,891 126,902 16,162 173,868 8,360

582,646

1,311 191 17 18 3

189 20 234

29

Source : Population Proiections for Kenya 1980-2000, Central Bureau ot Statistics, Nairobi, March, 1983 and Statistical Abstracts 1982, Central Bureau of Statistics.

Table 1.5 illustrates the interaction between some of the variables which must be taken into account when deciding the location of schools. For the purpose of this illustration, it has been assumed that the maximum distance a child should be expected to walk is 4 km. This gives a maximum catchment area of 50.27 km2 (1). Using this information, one can draw up Table 1.5 which shows the number of children likely to be seeking school places in different circumstances with regard to population density and enrolment ratios. For example, with a population density of 50 persons per km2, we see that the

(1) The formuia for calculating the area of a circle is:

area ot circle = Tfr where r = radius of circle ÎT = 3.142

In our case we have defined the radius as 4 km, the maximum distance we expect the child to walk to school. So the area of the (circular) catchment area would be TT x 16 km2 = 50.27 km2.

31

population of the catchment area of the school will be 2,514 persons. Assuming that the age-group 6-12 years corresponds to the population of primary school age, the number of children of primary school age in this area is 525 (see column 3). Tne remaining part of the table shows the number of pupils enrolled for various levels of the enrolment ratio. For example, for an enrolment ratio of 30%, this same area will have 158 primary school pupils. Depending upon the size of the class, whether or not the school should be run on one or more shifts, etc., one may determine the need for teachers and for classrooms.

This table and its utilisation will be explained further at the seminar.

Table 1.5 : Viable Schools in Relation to Population Density and Enrolment Ratios in Primary Education

: 1 : 2 : 3 : 4 :

: : Popula- : Of which : : : : tion in : 6-12 : > : Popula- :4 km radius : Years : Birolments, given Different : : tion per : : : Birolœnt Ratios (ft of Col.3) : : sq. km. : area : : : : : «Col.l : : J : : x 50.27) : : 20% : 30* : 40% : 50% : 60% : 70% : 80% : 90% : 100% : j s : s :

25 50 75

100 125 150 175 200 250 500

1,000

1,257 2,514 3,770 5,027 6,284 7,540 8,797

10,054 12,568 25,135 50,270

263 525 788

1,051 1,313 1,576 1,839 2,101 2,627 5,253

10,506

53 105 158 210 263 315 368 420 525

1,051 2,101

79 158 236 315 394 473 552 630 788

1,576 3,152

105 210 315 420 525 630 736 840

1,051 2,101 4,202

132 262 394 523 657 788 920

1,051 1,314 2,627 5,253

158 314 473 631 788 946

1,103 1,261 1,576 3,152 6,304

184 368 552 736 919

1,103 1,287 1,471 1,839 3,677 7,354

210 420 630 841

1,050 1,261 1,471 1,681 2,102 4,204 8,405

237 473 709 946

1,182 1,418 1,655 1,891 2,164 4,728 9,455

263 525 788

1,051 1,313 1,576 1,839 2,101 2,627 5,253

10,506

1.2.7 The distribution of the Population bv Sex and Aae

A study of the distribution of the population by age and sex is very important both to the demographer and to the educational planner. From the point of view of demographic analysis it summarises the history of a nation's population and also governs to a large extent its future growth. For the educational planner it makes possible calculation of the size of the school-age groups in the population (and therefore of enrolment ratios), and indicates the degree of strain on the working population involved in providing schooling for the young.

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The division of population by age and sex may be graphically represented by a widely used descriptive device known as the "population pyramid". Illustrations of population pyramids are shown in Figures la and lb for France and Kenya. The pyramid for France has been included in order to illustrate the difference in age-structure between a developed and a developing country. The method used in constructing these pyramids will be explained at the seminar. Both pyramids refer to 1981.

Figure la: Population Pyramid for France. 1981.

5QUCSÊ.: Donnera ffQCialep. Institut National de la Statistique et des Etudes Economiques, Paris, 1981, p. 11.

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The way in which the pyramid reveals the past history of a population is well illustrated by the case of France in Figure la. It shows, for example, the effects of death in World Wars I and II on the age-distribution of the male population, and the effects of the deficits of births during the two wars on the age-distribution of both males and females.

However, the most important piece of information revealed by France's pyramia is the gradient (angle of steepness) of the sides of the pyramid. In this case the gradient is steep suggesting that the'annual increment of births has been small or in some years even negative over a long period. This rather steep-sided pyramid up to the age of about 70 and rapidly tapering only after that age can be taken as broadly representative of the general shape of population pyramids in developed countries. These contrast with typical pyramids for the developing countries with relatively high rates of fertility and mortality, resulting in pyramids which are broad at the bottom and narrow at the top. In addition, the gradient of the pyramid for developing countries tends to be shallower at the base, and steeper at the top, than for developed countries. This shape results from annual population growth rates over quite a long period of 2-3%, whereas the corresponding figure in Europe is, and has been, much lower.

34

Figure lb: Population Pyramid for Kenyaf 1981

r\*tfS

1

1

1

100

to

is

to

H M kS 10

SS

so

«

10

3S

30

ts

IS

10

5

0

^

Tfri tfS

—H ^

-

-J !

Source: Based on Table 1.6

35

It was also claimed above that the age and sex structure of the population governs the future growth of population as a whole. This is true in the sense that birth rates ultimately depend on the proportion of women who are or will be of chila-bearing age. One can see at a glance from Figures la and lb that the proportion of the female population past child-bearing age is far higher in France than in Kenya. Moreover, within the group of women of child-bearing age of say, 15-49, a higher proportion is at the more fertile ages (15-29) in Kenya (about 61%) than in France (about 48.7%), and this feature will persist.

Table 1.6 shows the distrioution by age and sex of the Kenyan population in 1981. Column (7) shows the sex ratio, i.e. the number of boys per 100 girls in eacn age-group. In most countries this ratio exceeds 100 for the younger ages (i.e. the number of boys exceeds the number of girls) and then declines continually through the ages. This reflects the fact that at birth the number of boys normally exceeds the number of girls. In most (but not all) countries, this is counterbalanced by a higher mortality for men than for women, implying higher life expectancies for females than for males and a predominance of women in the higher age-groups.

36

Table 1.6: Total Population of Kenya by Age and Sex. 1981

Both sexes : Males : Females

Age-Groups

0-4 5-9

10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-34 55-59 60-t>4 65-69 70+

Total

: 1 : (

3 2 2 1 1 1

17

Number in 000)

725.5 833.3 197.2 752.9 363.8 075.4 894.3 719.6 593.4 501.2 419.3 343.3 271.3 202.6 261.7

154.8

%

21.7 16.5 12.8 10.2 8.0 6.3 5.2 4.2 3.5 2.y 2.4 2.0 1.6 1.2 l.b

100.0

: Number : (in 000)

1 867.7 1 415.3 1 092.4

871.2 676.3 530.7 440.1 353.6 291.0 244.4 202.6 163.9 127.5

93.3 114.2

8 484.2

%

10.9 8.2 6.4 5.1 4.0 3.1 2.6 2.1 1.7 1.4 1.1 1.0 0.7 0.5 0.6

49.5

: Number : (in 000)

1 857.8 1 418.0 1 104.8

881.7 687.5 544.7 454.2 366.0 302.4 256.8 216.7 179.4 143.8 109.3 147.5

8 670.6

% : • •

10.8 8.3 6.4 5.1 4.0 3.2 2.6 2.1 1.8 1.5 1.3 1.0 0.9 0.7 0.9

50.5

Sex rati

101 100 99 99 98 97 97 97 96 95 93 91 89 85 77

98

Source : United Nations Population Division. 1980 Assessment (medium variant).

I.2.b Literacy Rates and Educational Attainment

Tne educational attainment of the population as a whole changes only slowly, as people generally have their schooling at the start of their lives and do not significantly add to it thereafter through any formal courses. Although the idea of continuing education is gaining ground in a number of developing countries, it still remains true that in most countries the vast majority of people do not return to the classroom once they have left it in their youth. For this reason one should be cautious about assigning to education any dramatically large impact in the short term on a country's economic and social life. These effects are more gradual and are felt over decades rather than in a few years. It may conversely be true that we can expect only limited versatility and responsiveness to change in populations with a restricted educational background.

For statistical purposes, the educational attainment of a person is defined as: "... the highest grade completed and/or the highest level of education attained or completed by the person in the system of regular, special and adult education of his own or some other State". (1) Normally this type of statistic is collected through population censuses.

(1) Confer : "Revised Recommendation concerning the International Standardization of Educational Statistics", Unesco, Paris, 27 November 1978, p. 2.

37

Another very useful type of information on the educational situation of the adult population of a nation is statistics of illiteracy. Such statistics are commonly collected through population censuses, but they may also be obtained by conducting special surveys. In interpreting illiteracy statistics, the reader is reminded that they are usually based on self-enumeration (rather than on literacy tests) and that the borderline between illiteracy and literacy is thus quite hazy. The definition of illiteracy given in the Recommendation quoted above is: "A person is illiterate who cannot with understanding both read a short simple statement on his everyday life".

In the Kenyan context, literacy is simply defined as the ability to read and write in any language. Kenya has devoted and continues to devote a considerable amount of effort to eradicating illiteracy. Adult education is being emphasized, the objective of which is to provide the knowledge, skills and attitudes which adults require to participate meaningfully in social and economic development. The first stage towards achieving this objective is to reduce illiteracy. This task has been assigned to the Department of Adult Education of the Ministry of Culture and Social Services.

The data on levels of literacy in Kenya have been collected through two national sample surveys. The first one was conducted in 1976 and was limited to the rural population aged 15 years and above not enrolled at school full-time. It was based on self-enumeration i.e. by the respondents' own judgement of their literacy ability. A 46% literacy rate was established by this first survey. To further confirm and monitor any changes in literacy levels, a second literacy survey was conducted in 1981/82. To eliminate any possibility of exaggeration on behalf of the respondents, objective tests were administered to those who indicated that they were able to read and write. A respondent was not tested in any language he/she indicated that he/she could not understand. The results revealed that 48% of the rural population aged 12 years and above were able to read. A comparison of the results of self-assessment which was covered in the first part of the questionnaire and the results after administering the objective tests revealed that the amount of exaggeration was minimal. The results of the survey are detailed in Table 1.7.

The procedure used in conducting the 1981/82 literacy survey and the application of objective tests will be explained in further detail during the seminar. It should be noted here that statistics on literacy in Kenya have not been collected through population censuses.

Table 1.7: Percentage Distribution of Population Aged 12 Years or more in Rural Kenya able to read in any Language by Province,

1981/82. Rural Literacy Survey

Province : Both sexes : Males : Females

(%) (%) (%) Coast 45 58 35 Eastern 48 62 39 Central 65 77 57 Rift Valley 41 53 30 Nyanza 39 54 29 Western 48 62 38

Rural Kenya Total 48 61 38

Source: Central Bureau of Statistics, Nairobi, 20% sample survey of rural areas.

38

Figure 2 shows illiteracy rates for major regions in 1985. We note that the average level of illiteracy in Africa exceeds to a considerable extent that of Kenya.

Figure 2: Illiteracy Rates in the Major Regions by Sexf Age 15+, 1985

Figure 2. By Sex and Region, Age 15+f 1985.

Source; Unesco Office of Statistics (as assessed in 1982)

39

Figure 3 shows the trend of illiteracy rates by country or regions between 1970 and the year 2000. We note that the illiteracy level is dropping more rapidly in Kenya than in either Africa or Eastern Africa. The illiteracy level for the entire world is however, going down more gradually.

Figure 3: Percentage Illiterate Aged 15+ in the World, Atrica, Eastern Africa and Kenya. 1970 to 2000

Source; Unesco Office of Statistics, (1982 assessment).

40

Table 1.8: Population Aged 10 Year and Above, by Educational Attainment. Kenya, 1979 Census (%)

Province No

schooling (%)

Primary Secondary

1-4 (%)

5-7 Form 1-4 (%)

Form 5+

Higher Not

: stated : (%)

Nairobi Central Coast Eastern North Easter Nyanza Rift Valley Western

14.6 23.9 53.3 39.3 92.5 34.2 45.4 33.7

12.7 24.5 15.0 25.8 2.4 26.6 22.1 28.3

33.9 35.3 19.7 25.0 2.8 28.2 23.3 26.4

31.5 14.6 9.7 8.8 1.9 10.0 7.7 10.5

<-<-<-<-<-<-<-<-

-0.9 — -1 -0 -0.1 —

-0.5 — 0.5 — > 0.6

Total 1) 37.3 22.9 26. 11.1 -1.0 — > 0.8

Source; 1979 Population Census, Central Bureau of Statistics, Nairobi. 1) Total for all categories do not add up to 100% due to a large number

of people whose ages were not stated in the census and subsequently excluded from the above table.

Table 1.8 shows the educational attainment of the population of Kenya, by region, as revealed by the 1979 population census. For the nation as a whole, 37.3% of the population above 10 years had no formal education, 49.2% had attended primary school only, 12.1% had attended secondary school, etc. The table indicates quite large provincial differences in educational attainment. We note in particular the comparatively high levels of attainment in provinces such as Central, Nyanza, Coast and, especially, Nairobi.

We have so far discussed some impacts of a given population development upon the education system. However, as is well known, education may itself influence population growth and distribution in a number of ways. What is less well-known is exactly in what manner this influence operates. The causal links between education and fertility are not very clear, largely because, although the two variables are often observed to be related, success has so far been limited in isolating the effect of education from that of all the other factors influencing fertility. Such evidence as does exist suggests that the relationship is rather complex and varies considerably between countries and over time. Some authors distinguish between three main sets of effects. (1)

(1) See: D. B. Holsinger and J. D. Kasarda: "Education and Human Fertility: Sociological Perspectives", in R. G. Ridkar (ed.) Population and Development, John Hopkins University Press, Baltimore and London 1976.

Also: S. H. Cochrane: Fertility and Education: What do we really know?. World Bank Staff Occasional Papers, No. 26 , The Johns Hopkins University Press, Baltimore and London 1979.

41

(a) Education influences fertility directly by developing certain attitudes, values and preferences concerning family size and family planning. It increases the exposure to mass media and printed material concerning family planning, in particular as regards the knowledge and skill in using birth control devices.

(b) Education influences fertility indirectly by affecting a wide variety of variables whicn in turn have an influence on fertility. Many of the most important effects of education on fertility come under this heading, for example:

- education normally delays the age of marriage and thereby tends to reduce the total possiDie number of children. Delayed marriages also increase the average distance between generations, and thus tend to slow down population growth;

- education enhances a woman's opportunities and desire for a career outside the home, whicn competes with that of being a mother and housewife;

- education increases the aspiration for upward social mobility. This is shown to be related to a desire for smaller families;

- education reduces the perceived economic utility of children, This factor operates in several ways (1), for example:

(i) while attending school, children cannot work and they may have to pay fees;

(ii) rising education of parents makes them less dependent upon children for economic assistance;

(iii) educated parents have education aspirations for their children, implying higher costs and a desire for a smaller family;

(iv) jobs requiring education are generally located in urban centres where the costs of raising children are high and the economic benefits of cnild labour are lower than for families in rural areas.

- education affects fertility by reducing infant and child mortality (because if mortality is reduced, fewer births are needed to raise a family of a given size).

(c) Finally, education operates jointly with other exogenous variables such as urbanization and industrialization to reduce fertility.

For a government desiring to allocate public resources so as to reduce fertility, it would obviously be desirable to know the importance of each of the above factors, but our knowledge in these areas is still limited. Furthermore, it should be noted that the above-mentioned factors are to seme extent overlapping. It is also important to note that many of the effects listed above refer to the impact of education on the female population.

In short, the emerging consensus frem research in this area is that rising levels of education, especially of women, do tend to be associated with declining fertility. But the relationship between education and fertility is very complex. Education is related to some factors that tend to increase

(1) A theory has been developed with regard to the relationship between the economic value of children and fertility. A survey is given in H. Leibenstein: "An interpretation of the Economic Theory of Fertility Promising Path or Blind Alley?", Journal of Economic Literature, Voi. 12, No 2, June 1974.

42

and seme that tend to decrease natural fertility. Similarly, some results of education tend to increase and others to decrease the demand for children, although the latter usually predominate. The strongest and most consistent effect of education concerns knowledge about, attitudes toward, and the use of contraception. An analysis of the numerous channels through which education affects fertility explains why more education is sometimes associated with higher fertility and sometimes with lower.

Finally, it should be noted that education does not only affect fertility. It also affects the two other vital processes, i.e. migration and mortality. Because education is perceived as the major means of attaining occupational and economic mobility, many families migrate in search of better education for their children. The location of schools may, therefore, have considerable influence on internal migration as parents tend to move to areas where their children have better opportunities. Education affects mortality by improving health and nutrition standards. Here again it is difficult to isolate the effect of education from other variables, for example from the effect of the increased salary normally associated with more education.

1.1.9 Concluding Remarks on Part I

We have now completed our survey of the main demographic data which are commonly used by educational planners. Births, deaths, migration and the distribution of the population by sex and age help to analyse and project the size of the school population. The geographical distribution of population helps particularly in planning the location of schools and more generally in planning the distribution of educational resources in order to achieve the various objectives of social policy. The availability of resources must rest, ultimately, on the economic potential of the country. Wè have also surveyed briefly some possible impacts of education on the growth and distribution of a population. All these factors will be discussed further during the seminar.

43

PART II; ME1H0DS OF ANALYZING AND PROJECTING SCHOOL ENROLMENT

SECTION 1; ENROLMENT RATIOS

II.1.1. Introduction

Enrolment ratios are the most commonly used indicators for assessing a country's coverage of enrolment at a particular level of education, or of a particular age-group. There are several different types of such ratios, and we shall in this section define the main types used and discuss their limitations as measures of educational coverage and progress. We shall further consider briefly what kind of data are needed in order to calculate the different enrolment ratios. Finally, we shall calculate such ratios for Kenya.

An enrolment ratio is defined as the ratio between the number of pupils enrolled at a given age, or at a given level of education, and the size of the population in a given age-group. Hence, enrolment ratios are relative measures of numoers enrolled and the interpretation of such ratios varies with the pupils and the population being considered. For example, enrolment ratios may be calculated by the level of education or without regard to level, they may take into account the age of the pupils or disregard the age. Enrolment ratios may furthermore be calculated separately for boys and girls, for part-time and full-time education, private and public schools, urban and rural education, different ethnic groups, etc. The population data used in the denominator and the enrolment data used in the numerator refer to the same point in time. In practice this may create problems since population estimates may refer, for exampxe, to the middle of the calendar year while the enrolment data may refer to the beginning of the school year.

II.1.2 Definition of Enrolment Ratios

Wë shall limit our discussions to three types of enrolment ratios.(1) These are:

(a) Overall enrolment ratios (b) Level enrolment ratios (c) Age-specific enrolment ratios

For a more detailed discussion of the use of enrolment ratios, see B. FredriKsen: "Employing Enrolment Ratios and Intake Rates for Developing Countries: Problems and Shortcomings", in Population and School Enrolment, CSR-E-9, Unesco Office of Statistics, Paris, 1975, pp. 64-bl

(1)

44

(a) Overall (or Crude, or General) Enrolment Ratios

Tne overall enrolment ratio may be defined as:

t E

(13) Overall enrolment ratio = — x 100 t P

t where E = total enrolment at all levels of education in year t

t P = total population of school age in year t (generally

refers to all three levels of education).

Tnis is the least refined of the various enrolment ratios. It is not adequate for detailed study of enrolment development. Comparisons using this ratio between countries or regions within a country, or over time within countries, have important weaknesses. They give no information on the age of pupils. They do not distinguish the levels at which they are enrolled. They do not indicate the length of the various educational stages in the country concerned, which may or may not total the same number of years as the age span in the denominator. Therefore, the overall enrolment ratio should be used with considerable caution as a measure of educational coverage. As most developing countries now have the data required for calculating the more refined ratios discussed below, the overall enrolment ratio is not often used in practice and we have included it here mainly for the sake of completeness.

(b) Level Enrolment Ratios

Tne level enrolment ratio is perhaps the most commonly used measure of enrolment. It may also be called the level-specific enrolment ratio, and is often referred to as the enrolment ratio for primary, secondary or higher education. We shouia distinguish between :

(i) the gross level enrolment ratio, and

(ii) the net level enrolment ratio.

The gross level enrolment ratio relates total enrolment, regardless of the age of those enrolled, to the population which according to official national regulations should be enrolled at this level. Thus:

t E h

(14) gross level enrolment ratio = x 100 P a

45

t where E = enrolment at school level "h" (primary or secondary

h or higher, as specified) in year "t"

t P = population in that age-group "a" which officially a corresponds to level "h", in year "t".

The net level enrolment ratio on the other hand includes in the numerator (enrolment "E") only those enrolled pupils of the "correct" age. Thus the same age-group is included in both the numerator and denominator. For this reason, the net level enrolment ratio is sometimes termed the age-level specific enrolment ratio.

t E h,a

(15) net level enrolment ratio = x 100 t P a

t where E = enrolment in age-group "a" at level "h", in year "t".

h,a

To calculate this ratio we need data on enrolment by age, a type of statistic whicn is not always available in developing countries. Also, the information on the age of pupils is sometimes not very reliable.

Tabulations showing gross level enrolment ratios for countries with different educational structures often employ the term adjusted enrolment ratio. This means that the age-range of the population used in the denominator of the enrolment ratio for a given level, has been adjusted for each country to the prescribed duration of this level. For example, while the population aged 6-12 wotud be used for a country where the official admission age is six and the duration of primary education is 7 grades, the population aged 7-12 would be used for a country where the official admission age is seven and the duration is six grades. Following this approach, the official age-group for primary education for Kenya is the group 6-12 years, that of junior secondary education 13-16 years, and that of senior secondary education 17-18 years.

Before population data by single years of age became available on an international scale, unadjusted gross level enrolment ratios were used. These were obtained for all countries by dividing the enrolment at a given level by the same population age-group without taking into account the differences between countries with respect to length of schooling and entry age. In the case of Africa, the official age-groups for primary and secondary education vary considerably between countries as shown in Table 2.1.

46

As compared to the use of overall enrolment ratios, gross level enrolment ratios calculated separately for primary, secondary and higher education represent a major improvement for measuring changes in educational coverage either over time for a given country or for international comparison. In cases where schools utilise all their capacity, these ratios can be used as measures of the enrolment capacity at each of the levels of education, compared to the age-group which, according to national regulations, should be enrolled at the same level. In developed countries, where almost all new entrants start school at the normal entry age, and where repetition is very low, there are few under- and over-aged pupils at each level. In this case, the gross level enrolment ratio is close to the net level enrolment ratio which measures the proportion of normal-aged children who are enrolled in school at each level.

In many developing countries, on the other hand, there is considerable difference between the gross and net level enrolment ratios because of late entrants and repeaters. Neither of them gives precise information concerning the educational coverage at a particular level measured relatively to the size of the age-group in the population to which the pupils belong. The net level enrolment ratio gives only a partial picture, since it excludes pupils outside the official age-group, while the gross level enrolment ratio gives an ambiguous measure since its numerator and denominator do not refer to the same ages.

It should be borne in mind when using gross enrolment ratios that it is possible to have such enrolment ratios exceeding 100%. This may be either because some children enter school late (or early, e.g. entrance of five-year-olds in the case of Kenya) or because pupils' progress through school is delayed by repeating. It may also be due to errors in the population and/or enrolment data used. There may, for example, be over-reporting of enrolment. The population data used, particularly for regions or districts, may also be incorrect, due to migration. Furthermore, the enrolment in a given district or region, may not correspond to the population data, due to the fact that some children may live in one district and attend school in another.

Net level enrolment ratios are less frequently used in practice than gross level enrolment ratios. It should be noted that while the latter ratio may (and often does) exceed 100%, the former has 100% as its possible maximum. Very often, however, it will be below 100% in developing countries where a fixed entry age to each school level may not be imposed. This means that consecutive levels of education may overlap in terms of the ages of the pupils, which implies that the net enrolment ratio cannot reach 100% for either level, even if all children of primary and secondary school age were enrolled at school.

If we want to know how many children of a certain age are enrolled in the education system at whatever level, then we must use a different kind of enrolment ratio, the age-specific enrolment ratio.

47

Table 2.1 National Education Structures In Africa (latest information available)

: Country

Algeria Angola Benin Botswana Burundi

Cape Verde Central African Republic Chad Comoros Congo

Djibouti Egypt Equatorial Guinea Ethiopia Gabon

Gambia Ghana Guinea Guinea-Bissau Ivory Coast

Kenya 1) Lesotho Liberia Libyan Madagascar

Malawi Mali Mauritania Mauritius Morocco

Mozambique Namibia Niger Nigeria Rwanda 2)

Sao Tome and Principe Senegal Seychelles Sierra Leone Somalia

Sudan Swaziland Togo Tunisia Uganda

Rep. Cameroon On. Rep. Tanzania Upper Volta Zaire Zambia

Zimbaowe

1st Level

Entrance Age

6 6 5 6 6

6 : 6

6 6 6

7 6 6 7 6

8 6 7 6 6

6 6 6 6 6,7

6 6 6 5 7

6

"7" 6

7

7 6 6 5 6

7 6 6 6 6

6 7 7 6 7

7

Duration (Years)

6 4 6 7 6

4 6 6 6 6

6 6 6,8 6 6

6 6 6 6 6

7 7 6 6 6

8 6 7 6 5

4

*6* 6 8

4 6 6 7 6

6 7 6 6,8 7

6,7 7 6 6 7

7

2nd Level

Entrance Age

12 10 11 13 12

10 12 12 12 12

13 12 12 13 12

14 12 13 12 12

13 13 12 12 12,13

14 12 13 11 12

10

13* 12 15

11 12 12 12 12

13 13 12 12 13

12,13 14 13 12 14

14

(General) :

Duration : (Years) :

4 + 3 4 + 2 4 + 3 3 + 2 4 + 3

2 + 3 4 + 3 4 + 3 4 + 3 4 + 3

4 + 3 3 + 3 4 + 2 2 + 4 4 + 3

4 + 2 4 + 3 3 + 3 3 + 2 4 + 3

4 + 2 3 + 2 3 + 3 3 + 3 4 + 3

2 + 2 3 + 3 3 + 3 4 + 3 4 + 3

2 + 5

4 +*3 5 + 2 3 + 3

2 + 5 4 + 3 2 + 5 5 + 2 4

3 + 3 3 + 3 4 + 3 3 + 4 4 + 2

4+3 ; 5+2 4 + 2 4 + 3 2 + 4 3 + 2

6

1) Kenya's education structure will be changed from 1985 to 8 years duration in first level and 4 years in second level.

2) This system, introduced in 1979, is being implemented gradually.

Source: "Development of Education in Africa: A Statistical Review", Unesco Office of Statistics, Paris, 1982, p. 23.

48

(c) Age-Specific Enrolment Ratios

An age-specific enrolment ratio relates the enrolment of a given age or age-group in a given year to the population of that age in that year.

t E a

(16) Age-specific enrolment ratio = x 100 t P a

Note that in this formula t t t t E = E + E + E where P, S and H refer to primary, a P,a Sra H,a secondary and higher levels respectively.

Tne age-specific enrolment ratios may be calculated by single years of age or by age-groups (in which case the subscript denotes an age-group). It shouxa however be noted that only age-specific enrolment ratios calculated by single years of age are not affected by changes in the age-structure of the population. Thus, a shift towards a more youthful population can increase an age-specific enrolment ratio calculated for an age-groupf by placing more persons in the typical enrolment ages, even if all the enrolment ratios by singie years of age remain unchanged. Likewise, a decline in the birth-rate leading to a shift toward an "older" population might lead to a decrease in an age—specific enrolment ratio calculated for an age—group, by giving higher relative weights to the ages having a relatively low school participation. This may happen even if all the enrolment ratios by single years of age were to increase. Sucn shift in the age-distribution took place, for example, in many European countries after the Second World War as a consequence of the postwar "baby boom".

II.1.3 Enrolment Ratios for Kenya

Table 2.2 shows the development of the gross enrolment ratios for primary and secondary education for Kenya. For primary education we note the very large enrolment increase after the elimination of school fees for the first four years of primary education beginning 1974. Between 1970 and 1975, there was an impressive increase of 40.5 percentage points in the enrolment ratio. This meant the number of primary school pupils more than doubled during this five-year period, from 1,427,589 in 1970 to 2,881,155 in 1975. The largest increase took place between 1973 and 1974 when enrolment at the first level rose by 49% (i.e. by 889,861 pupils), and Grade 1 enrolment by 577,474 pupils (152%). In 1975 enrolment in Grade 1 dropped below its 1974 level when the number of new entrants already exceeded the population aged 6 years. One objective of the tremendous enrolment increase in Grade 1 in 1974 was to catch up with the back-log of non-enrolled children who were already older than 6 years.

49

Table 2.2 : Gross Enrolment Ratios for Primary and Secondary Education, by Sex, 1960-1982. Kenya.

: Year

: 1960 : 1970 : 1975 : 1976 : 1977 : 1978 : 1979 : 1980 : 1981

: Primary education :

: MF

51.8 64.4 104.9 101.0 99.4 95.8 113.2 114.8 111.0

H

70.8 75.7 114.1 108.9 106.4 102.3 119.9 121.2 116.3

F :

33.0 53.2 95.7 93.1 92.4 89.3 106.4 108.6 105.6

Secondary Forms • - • -

MF

• • • 12.7 18.0 21.3 23.3 25.2 25.5 26.3 28.3

M

... 17.9 23.1 26.9 28.7 30.2 30.2 31.1 34.1

I-IV

F

• • • 7.6 13.1 15.9 18.0 20.3 20.9 21.6 22.5

: Secondary

: MF

• • • 1.1 1.7 1.8 1.8 2.0 2.6 3.1 3.4

M

• • • 1.7 2.6 2.7 2.7 2.9 3.6 4.4 4.2

Forms V-VI :

F :

• • • • 0.5 : 0.9 : 1.0 : 1.0 : 1.1 : 1.6 : 1.9 : 2.7 :

Sources : Enrolment data; Statistics supplied by the Statistics Unit or the Ministry of Education, Science and Technology.

Population Data; UN Population Estimates and Projections as assessed in 1980 (Medium Variant)

Table 2.2 also shows that although there has been a considerable decrease in the disparity between first level enrolment of boys and girls between 1960 and 1978, proportionally more boys than girls are presently enrolled. Furthermore, there are still considerable regional disparities in the provision of first level education, as can be seen in Figure 4.

Table 2.2 also shows the development of the gross enrolment ratios for the lower stage (Forms I-IV) and upper stage (Forms V-VI) of secondary education. The enrolment ratios for both stages showed a very modest increase since 1970. As illustrated by Figure 5a, the enrolment ratio for secondary education in Kenya is higher than that of most other African countries. The development of secondary education will be further discussed in Section II.4.8.

Tne provision of higner education is relatively low in Kenya compared to say Libya, Congo or Mauritius. It is however one of the highest (after Zambia) among the Eastern African countries, (see Fig. 5b).

50

Figure 4 : Proportion of children aged 6-12 enrolled by province Kenya, 1980

(cffrr"-<AL)

U Population Age 6-12

H Enrolment in Primary Education

( ) Gross Enrolment Ratio in Primary Education

Source. Derived from figures from the Ministry of Education, Science and Technology.

51

Figure 5a: Gross Enrolment Ratios for Second Level Education, 1970 and 1980

(Countries are ranked according to the 1980 ratio).

SHI , Nigeria Libyan A.J.

Congo

Mauritius

Egypt

Gabon

Ghana

Swaziland

Togo

Algeria

Kenya

Tunisia

Morocco

Cape Verde

Zaire

Botswana

Liberia

Lesotho

Cameroon

Equatorial

Guinea

Ivory Coast

Zambia

Sudan

Guinea

:

a

Madagascar

Benin

Gambia

Sierra Leone

Central African Rep.

Senegal

Ethiopia

Guinea-

Bissau

Mali

Zimbabwe

Mozambique

Somalia

Uganda

Mauritania

Malawi

Niger

Chad

Tanzania

Burundi

Upper Volta

Rwanda

J

20 I

40 60. I I

B0 100 % 20 40 60 80 100 %

• I ' •

SQurse.: Unesco Office of Statistics

53

1 EXERCISE III 1

: Use the statistics below on enrolment and population by single : : years of age for Kenya for 1979 to calculate:

i (a)

i (b)

i (c)

: above

the net and gross enrolment ratios for primary education; :

the net and gross enrolment ratios for secondary education; :

the age-specific enrolment 6-12 and 13-18 years.

: Age

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20

TOTAL

Primary Education

360,409 522,082 487,938 436,475 422,148 383,707 378,754 328,712 378,021

3,698,246

ratios for the two age-groups :

> Secondary General Education

11,618 1) 32,679 58,200 81,777 75,495 57,173 37,568 18,786 11,093

: Population :

570,000 i 540,800 : 513,100 : 487,500 : 463,800 : 441,100 : 420,400 : 401,500 : 384,100 : 368,000 : 353,300 : 338,300 : 321,800 : 304,700 : 288,800 : 273,700 :

5,932,100 :

384,389 12,403,700 :

1) 13 years and under Sources; Enrolment data: Education Statistics Unit of the Ministry of Education,

Science and Technology. Population data: United Nations Population Division (1980 Assessment).

54

SECTION 2 : Education Flow Models

II.2.1 Introduction

There is a variety of mathematical models which have been used throughout the world in educational planning. This paper is restricted to a discussion of the two educational flow models which are most commonly used for:

(i) analyzing wastage in education; (ii) projecting enrolment by grade; (iii) analyzing the effects of changes in educational policy as

regards new intake, repetition and drop-out on wastage, enrolment by grade, teacher requirements, etc.:

These types of analyses form the basis for any planned use of resources in the educational sector.

Educational flow models quantify the flow of pupils into, through and out of the educational system The fundamental objective of such models is to provide an explicit, logical and integrated framework in which to fit available data describing the flow of pupils through the system. Having developed such a framework, it may be used to project - that is, to demonstrate the implications for enrolment at future dates of explicit assumptions about the continuation of past and current trends. The models may also be used to reconstruct the flows of a cohort through a cycle of education. Flow analysis of this type is used to estimate the extent of wastage in education due to repetition and drop-out (see Section 3 below).

The major purpose of this section is to introduce and explain the techniques of the two basic flow models most commonly used in developed as well as in developing countries. The following two sections will illustrate how to apply these two models for analyzing wastage in education and for projecting school enrolment by grade.

The first model we shall discuss is the Grade Transition Model. This is the most commonly used model for enrolment projections. In order to employ this model we need data on enrolment by grade for at least two successive years, as well as data on repeaters for the latter of these years. If we want to study changes over time in the transition rates (i.e. the promotion, repetition and drop-out rates, see below for definition), we need, of course, data for more years (1). We shall in Section II.2.6 below illustrate how, on the basis of this type of data, we may calculate promotion, repetition and drop-out rates by grade.

(1) For a more complete presentation of this as well as of other flow models, see T. Thonstad, in co-operation with the Divison of Statistics on Education,Unesco Office of Statistics: Analyzing and Projecting School Enrolment in developing Countries: A Manual of Methodology, Statistical Reports and Studies No 24, Unesco Office of Statistics, Paris 1980.

55

In cases where the data available are limited to enrolment by grade only, i.e., no data on repeaters are available, the Grade Transition Model cannot be applied and we have to use a more simple method. The most common model among these simplified methods is the Retention Model, also referred to as the Grade Ratio Model. This model may also be used when the level of repetition is very low. However, as data on repeaters are available for Kenya, we shall in this paper base most of the discussion of pupil flows on the Grade Transition Model as this is the more satisfactory of the two models. But the Grade Retention Model will also be reviewed briefly, see Section II.3.4 and II.4.14.

It is worth stressing here that the discussion is restricted to the introduction of the basic flow model as applied to primary and, to some extent, to secondary education. The particular issues raised by planning at the third level of education will not be treated here. The principle of the use of the method is, however, the same at all levels of education. The particular data problems experienced at the second and third levels (e.g. transfer between different types of education and different fields of study) will be discussed at the seminar.

Before entering the discussion of the two models mentioned above, we shall however discuss some general questions which often arise when applying these models.

II.2.2 Characteristics of Educational Flow Models

Certain characteristics of educational flow models should be clarified at the very outset of the discussion.

Tneir use does not impiy or necessitate any particular approach to educational planning, or any particular set of fundamental objectives which educational systems may be supposed to pursue. Whether schools are intended to satisry the social demand for education; or to meet the manpower "requirements" of economic development plans; or to maximise the rate of return to the investments made by individuals and society in the educational system; or to satisfy all three or indeed other objectives, an educational flow model is quite neutral. It is essentially a technical, mathematical tool of analysis which can, if its limitations are properly understood, be valuably applied to planning educational systems with any mixture of objectives.

The flow models most commonly used do not seek to explore or explain the behavioural relationships which determine in part the parameters playing such an important role in the model (1). For example, current repetition rates and prediction of their future magnitudes are important parameters in the

(1) Flow models including behavioural relationships have however been developed, particularly for individual institutions of higher education, see for example: Mathematical Models for the Educational Sector; A Survey, OECD Paris 1973

56

models. Repetition rates themselves, however, depend on several factors such as, for example, the existing regulations on the level of educational performance expected of a pupil if he/she is to be promoted to the next grade at the end of the school year. Similarly, drop-out rates are important parameters in determining the future development of enrolments. In secondary and higner education particularly, drop-out rates may in part reflect individuals* perceptions of their short-term and longer-term employment and earnings prospects, and so in principle may be influenced by social policies on work and pay for school leavers. Drop-out rates will also reflect factors on the education supply side; for if the national educational structure is not complete in some areas - for example, some elementary schools do not contain all grades - pupils may be forced to leave school against their own wishes.

II.2.J Distinction Between Enrolment Projections, Forecasts and Targets

A pronection (as has already been made explicit above in the discussion of population projections) is a conditional statement about the future. It is the elaboration of the effects in the future of making sets of assumptions about trends in the parameters characterising the educational system. Thus a projection does not necessarily offer the most probable (in some person's judgement) outcome. Rather, its main function is to demonstrate to the decision-maker the results which follow from changing some of the parameters (of from leaving them unchanged). Depending on the desirability to the decision-maker of the projected outcomes, he/she may intervene with policy changes to affect the underlying trends.

A forecast, by constrast, attempts to give the most likely outcome of future school enrolment. It will be obtained by combining with projections further data concerning future policies, plans or expectations, of "best guesses" about future developments in values of the parameters such as the intake, promotion, repetition and drop-out rates. Thus an element of judgement, lacking in projection, enters into forecasting.

Targets sometimes form the basis for the estimation of future required enrolments. For example, a target such as "x% of the 6-12 year -old population should be enrolled in primary education by 1987", could be specified. The job of the educational planner would then be, using techniques including the flow model, to make explicit the implications of meeting such a target for the required intake, promotion and other rates, as well as the number of teachers, new school buildings, etc. Target-setting thus goes beyond the work of projection, with its emphasis on technical relationships between the various parameters, and beyond the probable outcomes of the forecaster; it introduces the idea of desirable outcomes.

Tnus, whether the objective of a particular exercise is to make proiections, forecasts or analyse the requirements implied by the adoption of targets, the educational flow model may be utilised.

57

II.2.4 The Advantages of Mathematical Models

Mathematical models, as opposed to less formal modes of reasoning such as the purely verbal, have certain distinct advantages.

(a) Specification and quantification of relationships

Tne planner is obliged to specify the relationships seen as relevant, i.e. to state explicitly which factors relate to which. Secondly, he must attempt to quantify the parameters of the model using the available data. This quantification can make explicit both the internal relationships within the educational system and the relationships between education and other sub-systems such as manpower and population.

(b) Research and data requirements are frequently clarified by the construction of a mathematical model. Data

collection and research are resource consuming. Models can help in the assessment of priorities for expenditure in these areas.

(c) Logical consistency between separate analyses within the educational systems is ensured by the

explicit specification and estimation of relationships which often involve large and complex quantities of information.

(d) Rapid calcination of the future implications or alternative educational policies is facilitated by the use of such

models, particularly if computerised, i.e. models permit simulation analyses.

(e) Intranational and international comparative analyses may be made more readily through the models' specification and

quantification of key relationships. Such comparisons may help in forming future educational strategies based on other countries' experiences.

II.2.s The Flow of Pupils Through a Cycle of Education as Analysed by the Grade Transition Model

At the end of a given school year, a pupil enrolled in a given grade may:

(a) be promoted to the following grade, (b) have to repeat the same grade during the following year, (c) have dropped out, either because he has left the school system or died.

If this is the final grade of the cycle, the pupil may further:

(d) have graduated.

Consideration must also be given to the fact that pupils originally enrolled in a given divison, district or other administrative area may have:

58

(e) transferred to another country, division, district or administrative area. Further, in a country in which both public and private schools exist, transfers between these two sub-systems must be allowed for in making separate enrolment projections for the two sub-systems. We shall expand on this in II 2.7 below.

Similarly, if we consider the pupils who enter a given grade in a given year, they may be:

(1) new entrants, i.e. they have never been enrolled before in the case of primary education, or they come from the last grade of primary education in the case of lower secondary education,

(ii) promoted from the preceding grade,

(iii) repeating the same grade,

(iv) transferred from other countries, divisions or districts, depending on the level of aggregation of our analysis,

(v) re-entrants, i.e. they were previously enrolled but left the school system for one year or more due, for example, to sickness.

The meaning of the terms "failures", "repeaters", "passers" and "prcmotees" is sometimes unclear.

Disregarding transfers for the moment, Figure 6 illustrates what may happen to the pupils entering Grade g in a given school year. Some of them may drop out during the school year (the intravear drop-outs), and the rest complete the school year (the completers), with or without passing the final examination or assessment. The intrayear drop-outs may either drop out permanently, or repeat the grade the following school year. Some of the completers pass the requirements (the passers), and some fail to do so (the failures). Among the passers, some proceed to the next grade, some repeat the same grade the following school year and some leave the school system. The failures may either drop out, or they may repeat the grade the following year.

59

Figure 6 : What happens to pupils entering Grade g of primary education?

Initial enrolment in Grade g

Intrayear drop-outs

Permanent intrayear drop-outs

School-year completers

Intrayear drop-outs repeating Grade G next school-year

Failures dropping out

Passers

Failures repeating Grade g next school year

Passers leaving the primary school system *

Passers repeating Grade g next school-year

Passers proceeding to next grade

If Grade g is the last grade of a cycle, these pupils are graduates leaving primary education, who may or may not enter secondary education in the following school-year. Otherwise, they are drop-outs.

60

We may in this way distinguish between three groups of repeaters, i.e. repeaters among intrayear drop-outs, repeaters among failures and repeaters among the pupils who passed the grade examination. The latter group may include pupils who repeat because of lack of capacity in higher grades. Hence "repeaters" as defined here are not synonymous with "failures" since some of the latter may drop out while some of the intrayear drop-outs and some of the "passers" may join the remaining failures in repeating. Likewise, not all those who at the end of the school year are granted permission to go on to the next grade will actually be found in this grade the following school-year. Some may, for various reasons, drop out or repeat.

It is important to realise that the models discussed later on in this document are based on the concepts of promotion, repetition and drop out as defined under points (a), (b) and (c) above. The models do not deal with "passers" and "failures".

With the above discussion in mind, we shall now illustrate the fundamental concepts involved in the Grade Transition Model. Let us, for example, examine the flows of pupils between grades in primary education. The enrolment in a specific grade in a given year may be written inside a rectangle. As an example, in Kenya in 1980 the number of girls enrolled in Grade 1 in public and primary schools was:

Grade 1

1980 438,703

We now ask: where were these 438,703 pupils in the following school year, i.e. in 1981? According to the explanations given above, and as long as transfer is disregarded, the pupils may either have been promoted to Grade 2, they may have repeated Grade 1 or have dropped out. To illustrate these flows we shall adopt the following notation:

drop-outs

graduates (the final grade)

_ promotees repeaters

As will be explained below, most countries do not collect information on all these flows. Normally, countries collect data on repeaters in all grades and on graduates from the final grade of the cycle. Using these data in conjunction with data on enrolment by grade for consecutive years, it is possible (under the conditions explained above) to derive the number of promotees and drop-outs by grade. The procedure will be explained below.

^

61

Table 2.3: Enrolment and Repeaters by Grade in Primary Education. Girls. Kenya. 1980 and 1981.

Year Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

1980 Enr. 438,703 345,393 259,802 237,951 220,111 212,198 149,856

1981 Enr. 408,247 342,150 300,956 247,773 222,031 221,402 160,029

Rep. 58,148 41,731 33,232 31,586 29,594 34,356 18,512

.Souicje.: Education Statistics Unit, Ministry of Education, Science and Technology.

Table 2.3 shows the number of girls enrolled by grade in public primary education in Kenya in 1980 and 1981 as well as the number of repeaters by grade for the latter year. Wë shall now use the data given in Table 2.3 to illustrate how pupil flows are analysed by means of the Grade Transition Model. Let us consioer the enrolment in Grade 1 in 1980. Where were these 438,703 pupils in 1981. The table shows that 58,148 of them repeated Grade 1. According to the assumptions behind the Grade Transition Model, the rest of the pupils were either enrolled in Grade 2 (as promotees) or had dropped out. Table 2.3 shows that 408,245 pupils were enrolled in Grade 2 in 1981. However, not all of these pupils were enrolled in the previous year since the table also shows that Grade 2 enrolment includes 41,731 repeaters. Thus, under the assumption that there are no other inflows to Grade 2 than promotees and repeaters, we estimate that 342,150 - 41,731 = 300,419 pupils were promoted to Grade 2. Further, as we have assumed that pupils have only three possiDilities, i.e. to repeat, to be promoted or to drop out, we estimate the number of drop-outs frcm grade 1 to be 438,703 - 58,148 - 300,419 = 80,136. The flows out of Grade 1 may thus be written:

Grade 1

1980 438,703

58,148

80,136

-300,419

Tnus, we find that 300,419 + 58,148 = 358,567 of the 438,703 girls enrolled in Grade 1 in 1980 were still enrolled at school in 1981, 58,148 were enrolled in Grade 1 (repeaters) and 300,419 in Grade 2 (promotees). So far, 80,136 have left school. We have assumed that they have dropped out. But it is possible that some of them transferred to schools in other countries, or left school temporarily due, for example, to illness or other reasons. On the other hand, some of the pupils or promotees in Grade 2, may be intransfers from other countries, or have returned to school following a temporary break. As we have no data on transfers it is not possible to say to what extent the data available have been affected by such movements of pupils. We shall discuss this aspect further in Section II.2.7.

We may now ask where the 358,567 pupils who remained enrolled at school in 1981 were in 1982. Before trying to answer this question we shall introduce the promotion, repetition and drop-out rates.

62

II.2.6 Calculation of Promotion, Repetition and Drop-out rates

In the example given above, the numbers of promotees and drop-outs were estimated from data on enrolment and repeaters. This example may now be taken one step further as we may compute the proportion of pupils enrolled in Grade 1 in 1980 that, in the following year, repeated this grade (the repetition rate), was enrolled in Grade 2 as promotees (the promotion rate) or dropped out (the drop-out rate). These proportions are normally called transition or flow rates.

Rates of promotion, repetition and drop-out may be calculated in the following way:

Tne promotion rate

t (17) the promotion rate (p )

i

number of students promoted to grade i+1 in year t+1

number of students in grade i in year t

or in symbols:

t+1 P

t i+1 P = • i t

E i

Using as an example the data presented in Table 2.3, it may be seen that:

1981 P

1980 2 342,150 - 41,731 p = = _ _ = 0.685 1 1980 438,703

E 1 • - . • •

63

The repetition rate

t (18) the repetition rate (r )

i

number of students repeating grade i in year t+1

number of students in grade i in year t

or in symbols :

t+1 R

t i r = ___. i t

E i

Again using the data given in Table 2.3 we obtain :

1981 R 1 58,148

• _ _ _ _ _ • 0.133 1980 438,703

E 1

The rate of drop-out

t (19) the rate of drop-out (d ) =

i

number of students dropping out from grade i in year t

number of students in grade i in year t

or in symbols :

t t+1 t+1 E - (R + P )

t i l i+1 d = ____. i t

E i

1980 r

64

However, an easier approach is to derive the drop-out rate as the complement of the sum of the rates of promotion and repetition since these three rates must add up to unity for any given grade, i.e. :

1980 1980 d = 1 - p 1 1

1980 r = 1 - 0.685 - 0.133 = 0.182. 1

We have now computed the promotion, repetition and drop-out rates for Grade 1. Following the same procedure, the corresponding rates may also be calculated for the remaining grades. The results have been shown in Table 2.4.

Table 2.4 : Rates of Promotion, Repetition, Dropout and Graduation by Grade in Primary Education.

Girls. 1980. Kenya

Rates Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Grade 6

Grade 7

Promotion Repetition Drop-out

.685

.133

.182

.775

.121

.104

.832

.128

.040

.809

.133

.016

.849

.135

.016

.667

.163

.170

.876*

.124

* This rate includes all pupils not repeating Grade 7, including those who drop out.

Source : Table 2.3

Directly resulting from their definitions the rates may be interpreted as relative frequencies. That is, they represent the probabilities for any individual taken at random from a cohort, of his promotion, repetition or drop-out.

This information may be used in two related but different ways:

(a) to reconstruct the school history of a given cohort. This is discussed in Section 3 below;

(b) under certain assumptions concerning the future development of these rates, to project the future development of enrolment by grade. This is discussed in Section 4 below.

65

II.2.7 Some Aspects of Migration and Transfers Between Schools (1)

Some of the most difficult problems in analysing and projecting pupil flows are related to the often extensive migration in many developing countries, particularly from rural to urban areas. Three main problems may be distinguished:

(i) Reliable data on past migration often do not exist, at least not data on migration of the school-age population by age, and of the population of less than school-age (who are potential school entrants).

(ii) Data on transfers of pupils between schools are often not collected. Thus, one often lacks data on transfers from schools in one region to schools in another, and from one sub-system of schools to another (e.g. from private to public schools).

(iii) Even if data on migration and transfers of pupils were available, it would not be easy to project future transfers and future migration.

Before going any further into these difficulties, it is useful to try to classify the relevant types of migration and transfers between schools.

(1) This Section is partly based on Section 4.1 of T. Thonstad, in co-operation with the Division of Statistics on Education, Unesco Office of Statistics, Analysing and Proiecting School Enrolment in Developing Countries: A Manual of Methodology, Unesco, Paris 1980.

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67

(a) Types of Migration and Transfers

First of all, one should differentiate between changing residence (migrating) and changing school or school district (transferring). It is, of course, possible for a family to move to another area while the children remain in the same school, and also for the family to remain in the same residence while the children transfer to another school or school district. In what follows, we shall use the term migration to mean change of residence (1) and school transfer, or simply transfer to mean moving from one school to another, regardless of whether the pupils changes residence or not.

As examples of transfers between schools, school systems or school districts without changing residence, one may mention:

(a) A pupil may transfer between a public and a private school system in the same area.

(b) A student may transfer to a school in another area because there are no schools at that level available in his home area. For example, there may be no secondary school. Therefore, in secondary education, and even more so in higher education, a large proportion of the students study away from their homes, living in hostels, boarding schools or with relatives. It should be mentioned, in this connection, that in some developing countries it is not always clear what the home or residence is. This is partly due to the existence of extended family patterns, where children often live with their grandparents or other relatives, while the parents live and work in another area. In the case of migratory workers, the area from which they originate may be defined as their residence.

However, despite the existence of transfers which do not involve migration, a large part of the transfers between schools is accompanied by migration, in the sense of changing residence. An important point in this connection is that their children have adequate educational facilities. Thus, the decision about the location of new schools, the school mapping (2), may have important effects upon internal migration, in particular between urban and rural areas. This is an example showing that not only do demographic factors such as the growth and distribution of population by sex, age and region influence the demand for education, but the supply of educational facilities may have impacts upon the demographic development, e.g. upon internal migration.

(1) Cf. Manuals on Methods of Estimating Population, Manual VI: Measuring Internal Migration, p. 2, op. cit.

(2) For a discussion of methods of school mapping see: J. Hallak, Planning the Location of Schools: An Instrument of Educational Policy op. cit.

Problems of low population density and the supply of schools are discussed pp. 57-59 in G. Jones: Population Growth and Educational Planning in Developing Nations, op.cit.

68

Next, one has to distinguish between which regions school transfers and migration take place. Suppose that a country is divided into a number of provinces, and that each province is divided into a number of districts. In such a case, one may classify transfers into:

(i) International transfers, i.e. transfers to and from foreign countries.

(ii) Inter-provincial transfers, i.e. transfers from one province to another.

(iii) Interdistrict transfers, i.e. transfers from one district to another within a provice.

Similarly, migration could be classified into:

(i) International migration, i.e. migration crossing national borders.

(ii) Inter-provincial migration, i.e. migration from one district to another within a province.

(iii) Interdistrict migration, i.e. migration from one district to another within a province.

From the above attempt at classification, it becomes clear that the problem of school transfers is rather different according to whether one is analysing pupil flows for the country as a whole, for a province, or for a district. Furthermore, since transfers to one area come from another area (if not from abroad), the different local projections of school enrolment should balance. For example, if there are two province, the projection of the number of transfers out of one province should, of course, match the projection of transfers into the other.

It should be noted that since pupils often go to school in provinces other than the place they are registered as living in, there are problems in estimating provincial or district ratios. This is due to the fact that provincial enrolment ratios are often estimated as the ratio between enrolment in a certain level of education or age-group in a province (without distinguishing between local and "foreign" pupils), and the population in the corresponding age-range in the same province. In provinces having many out-of-the-province pupils, while few of their own children go to schools in other provinces, the provincial enrolment ratios tend to be over-estimated. Conversely, in provinces sending many children to other provinces for schooling, the provincial enrolment ratios tend to be under-estimated.

(b) Effects on the Transition Rates of Ignoring Transfer

As explained above, data on transfers are often not available. Suppose for the sake of illustration that we wish to project separately the enrolment by grade in an undifferentiated system of primary education for two provinces of a country, Province A and Province B, which together cover the whole country. Assume, furthermore, that there are no international transfers of pupils to and from this country, and that all transfers go from Province A to Province B.

69

On the basis of data on enrolment and repeaters, we want to estimate the transition rates. Consider first Province B, which receives transfers from A, and where we observe the following data for Grades g and g + 1:

t E = enrolment in Grade g in school-year t in Province B. gfB

t+1 E = enrolment in Grade g+1 in school-year t+1 in Province B, g+l,B including in-transfers from Province A.

t+1 R = repeaters in Grade g in school-year t+1 in Province Bf gfB including repeaters who are in-transfers in Province A.

Suppose now that one does not have sufficient data to distinguish between pupils who were in Province B in the previous year and in-transfers from Province A. One is then frequently obliged to use the above-mentioned data in order to estimate the transition rates for Grade g in school-year t in Province B. The repetition rate is then estimated as:

t (20) r

g,B

t+1 R gfB

t E g,B

promotion rate is estimated as:

t P gfB

t+1 t+1 E - R g+l,B g+l/B

t E g,B

i.e. the promotees in Grade g+1 in school-year t+1 divided by enrolment in Grade g in school-year t. Finally, assuming that there are no graduates from Grade g, the drop-out rate is estimated as the residual:

+ t (22) 1 - r1, - p .

g^B g.B

Suppose now that we wish to use these three rates to describe what happened t

to the enrolment E in the following year. Assuming, as above, that all g.B

transfers go from Province A to Province B, we find:

70

(i) The repetition rate is overestimated, since seme of the repeaters are in-transfers from Province A.

(ii) The promotion rate is also overestimated, since some of the promotees in Grade g+1 in year t+1 are in-transfers from Province A.

(iii) Since the above two rates are overestimated, the drop-out rate is underestimated. One may even arrive at negative drop-out rates by using the above method.

In Province A, experiencing transfers out of the province, it is easy to see that the results would be the opposite. By a similar procedure as above, one would understimate the repetition and promotion rates and overestimate the drop-out rate.

Let us next turn to the implications of using such distorted transition rates. Suppose that one uses the distorted transition rates for analysing wastage, i.e. the effects of repetition and drop-out on the progression of the cohort through a cycle of education. In Province B, one would over-estimate repetition and under-estimate drop-out. One would thus over-estimate the number completers for a given cohort of school entrants. In province A, the effects of the distorted transition rates upon estimation of wastage would be the opposite. Thus, not explicitly taking transfers into account could seriously distort the results of a comparative analysis of wastage by province.

Suppose next that such distorted transition rates are used for projecting school enrolment. If one is interested in projecting the numbers enrolled in each province, the distortions of the transition rates may not distort projections appreciably, if the flow of transfers remains "stable" (in the sense that the influence upon the transition rates does not change). However, a flow of transfers which keeps the observed transition rates in the receiving province constant may change the transition rates of the sending province.

We have discussed above the transfer between provinces within a country. The same line of reasoning would be valid for transfer between two different streams of secondary education. The effect of international migration can also be analysed within this framework.

71

SECTION 3: USE OF FLOW MODELS FOR RECONSTRUCTING THE SCHOOL HISTORY OF A COHORT

II.3.1 Introduction

The most reliable way of studying the progress of a group of pupils through a cycle of education is on the basis of an individualised data system where each pupil is given a code number and can be followed throughout his school career. This method is often referred to as the true cohort method. To establish and operate an individualised data system is, however, very costly and only a few developed countries have done it so far. A more inexpensive approach would be to introduce a "cohort coding system" whereby all pupils in a cohort experiencing the same educational events receive the same code number. The data thus collected year by year would permit us to analyse some aspects of the flow of this cohort through a cycle of education. (1)

For want of data collected by means of the above two approaches, educational statisticians and planners have developed various simplified methods which, under certain hypotheses, permit us to reconstruct the progression of a cohort through a cycle of education. The reconstructed cohort method is the one most frequently used when data are available on promotion, repetition and drop-out rates. This method is based on the same assumptions as the Grade Transition Model presented in the previous section. Section II.3.2 will explain how this method can be used to reconstruct the flow of a cohort through a cycle of education. The results derived from such a flow analysis are often used by educational planners and statisticians to estimate the extent of "wastage" or "inefficiency" in education due to repetition and drop-out. Section II.3.3 will demonstrate how this can be done.

As already explained, to reconstruct the progression of a cohort through a cycle of education using the above method we need, in addition to data on enrolment by grade, data on repeaters. Where data are not available on repetition, a more approximate method, referred to as the apparent cohort method, is generally used. This method will be presented in Section II.3.5 where we shall also discuss the differences between the above two methods of analysing pupils flow.

(1) For example of how such a system may be applied in practice, see: A. Sammak: "School enrolment Coding Systems", in Statistical Methods for Improving the Estimation of Repetition and Dropout: Two methological Studies, CSR-E-40, Unesco, Paris 1981.

72

II.3.2 Cohort Reconstruction

We shall now use the data given in Table 2.3 to illustrate how one may use the Grade Transition Model to reconstruct the flow of a cohort of pupils througn a cycle of education. Before computing the flows we note that it is easier to work with relative than with absolute numbers. For example, instead of starting with 438,703 girls in Grade 1 in 1980 and saying that 58,148 repeated, 300,419 were promoted and 80,136 dropped out, one may as well base the calculations on the promotion, repetition and drop-out rates for Grade 1. In this example, these rates have already been computed as, respectively, 0.685 0.133 and 0.182. This means that out of every 1,000 pupils, 685 would be promoted, 133 would repeat and 182 drop out. In addition to simplifyiung the calculation when working with large numbers, this approach also facilitates the interpretation of the results since every figure computed may be read as "per thousand". Thus, following this approach, the flows may be illustrated by the following flow diagram:

Year Grade 1

182

1980 1000

I 1981 133 " 685

This shows that, for every 1,000 girls enrolled in Grade 1 in 1980, 685 were enrolled in Grade 1 (promotees), 133 were enrolled in Grade 1 (repeaters) and 182 have dropped out. Thus, 818 were still enrolled at school in 1981. What happens in the following year? We can compute the flows between 1981 and 1982 if we know the promotion, repetition and drop-out rates. Such rates are given in Table 2.4 for the school-year 1980/1981. To illustrate the technique of reconstructing cohorts, we shall assume that these rates will remain constant over the whole period members of this cohort are enrolled. Of course, in real life situations flow rates do change over time and these changes should be taken into account. The technique is, however, the same whether the rates used remain stable or change. In addition, a cohort reconstruction based on constant rates provides interesting information as regards the future implications of maintaining constant existing rates. One may also use the technique to make simulations, examining the implications of given future changes in the rates.

We shall now use the flow rates given in Table 2.4 to extend the flow diagram shown above to cover all grades of primary education for girls in Kenya. The results are shown in Figure 7. Before discussing the assumptions behind this technique, we shall explain briefly how this flow diagram has been constructed and show what type of indicators of cohort flows may be derived from such a diagram.

73

Tne procedure followed in drawing up Figure 7 is easily understood and will be explained in further detail during the seminar. Of 1,000 pupils enrolled in Grade 1 in 1980, 133 repeated this grade in 1981. 685 were promoted to Grade 1, and 182 dropped out. These figures are obtained by applying the promotion, repetition and drop-out rates shown in Table 2.4. They are entered in the diagram against their respective arrows. By applying the promotion, repetition and drop-out rates of Grade 2, we find further that of the 685 pupils enrolled in this grade in 1981 (i.e. the pupils promoted from Grade 1 in 1980), 685 x 0.775 = 531 were promoted to Grade 3 in 1981, while 685 x 0.121 = 83 repeated Grade 2 in this latter year. In order to obtain the figure 174 in the rectangular box (a figure showing how many of the original 1,000 pupils would be in Grade 2 in 1982 after having repeated once, either Grade 1 or Grade 2), we must add to these 83 pupils those who are promoted to Grade 2 after having once repeated Grade 1, i.e. 133 x 0.685 = 91.

All the other figures in the flow diagram may be obtained in the same way, employing for each year and grade the promotion, repetition and drop-out rates given in Table 2,4. The row of boxes at the foot of the diagram and the table in the right hand corner will be explained later.

74

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

Figure 7 Cohort Reconstruction for

Primary Education in Kenya Girls

I'UI.II / r „ r t

Cr««l« I 1,153 " 2 898 M 3 799 " 4 768 " 5 718 " 6 729 " 1 556

Total 5,621 ;

Out-put 4 8 6

Pupll/ïa.r. U - 5 7

liiput/Out|iut 1.65

iWfc I 304

51

' W P N i . » 15 X203

Source : Table 2.4

Survival by Grade

j 1,000 1 789

21] ? ^ 92 3 ft 4 4^ 5 J

-*j 665 \ 1 697 622

2 J_JM_L. 610 486 '486

75

II.3.3 Discussion of the Assumptions behind the Cohort Reconstruction

The main assumption behind the cohort reconstruction given in Figure 7 may be summarised as follows:

(a) We want to estimate how the girls enrolled in Grade 1 of primary education in Kenya in 1980 may progress through this cycle of education on the assumption that the transition rates were to remain constant in the future. For the sake of analytical convenience and clarity, we have based the calculations on a hypothetical cohort of 1,000 new entrants instead of on the number of pupils actually enrolled in Grade 1 in that year. As explained above, this approach facilitates the computations as well as the interpretations of the results.

(b) As we are thus reconstructing the flows of one given cohort, there are no new entrants to this cycle after 1980. Nor does migration or transfer take place. It is also assumed that no pupils interrupt temporarily their schooling due, for example, to illness. This implies that there are no temporary drop-outs followed by re-entrance in later years. Moreover, the reconstruction implies that no pupils skip grades or, inversely, are sent down to lower grades.

(c) The reconstruction assumes that the same promotion, repetition and drop-out rates apply to all pupils enrolled in a given grade, regardless of whether or not they have previously repeated this or preceding grades once or more. This assumption is usually referred to as the hypothesis of homogeneous behaviour. We shall discuss it further below.

Although some of the flows mentioned under point (b), and which are disregaded when reconstructing cohorts, may be important for certain grades in seme countries, they are generality negligible and may be disregarded without risk of significantly affecting the results. This is particularly so when the reconstruction refers to a nation as a whole. But when the analysis refers to a given region within a country, then it is often important to take into account transfers between schools in the different regions. However, to take transfers into account requires that statistics be available on such flows. This is normally not the case.

The assumption listed under point (c), i.e. the hypothesis of homogeneous behaviour, is normally considered to be the most crucial assumption behind use of the Grade Transition Model for cohort reconstruction. This is particularly so when the level of repetition is high. There are several reasons for expecting that pupils1 behaviour with respect to promotion, repetition and drop-out is affected by previous repetitions. (1) This would mean that, for example, the flow rates depend not only on the grade in which pupils are enrolled now, but also on the grade in which they were enrolled in the previous year. Even pupils1 earlier school history may influence their transition rates. For example, pupils who have already repeated Grade 1 and 2 may have a different propensity to repeat Grade 5 than pupils who have not repeated at all or who have repeated Grade 3 only.

(1) A discussion of how previous repetition may affect flow rates is given in: B. Fredriksen: Internal Efficiency of School Systems : A Study in the Use of Pupil Flow Models for Developing Countries, Report 78, Norwegian Institute of International Affairs, Oslo January 1983. See pp. 114-120.

76

One aspect of the hypothesis of homogeneous behaviour which has been of particular concern to users of the Grade Transition Model for reconstructing cohort flows is the fact that this assumption inplies that pupils may repeat grades without any limits. The discrepancy between reality and the assumption of unlimited repetition is particularly unsatisfactory in cases where countries are known to apply clearly defined limits to the number of repetitions permitted. This has led sane educational planners to question the validity of indicators derived on the basis of the Grade Transition Model under such circumstances.

It is not possible here to enter into a detailed and technical discussion of this question. This would imply constructing models which take restrictions on repetition explicitly into account and then comparing indicators derived from such models to the corresponding indicators derived on the basis of the Grade Transition Model. However, as this is an important issue, we shall summarise the main conclusions of the study quoted above which was conducted mainly to throw light on the following question: (1)

"Consider a cycle of education for which cohort flow indicators have been derived by means of the Grade Transition Model. To what extent will these estimates describe correctly the flows which actually take place if the data on which they are based have been generated, not by a system where there is no restriction on repetition, but by one where such restrictions both exist and are applied in pratice? In other words, how would indicators derived on the basis of the Grade Transition Model differ from the corresponding indicators derived by means of the 'true model', i.e. the model which takes explicitly into account existing regulations governing repetition?"

The results presented in the study show that while seme of the indicators normally derived frcm cohort reconstruction can be rather insensitive to restrictions on repetition, others may be affected quite significantly. In the next section we shall define the cohort flow indicators most commonly used and explain which are most sensitive to such restrictions. Suffice it to say here that the indicators which are most commonly used by educational planners, i.e. those referring to what eventually happens to the cohort (in terms of enrolment, drop-out, graduation, wastage and average study-time) are quite insentive to rules governing repetition. The indicators which may be very sensitive to such regulations are those referring to enrolment, drop-out, repetition and graduation in any specific school-year originating from this cohort. These latter indicators are particularly useful to manpower planners, but are less important for someone concerned with analysing the internal efficiency of school systems.

(1) Ibid, chapter 4.

77

To summarize we may say that, despite the fact that the Grade Transition Model assumes homogeneous behaviour and thus disregards restrictions on grade repetition, this model may normally be expected to yield satisfactory results for most of the indicators most commonly used for analysing wastage in education. As the statistical data required to take such restrictions into account are available in practically no country, the method can therefore be used to derive approximations for how a given cohort of pupils flows through a cycle of education.

We shall now proceed to discuss the various indicators which may be derived from Figure 7.

EXERCISE V

Using the results obtained from completion of Exercise IV, participants working in groups, will reconstruct the school history of the cohorts, it should be assumed that the flow rates calculated in exercise IV will remain constant over the entire period of the evolution of the cohort

II.3.4 Cohort Flow Indicators derived from Cohort Reconstruction

Tne main purpose of constructing Figure 7 is that this permits us to derive a number of indicators describing the flow of a cohort of pupils througn a cycle of education. We may distinguish between four groups of such cohort flow indicators:

(A) indicators of retention for survival by grade;

(B) Indicators of retention by years spent in the cycle;

(C) Indicators of duration of study;

(D) Indicators of wastage in education.

We shall briefly explain how these indicators may be derived from Figure 7.

A. Indicators of retention by grade

Three such indicators may be derived from Figure 7.

A.l Survival by grade

This indicator is given by the figures included in the row of boxes shown at the foot of the flow diagram. For example, the figure included in the box for Grade 2 shows that of the 1,000 pupils starting Grade 1 in 1980, 789 will eventually reach Grade 2. This figure is found by adding up the number o9f

78

pupils promoted from Grade 1 to Grade 2 in each of the years, i.e. 685 + 91 + 12 + 1 = 789. Thus, the proportion of the cohort which eventually reaches Grade 2 is higher than indicated by the annual promotion rate for Grade 1.

A.2 Dropout by grade

This indicator can also be derived from the row of boxes shown at the foot of the flow diagram. The number of drop-out between two subsequent grades is found either by adding up the drop-outs shown in the flow diagram or, more easily, as the difference between the number of pupils surviving to each of these two grades. For example, the number of drop-outs between Grades 3 and 4 is computed as 21 + 8 + 2 + 1 = 32 or as 697 - 665 = 32.

A.3 Number of graduates from the final grade

From the flow diagram we find that 486 of the 1,000 pupils will eventually reach Grade 7. As data were not available on school leavers, it has been assumed for the purpose of this exercise that all these pupils graduate.

B. Indicators of retention by years spent in the cycle

As discussed in the previous section, this type of cohort flow indicator, showing enrolment, drop-out and graduates by years of study, may be affected by non-fulfillment of the hypothesis of homogeneous behaviour.

B.l Enrolment by years of study

This indicator of survival by years of study is found by adding up the figures included in each of the boxes of the flow diagram for the year in question. For example, for 1983 we find that 2 + 33 + 203 + 442 = 680 pupils of this cohort are still enrolled. The last year in which members of this cohort would be enrolled is 1992 (2 pupils in Grade 7).

B.2 Dropouts by years of study

The number of drop-outs by years of study is found either by adding up the drop-outs from each grade for the relevant year or, if Indicator B.l has already been calculated, as the difference between the enrolment in two subsequent years. For example, in 1983 we find that 1 + 3 + 8 +25 = 37 pupils drop out. Alternatively, this figure could have been found as enrolment in 1983 minus enrolment in 1984, i.e.:

(2 + 33 + 203 + 442) - (5 + 52 + 228 + 358) = 37

The last drop-out from this hypothetical cohort would take place in 1989 when 3 pupils drop out from Grade 6 after having spent 10 years at school, i.e. after having repeated four times.

B.3 Graduates by years of study

As explained above, since data were not available on successful primary school leavers, it has been assumed in this illustration that those reaching Grade 7 either graduate or repeat the same grade. The diagram shows that 178 pupils would graduate in 1986 after 7 years of study (i.e. without repetition), 166 would graduate in 1987 (one repetition), and 88 pupils would graduate in 1988 (two repetition) and so on.

79

C. Indicators of duration of study

C.l Average duration of study for graduates

Figure 7 shows that 178 pupils graduate after 7 years of study, 166 after 8 years and 88 after 9 years, 36 after 10 years, 12 after 11 years, 4 after 12 years and 2 after 13 years. The total number of pupils-years (1) spent at school by the 486 graduates is hence: (178 x 7)+(166 x 8)+(88 x 9)+(36 x 10)+ (12 x 11)+14 x 12)+(2 x 13) = 3932 pupil-vears.

Dividing this total by the number of graduates gives average study time for graduates:

3932 = 8.09 years

486

C.2 Average duration of study- for drop-outs

From Figure 7 we find that of those dropping out, 182 spent one year at school, 24 + 71 = 95 spent two years, 4 + 18 + 21 = 43 spent three years, and so on. This approach assumes that all drop-out takes place at the end of the school-year. The total number of pupil-years used by drop-outs is hence: (182 x 1) + (95 x 2) +(43 x 3) + (37 + 4) + (21 x 5) + (60 x 6) + (46 x 7) + (20 x 8) + (7 x 9) + (3 x 10) = 1689 pupil years.

Dividing this number by the number of drop-outs we obtain:

1,689 Average study time for drop-outs: = 3.29 years

514

C.3 Average study time for the cohort

The average duration of study for all cohort members is found by dividing all pupil-years used by graduates and drop-outs by the size of the cohort:

3,982 + 1689 Average study time for the cohort: = 5.62 years

1,000

This figure could also have been derived as a weighted average of the average study time of drop-outs and graduates, i.e. :

(3.29 x 514) + (8.09 x 486) = 5.62 years

1,000

(1) One pupil spending one year is said to have used one pupil-year

80

D. Indicators of wastage in education

We complete this brief survey of cohort flow indicators by presenting three indicators commonly used to estimate the extent of wastage in education.

The Reconstructed Cohort Method defines wastage in education as the number of pupil-years spent on repetition and drop-out. It is recognised that this concept of wastage constitutes a rather crude view as regards the benefits a pupil may draw from the education received before dropping out and of the advantages a pupil may derive from spending an extra year in a grade. It is not the purpose of this introduction to the use of cohort flow indicators to present an evaluation of this concept. Nevertheless, some factors which should be taken into account when interpreting the indicators presented below need to be mentioned.

Firstly, the extent to which drop-out should be regarded as wastage will depend on the structures and objectives of each educational system. It will, moreover, depend on the educational attainment reached by those dropping out, and from which level of education the drop-out takes place. As regards primary education, the main objective, at least of the first few grades, is to achieve literacy. Those who leave school without having completed the cycle are not likely to have strengthened basic literacy and numeracy to the point where that it becomes resistant to forgetting. To the extent that such pupils relapse into illiteracy, one may argue that the resources that have consumed are, at best, inefficiently used and, at worst, completely wasted. This definitiion of "waste" implies that the resources used on drop-outs have an alternative use which would somehow be more "efficient"; they could for example have been spent on other pupils or could simply represent savings which could be used for meeting other needs of society.

However, even if one could devise some sort of test for distinguishing the new entrants who would drop out from those who would complete the cycle, to apply this type of selection would generally not be acceptable. Practically all countries aim at providing all children with some basic schooling. It is, therefore, useful to stress again that the main purpose of the wastage indicators is to throw light on the effects of repetition and drop-out on pupil flows. In the case of "high": levels of wastage, this information is an indication of a need to study the factors causing this waste. It is not an indication of a need to exclude some pupils from entering primary school.

For pupils who drop out from grades towards the end of the primary cycle after having spent, say, five to seven years at school, the argument of complete waste implied by the Reconstructed Cohort Method seems even more questionable. On the one hand, these drop-outs use a high number of pupil-years, thus contributing significantly to the level of wastage. On the other hand, to the extent these drop-outs have acquired some of the skills the system, sets out to teach them, they also represent some output.

For secondary education the relationship between "drop-out" and "waste" is much more complex than for primary education. On the one hand, the fact of not completing a stage of secondary education is all the more striking since entry to this level in most developing countries is based on selection. On the other hand, one may argue that pupils will benefit in various ways from a few years of secondary schooling regardless of whether or not they complete the cycle successfully.

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Secondly, the extent to which repetition should be regarded as wastage is also a moot point. The supporters of repetition usually claim that it serves two major purposes: to remedy inadequate achievement and to aid pupils who are judged to be emotionally immature. Conversely, to promote pupils' automatically is claimed to lower academic standards, to destroy pupils incentive to learn and teachers' motivation to teach, and to create pedagogical problems in the class by increasing the ability range within each grade. Thus, according to this view, repetition does not represent a waste of resources. On the contrary, it is considered as a necessary and appropriate investment to assist pupils with academic or adjustment difficulties.

The proponents of automatic promotion reject the pedagogical assumptions on which a repetition policy is based. Firstly, supported by a number of studies which conclude that schooling has little independent impact on achievement, they claim that out-of-school variables such as family background and personal pupil characteristics are equally, or possible more, important in determining pupils' progress at school. (1) Thus, to provide a slow learner with another year of the same programme is not necessarily the best way of improving this pupil's achievement. Secondly, they contest the validity of the tests generally used to assess pupils' progress. Thirdly, they claim that it is far from obvious that repetition of the same grade will improve the achievement of slow learners more than being promoted to the next grade. Lastly, to stigmatize pupils as "failures" may have a negative effect on their incentive to learn as well as on their self-respect.

In short, the views on the value of repetition held by the proponents of automatic promotion correspond quite closely to the basic implication underlying the Reconstructed Cohort Method, i.e. repetition is largely a waste of resource.

As should be clear from the above discussion, the factors leading to failure and consequent repetition are complex, and it would be wrong to believe that their negative effects on achievement could be eliminated simply by one administrative promotion. The real issue is not to design measures that merely ensure no repetition, but measures that improve the achievement among

(1) For a review of research in this area see, for example:

- Simmons, J. and Alexander, L. : "The Determinants of School Achievement in Developing Countries : A Review of Research", in Economic Development and Cultural Change, Volume 26, No.2, 1978.

- Schiefelbein, E. and Simmons, J. : The Determinants of School Achievement : A Review of the Research for Developing Countries, International Development Research Centre, IDRC-MR9, Ottawa May 1979.

Note however that research also suggests that school variables are likely to be more important for academic achievement in developing than in developed countries, see S.P. Heyneman : "Differences between Developed and Developing Countries : A Comment on Simmons' and Alexander's Determinants of School Achievement", in : Economic Development and Cultural Change, January 1980.

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low achievers. The fact that sane of the few developing countries which had introduced automatic promotion during the last two decades have reintroduced the possibility of repetiton (e.g. Costa Rica, Egypt, Singapore and Venezuela) might possibly be taken as an indication that automatic promotion alone is not sufficient. (1)

We shall not pursue this discussion further. It is sufficient for our purpose to reiterate that the sole purpose of computing the type of .indicators of wastage used by the Reconstructed Cohort Method is to throw light on the effect of repetition and drop-out on pupil flows. "High" levels of wastage caused by drop-out simply indicate a need to study the factors (internal and external to the educational system) which make pupils leave school prematurely. But, as already stressed, "low" wastage as measured by this method does not necessarily indicate that wastage is low if output was measured otherwise, e.g. in terms of pupils' achievement. It simply indicates that there is little repetition and drop-out in the system.

To summarize, whatever opinion one may have as regards the benefits derived from attending school by pupils dropping out, or as regards the value of repetition, it is still important for educational planners and policy-makers to know the magnitude and pattern by grade of these two events. In spite of their crudeness, the indicators presented below do provide interesting information in this regard.

D.l Input-output ratio

This is an indicator of the "efficiency" with which a school produces a given number of graduates. Efficiency is a concept which has been developed and refined particularly by economists. It refers to the relationship between the inputs into a system (be the system, e.g. agricultural, industrial or educational), and the outputs from that system (be they wheat, vehicles or educated individuals). An activity is said to be "efficient" if maximum output is being obtained from given inputs, or if a given output is being obtained with the minimum possible inputs. Inputs and outputs have somehow to be valued so that they may be aggregated; and usually prices are used to perform this valuing function. The problems of measuring efficiency in education, however, are considerable. They stem mainly from difficulties in measuring educational output, as well as from quantifying the relationship between inputs and outputs. How educational output is to be measured depends, of course, on the nature of the objectives of the educational system. Depending on the analytical and philosophical viewpoint adopted, the objectives may differ considerably.

(1) For a discussion of the effects of repetition, readers are referred to W. Haddad : Educational and Economic Effects of Promotion and Repetition Practices, World Bank Staff Working Papers No 319, Education Department, World Bank, Washington 1979.

83

Educational statisticians and planners, whilst recognising the diversity of the objectives of education, often need to measure the output of the school system in a simple way. One such approach consists of considering the output of a given cycle of education to be the number of pupils who successfully complete this cycle (the graduates). This is naturally a rather restricted definition since the drop-outs no doubt have acquired some of the skills which the system set out to teach them. As explained above, in a more complete definition of output, the educational attainment of the pupils dropping out should therefore be taken into account. Nevertheless, this way of measuring output still gives us some useful insignts into the functioning of an educational system.

Educational injguis comprise buildings, teachers, text-books, etc., which may all be aggregated financially in terms of expenditures per pupil-year. The inputs also include the income foregone by students while studying. However, in the context of the Reconstructed Cohort Method, the input indicator most commonly employed is the number of pupil-vears used by the cohort. To some extent, the amount of input expressed in monetary terms is related to number of pupil-years used.

The table in the upper right hand corner of Figure 7 shows the number of pupil-years spent in each grade by the cohort in the above example. The total for a given grade is obtained by adding up the figures inside the boxes of the diagram referring to this grade. For instance, one can see that a total of 1,153 pupil-years were spent in Grade 1, i.e. 1,000 in 1980, 133 in 1981 by pupils repeating once, and 18 in 1982 by pupils repeating twice and 2 in 1983 by pupils repeating three times. Considering all seven grades, the total number of pupil-years spent by this cohort is 5,621. This represents the total input. The "output",i.e. successful completers of this seven-year cycle, as we have seen, is 486. The average number of pupil-years per successful completer was therefore :

5,621 = 11.57

486

Had there been no repetition or drop-out, the 486 pupils would have needed 486 x 7 = 3,402 pupil-years to complete the cycle. By dividing the number of years actually spent by this cohort (i.e. 5,621) by this optimal number, one obtains an indicator of efficiency generally referred to as the input-output ratio, which in this case is :

5,621 = 1.65

3,402

In a "perfectly efficient" system, this ratio would equal 1.00. Thus, this

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cohort used 1.65 times the input required in a system without repetition or drop-out.

Another way of expressing thie indicator is in terms of "the percentage of the total numoer of pupil-years wasted". In the above case, 5,621 - 3,402 = 2,219 pupil-years were wasted, i.e. 39.5% of the total.

D.2 Proportion of tnt-gl wastage spent on repetition and drop-out respectively

This indicator splits total wastage on the two events causing waste, i.e. repetition and drop-out. In the above example, a total number of 3,219 pupil-years was spent on repetition and drop-out. Using the figures for drop-out by grade given in the row of boxes at the foot of Figure 7, we may calculate the numoer of pupil-years wasted on drop-out (note that this calculation excludes wastage due to repetition among pupils who later drop out) : (211 x 1) + (92 x 2) + (32 x 3) + (43 x 4) + (12 x 5) +(124 x 6) = 1,467 pupil-years.

Thus, 1.467 x 100 = 66.1% of the pupil-years wasted by this cohort was due to 2,219

drop-out. Consequently, 33.9% of the total wastage was due to repetition. Some of this wastage was due to repetition by pupils who eventually graduated, while some was due to repetition by pupils who later dropped out.

D.3 Proportion of total wastage used by, respectively, graduates and drop-outs

Within the framework of this method, wastage by graduates can only be due to repetition. The number of pupil-years spent on repetition by graduates may be derived directly from Figure 7 which shows that 166 pupils graduated after having repeated once, 88 after having repeated twice, 36 after having repeated three times, 12 after repeating four times, 4 after repeating 5 times, and 2 after repeating 6 times. Thus, the total number of pupil-years spent on repetition by graduates equals:

(166 x 1) + (88 x 2) + (36 x 3) + (12 x 4) + (4 x 5) + (2 x 6) • 530 pupil-years.

530 This means that x 100 = 23.8% of all wastage for this cohort was

2,219 accounted for by graduates repeating grades. The remaining part, i.e. 76.2% was accounted for by drop-outs.

* * * * *

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The above concludes our discussion of cohort flow indicators derived by means of the Grade Transition Model. How well these indicators describe the way in which a cohort actually progresses through a cycle of education depends on the realism of the assumptions on which this model is based and the quality of the statistical data available for estimating the flow rates. The quality of the statistics available in developing countries on pupil flows often leaves much to be desired.(1) The collection of education statistics in Kenya will be discussed in detail at the seminar, including problems related to quality as well as paucity of data.

The validity of the assumptions on which the Grade Transition Model is based was discussed in the previous section. It was pointed out that the hypothesis of homogeneous behaviour of all pupils enrolled in a given grade is the most crucial one, particularly since this implies assuming that pupils may repeat grades without any limits. Possible effects of non-fulfillment of this hypothesis were discussed. It was concluded that while some of the 12 indicators listed above are rather insensitive to restriction on répétition, others may be affected quite significantly. The former group includes the indicators used for quantifying average study time as well as the level of drop-out, graduation and wastage associated with a given cohort, i.e. Indicators A.l, A.2, A.3, C.3, D.l and D.2 above. For these six indicators, the Grade Transition Model may thus be expected to yield satisfactory results even for systems in which the number of repetitions permitted is limited.

As the above six indicators are those which are probably most commonly used for analysing cohort flows and wastage, this conclusion also has a bearing on the data collection priorities in the field of education statistics. For example, it is likely that the returns to any investment aimed at improving the quality of this group of indicators would, in most countries, be higher if these resources were used to improve the accuracy of the statistics collected on total enrolment and, especially, repeaters by grade rather than to collect more detailed flow statistics permitting the use of models which are more sophisticated than the Grade Transition Model.

The indicators which may be quite significantly affected by the rules governing repetition are those which refer to enrolment, drop-out and graduation in any speciic year originating from a given cohort (e.g. Indicators B.l, B.2 and B.3) as well as indicators referring to sub-groups of pupils belonging to this cohort (e.g. Indicators C l C.2 and D.3). It follows from this that care should be taken when the Grade Transition Model is used to study, for example, yearly teacher requirement or yearly supply of educated labour associated with a given cohort.

(1) Some common errors found in the educational statistics of developing countries are discussed in B. Fredriksen: "Statistics on Education in Developing Countries: An Introduction to their Collection and Analysis", Unesco Office of Statistics, Paris 1983. See in particular Sections 2.4 and 5.2.5.

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To summarize we may say that, despite the fact that the Grade Transition Model assîmes homogeneous behaviour and thus disregards restrictions on grade repetition, this model yields results for Indicators A.l -A.3, C.3 D.l and D.2 whicn are normally rather insensitive to violations of this hypothesis. As these are the indicators most commonly used, this conclusion lends rather strong support to continued use of this quite simple model for deriving this type of indicator.

I EXERCISE VT §

: Using the results from the hypothetical cohorts constructed in the : : previous exercise, the participants will calculate the 12 cohort flow : : indicators explained above. :

II.3.5 Apparent Cohort Method

As explained above, to use the Grade Transition Model for reconstructing cohort flows, we need data on enrolment and repeaters by grade. When data on repeaters are not available, a method referred to as the Apparent Cohort Method is often used to estimate both the drop-out between grades and the survival of the cohort to successive grades in successive years. The approach is similar to that of the Grade Ratio Model or Grade Retention Model used for projecting enrolment by grade, confer the presentation of this model in Section II.4.14. As data on repeaters are available for Kenya the Apparent Cohort Method will be reviewed only briefly below.

The Apparent Cohort Method compares the enrolment in successive grades in successive school-years and assumes that the decline in enrolment between two successive grades in two subsequent school-years represents drop-out. For example, Table 2.3 gives the enrolment by grade in primary education in Kenya for the two school-years 1980 and 1981. Applying the Apparent Cohort Method we estimate the following surival rate between Grades 1 and 2:

342,150 Survival between Grades 1 and 2 : x 100 = 78.0%.

438,703

Thus according to this method, 78% of the cohort would reach Grade 2, i.e. 22% would drop out prior to this grade. Based on data on enrolment in Grade 3 in 1981, we could estimate the survival of the 1980 cohort to that grade, an so on for the survival to subsequent grades if we have data for later school-years. (1)

(1) In seme cases such survival rates are even calculated on the data for one single year. For example, employing the data for 1981 given in Table 2.3, this approach would estimate the survival until the final grade of primary education as:

87

Obviously, as the Apparent Cohort Method ignores repetition, the extent to which its estimates of cohort survival will correspond to the actual level of survival depends, inter alia, on the level of the repetition rates, it can also be shown that in cases where repetition takes place, even estimates based on time-series data on enrolment are affected by the rate of growth of new entrants. If there is no repetition, then the Grade Transition Model will be identical to the Grade Retention Model and the two models will give the same estimates of cohort survival.

Enrolment in Grade 7 in 1980 149,856 ; = • 0.34 or 34.2%

Enrolment in Grade 1 in 1980 438,703

This would imply that only 34.2% of those enrolled in Grade 1 in 1980 in Kenya would reach Grade 7 (not graduate) as compared to 48.6% given by the Reconstructed Cohort Method, see Figure 6.

This application of the Apparent Cohort Method on data for one year only is not to be recommended. In particular, it should not be employed for developing countries where the enrolment in primary education is generally growing rapidly. Under such conditions this method will grossly over-estimate drop-out. This is so because the enrolment in Grade 7 in 1980 does not depend on Grade 1 enrolment in that year but on Grade 1 enrolment in 1974 (as well as on the repetition and drop-out rates in all the 6 grades).

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Further, it can be shewn that the Apparent Cohort Method gives reasonably exact estimates of drop-out between grades and survival if the repetition rates are of very similar magnitude (1). However, the method will generally overestimate drop-out between two grades if the repetition rate in the first of these two grades is larger than in the second.

To summarize, the Apparent Cohort Method, based on time-series data, can be used to estimate drop-out and survival by grade in cases where one knows that there is no repetition. This method may also be used when the repetition rates are quite low, provided that their magnitude does not vary much between grades, the Apparent Cohort Method may over- or under-estimate considerably -the level of drop-out. For a country such as Kenya, where the level of repetition is high the Apparent Cohort Method is not appropriate as it does not give a good estimate of drop-out.

It should be noted that the Apparent Cohort Method can at best be used to estimate the three indicators of retention by grade presented in Section II.3.4 (i.e. Indicators A.1-A.3). None of the remaining 9 indicators can be estimated. As the level of repetition is not taken into account by this method, it can naturally not provide estimates of enrolment by years of study, average duration of studies or level of wastage.

Finally, it is important to realise that the estimates of drop-out and survival by grade derived on the basis of the Apparent Cohort Method are not comparable to the drop-out and promotion rates defined in Section II.2.6. Rather, the former two measures should be compared with the figures given in the line of boxes shown at the foot of Figure 7 denoted "survival by Grade". The promotion and repetition rates describe annual changes in enrolment stocks while estimates of cohort survival rates refer to what eventually happens to cohort members.

EXERCISE Y H

Based on the data on enrolment by grade shown in Exercise IV, use the Apparent Cohort Method to estimate drop-out by grade. Compare the results thus obtained to those calculated in Exercise VI for the evolution of the four corresponding cohorts. Explain why the two approaches give different results.

(1) This has been shown in: B. Fredriksen: Internal Efficiency of School Systems: A Study in the Use of Pupil Flow Models for Developing Countries, op. cit., Chaper V.

89

SECTION 4 : USE OF FLOW MODELS FOR PROJECTING ENROLMENT BY GRADE

II.4.1 Introduction

We have in the previous two sections described how to estimate sane flow rates (i.e. the promotion, repetition and drop-out rates) and have shown how, on the basis of these rates, we may reconstruct the flow of a cohort through a cycle of education. In this section we shall show how we may use the same technique to project the future enrolment of pupils by grade. Similar to the analysis of cohort flows, we shall also in this section present two models, one which requires data on repeaters and one which does not.

II.4.2 The Role of Education Projections in Educational Planning

Projections of the future number of pupils enrolled constitute the starting point of quantitative educational planning, as they provide the basis for estimating the future need for teachers, classrooms and other facilities. In Part III of this paper we shall give an example of how they may be used as a basis for estimating the future requirements for teaching staff.

In its simplest sense, the "projection" would be used only for exercises of the extrapolation into the future of past trends. Thus enrolment projections would inform us about how many pupils would be enrolled at some future time, assuming no changes in the educational system with past trends continuing unchanged in the future. The objective of such projections would be to give the planner a basic frame of reference for the future. Against this frame the planner could judge the validity of the assumptions behind the model, or the effects of changes in the parameters such as repetition, promotion and drop-out rates. Thus, to emphasize what has already been said, a projection of this type is not a forecast (except in the unusual circumstances that the changes expected to occur in the structure of the system or its parameters exactly replicate past changes).

In practice projections as actually made by educational planners are developed both through the extrapolation of certain unchanged trends, and by assuming particular changes in one or more of the others. This compromise allows the planner explicitly to take into account changes in educational policy during the period.

Hence enrolment projections are best understood as conditional forecasts of new entrants, total enrolments, and of leavers, as well as of the future structure of the educational system.

II.4.3 Preparing an Enrolment Projection

Four factors determine the future enrolment by grade in a given cycle of education : (1)

(1) Note that a fifth factor, the rate of drop-out, is not independent of the rates of repetition and promotion: the three rates must sum to unity. Note also that the factors are here specified as being independent in relation to the flow of students through an educational cycle. It is well known that where promotion from one cycle to another is in some sense selective, such an administrative restriction of the promotion rate may well result in a higher rate of repetition in the grades preceding the selective hurdle, in which case the rates might not be independent of each other.

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(a) the population of admission age;

(b) the admission rate to the first grade;

(c) the rates of repetition at different grades;

(d) the rates of premotion at different grades.

These four factors determine the inflow of students into the cycle, the manner in which they proceed through the cycle up to the planning horizon and the numbers of successful completers of the cycle in successive years. When applying the Grade Transition Model, all these flows are taken into account. The great advantage of this model is that it clearly demonstrates the role played by policy variables in determining the future development of enrolment. For planners should regard rates of admission/ drop-out and repetition as policy variables. They are capable of regulation in the pursuit of a country's welfare objectives. They are not exogenous, uncontrollable factors in the light of which other adjustments have to be made. Even the population of admission age is potentially influenced by avaiable policy measures, such as family planning or reduction in childhood mortality rates through better health care. The great potential for reduction of these rates will have profound long-term implications for the whole educational system's development.

In order to project the enrolment by grade for some future date, a minimum set of data must be available. In the context of the four factors (a) - (d) listed above, this data set will be:

(a) a projection over the plan period of the age-group corresponding to the admission age;

(b) a projection of the number of new entrants to Grade 1 of primary education;

(c) an estimation of the repetition rates, grade by grade, over the period;

(d) a similar estimation of the promotion (and hence, as a residual the drop-out) rates.

As regards the population of entry age, projections will generally be available to the educational planners, prepared by the national services responsible for demographic data collection and projections. In some cases the projections available refer to five-year age-groups and the planner may have to employ techniques such as Sprague multipliers to distribute the population in each of these five-year age-groups by single years of age. This technique is explained in Section II.4.4 below.

When projections of the population of admission age are prepared, the next step is to project the proportion of this age-group which will enter school in future years. An accurate projection of the new entrants is of crucial importance as this will affect the enrolment in all subsequent grades in the following years. In Sections II.4.5 to II.4.8 we shall discuss projection methods as well as several practical problems encountered when projecting new entrants to primary and secondary education.

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When projections of the number of new entrants are available for the pian-period, the next step is to project the progression through the educational cycle of these new entrants as well as of the pupils enrolled in each of the grades in the base year. Employing the Grade Transition Model, this may be done for given assumptions for the future development of two of the three flow rates for each grade (i.e. the promotion, repetition and drop-out rates). We shall discuss this further in Sections II.4.9 to II.4.13).

When data on repeaters are not available, we have to resort to a simpler (and less satisfactory) model for projecting enrolment by grade. We shall in Section II.4.14 discuss the use of one such model.

II.4.4 The Use of Sprague Multipliers for Estimating the Distribution of Population by Single Years of Are

It is frequently the case that certain demographic data are not available. In such circumstances, a number of techniques may be used for their estimation. For example, educational planners and statisticians may not have population data referring to inter-censal or post-censal years. In such cases methods of interpolation or extrapolation respectively are necessary. A problem frequently met is the estimation of the population by single years of age using data which are often more commonly available in the form of five-year age-groups. This process of interpolation may be perfomed by using the method of Sprague, multipliers.

This method uses sets of basic tables of co-efficients, or multipliers. In all, five sets of multipliers are needed, one for smoothing the "mid panels1, one for each of the "end panels", and one for each of the "next-to-end panels", follows:

Age-groups

0 - 4 end panel 5 - 9 next-to-end panel 10 - 14 etc. mid panels

85-89 90-94 next-to-end panel 95 - 99 end panel

In educational planning the high age panels are, of course, generally of little or no interest. The first three panels, however, are those required to estimate single years of age data for calculating enrolment ratios and estimating the size of the school intake.

Assume F is the number in the age-group under consideration and F , F o +1 +2,

F , the numbers in the three following age-groups. F and F are the +3 -1 -2 numbers in the two preceding groups. Further, assume that F , F , F , F and F ,

a b e d e represent respectively the first, second, third, fourth and fifth ages of each five-year group. The table of Sprague multipliers may be presented as in Table 2.5:

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Table 2.5 : Sprague Multipliers

•

: First table

: F : a

: F : b

: F : c

: F : d

: F : e

.•Second

: F : a

: F : b

: F : c

: F : d

: F : e

table

intermediate

F : F - 2 : -1

+0.0336

+0.0080

-0.0080

-0.0160

-0.0176

: F : o

+0.3616

+0.2640

+0.1840

+0.1200

+0.0704

+0.2272

+0.2320

-0.2160

+0.1840

+0.1408

: F : +1

-.02768

-0.0960

+0.0400

+0.1360

+0.1968

+0.0752

+0.0480

+0.0080

+0.0400

+0.0912

: F : +2

+0.1488

+0.0400

-0.0320

-0.720

+0.0848

+0.0144

+0.0080

+0.0000

-0.0080

-0.0144

F +3

-0.0336

-0.0080

+0.0080

+0.0160

+0.0176

1 table

: F : a

: F : b

: F : c

: F : d

: F : e

-0.0128

-0.0016

+0.0064

+0.0064

+0.0016

+0.0848

+0.0144

-0.0336

-0.0416

-0.0240

+0.1504

+0.2224

+0.2544

+0.2224

+0.1504

-0.0240

-0.0416 0

-0.0336

+0.0144

+0.0848

!

+0.0016 :

+0.0064 :

+0.0064 :

-0.0016 :

-0.0128 :

By way of illustration of the techinque, assume we wish to estimate for 1981 the number of boys aged seven years for Kenya given only the numbers of boys in the following five-year age-groups as estimated in that year (1)

0 - 4 age-group : 1,867.7 5 - 9 age-group : 1,415.3 10 - 14 age-group : 1,092.4 15 - 19 age-group : 871.2

(1) Source: See Table 1.6

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Using the second table of Sprague multipliers (the lower next-to-end panel, as defined above), the numoer of seven-year-olds will be derived using the multipliers shown against the line F . It will be the sun of the products

c of each multiplier by the site of the corresponding age-group. Thus the number of seven-year-olds may be estimated to be:

0.0080F + 0.2320F - 0.0480F + 0.0080F -1 o +1 +2

= (0.0080 x 1,867,700) + (0.2320 x 1,415,300) - (0.0480 x 1,092,400) + (0.0080 x 871,200)

= 14,942 + 328,350 - 52,435 + 6,970 = 297,«27

Thus, we have estimated that in Kenya in 1981 there were 297,827 boys aged six years old.

: EXERCISE VIII

: Table 1.6 gives the following data for the number of girls

Age-group

0 5 10 15

- 4 - 9 - 14 - 19

: Using the method of Sprague multipl : number of girls aged seven years in

Population

1,857,800 1,418,000 1,104,800 881,700

Lers and Table 2,5, Kenya in 1981.

in Kenya

estimate the

in 1981:

II.4.5 Methods of Pronectina New Entrants

It is of crucial importance to determine as accurately as possible the new admission to Grade 1, as this will influence the enrolment in all subsequent grades in the following years. Normally countries do not directly collect data on the number of new entrants, and these data are derived by subtracting the number of repeaters in Grade 1 for a given year from the enrolment in this grade for the same year. Thus, in countries where repetition is permitted, data on new entrants to Grade 1 can only be derived if data on repeaters are collected. Again we see the crucial importance for educational projections and planning of collecting these types of statistics. Apart from their use for analyzing wastage and for projecting the flow of pupils between grades, repetition data for Grade 1 are indispensable for reliable and consistent projections of new entrants, particularly if the repetition rate in this grade is relatively high. Without such information it is not possible to distribute the enrolment in Grade 1 between repeaters and new entrants. In particular, we cannot know when all children of a particular age-group have entered school.

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There are many possible methods for projecting new entrants, and the one to be chosen for a particular case depends mainly upon the data available for the country in question, the age distribution of the new entrants (i.e. do some of them come from ages other than the legal admission age?) and the proportion of the admission age-group entering school.

In a country where all new entrants start school at the same age, the number of new entrants to the educational system in a given year depends on the number of children of admission age and the proportion of this age-group which enters school (the intake rate). Assuming that all children start school at the age of 6, the number of new entrants in year t may be expressed as:

t t t (23) N = e P ,

6 6 6

t where N = number of new entrants aged 6 years in year t;

6

t e = proportion of 6-year-olds entering Grade 1 of primary 6 education in year t;

t P - population aged 6 in year t. 6

It is desirable to project the number of new entrants separately by sex. The pattern of admission is generally quite different for boys and for girls, particularly in developing countries.

In developed countries where practically all children enter school at the official age, the estimation of the future new entrants is mainly a question of estimating the future population of admission age. For developing countries, the situation is quite different. A large proportion of those chidren eligible for primary education are generally not enrolled and late entrants, i.e. entrants older than the official age of admission, are common. For countries having a rather low proportion of the children of admission age entering school, it may be sufficient to project directly the number of new entrants without relating it to the size of the population of admission age. However, in general it is desirable to use a model which takes explicitly into account the development of the admission age-group. This is particularly so for a country such as Kenya, where there has been a major effort in recent years to universalise the provision of primary education, and where as a consequence the intake rates have changed very drastically, see Figure 8. During such a period where the new intake increases much more quickly than the population of admission age, it is very important to take explicitly into account the growth of the population of admission age when projecting new entrants. If not, it is impossible to know when the capacity is sufficient to cater for everyone. As this is an important aspect for the projection of new entrants in Kenya in the future, we shall discuss it in some detail below.

95

In cases where new admissions are drawn frcrc several age-groups, starting by age 5, the number of new entrants in year t may be expressed as:

l=n t t t t t t t , t t

(24) nurnoer of new entrants N = e P + e P + . . . + e P = > e P , 5 5 6 n n / . i i

i=5

where :

t N • total number of new entrants in year t

t P = population aged i years in year t i

t e = proportion of population aged i years in year t i entering school that year

n = highest age from which new entrants are drawn.

To employ this formula requires tine-series on new entrants by single years of age. Such data are generally not available in developing countries. The most common approach is. therefore, to base the projection of new admission on the following equation;

t t t (25) N = e P

6

where N and P have been defined above and where e is the apparent intake rate in year t. We see that this ratio is derived by dividing the total number of new entrants in a given year, regardless of age, by the population of legal admission age, here assumed to be the population aged 6 years.

One of the weaknesses of basing the projection of new entrants on equation (25) is that the apparent intake rate may exceed 1, i.e. the number of new entrants may exceed the population of admission age. This may be seen by combining equations (24) and (25) which gives:

U6) t

e =

t P

t 5 e

5 t P

6

+ t

e + 6

t P

t 7 e

7 t P

6

+

t t P P

t 8 t 9 e + e + . . .

8 t 9 t P P

6 6

+

t P

t n e

n t P

6

96

t Since the maximum size of the e is 1 in the case where all 6-years-olds

enter school, entrance of children older or younger than 6 years will render e < 1. The apparent intake rate may of course also exceed 1 even if all 6-year-olds are not entering school in cases where there are a considerable number of under-agea and/or over-aged children among the new entrants. This situation is common to many developing countries. However, as will be demonstrated by a numerical example during the seminar, the apparent intake rate cannot exceed unity during a long period since after a while there will be no late entrants left to enter school.

If we have time-series data on new entrants by single years of age, this enables us to verify when all children from a single cohort have entered school, and thus to estimate the size of the pool of potential late entrants from successive cohorts. For if we consider the intake rate for a single cohort in successive years, it is obvious that the following constraint must hold good:

t t+1 t+2 t+3 t+n-5 < (27) e + e + e + e + . . . + e = 1 .

5 6 7 8 n

In other words, this inequality means that not more than 100% of a given cohort can enter school.

Where the age distribution of new entrants is available, two possible methods of projection of new intake suggest themselves. The first one would consist of extrapolating the past trends in each of the intake rates by single years of age included in formula (26), verifying afterwards that the constraint defining a new set of proportions based on the remaining part ot each age-group that has not so far entered school, and then projecting these new proportions. Both methods will be discussed further at the seminar.

To summarize, the projection of new entrants is particularly difficult for a country which is approaching universal intake to primary education following a period of very rapid enrolment expansion. In such a case, the projection should be made at a disaggregated level to take into account the fact that seme administrative areas and regions have already reached universal intake while others have not. Furthermore, some areas and regions will have reached universal intake for boys but not for girls. The national projection is then obtained by adding up the various projections made separately for each area or region.

II.4.6 Projecting New Entrants for Kenya

The projection of new entrants to primary education in Kenya involves one major complication. That is, the new entrants are drawn from a large number of age-groups. In 1981 for instance only 36.3% of the pupils enrolled in Grade 1 were 6-year-olds (the official age for admission is six years) and 3.5% were 10 years or older. The proportion of enrolment outside the official admission age-group was even higher in 1979 and 1980, see Table 2.6. As the level of repetition is high the age-distribution of the new entrants will correspond quite closely

97

Table 2.6 : Percentage-Distribution by Are of Grade 1 Enrolment

Both sexes. Kenya.

1979 1980 1981

: School- :

: year : 6 7

Age (in years)

8 9 10 11 12 13+ Total :

34.7 37.3 42.1 33.4 36.3 37.7

17.1 15.1 16.8

6.4 5.5 5.7

2.7 1.0 2.3 0.8 2.1 0.8

0.5 0.5 0.4

0.3 0.3 0.2

100.0 100.0 100.0

SojiEEÊ.: Statistics Unit, Ministry of Education, Science and Technology. Nairobi, Kenya.

to that of the total number of pupils (i.e. new entrants plus repeaters enrolled in Grade 1. The complication that this wide age-span causes in the projection of the future numoer of new entrants has been reviewed in the previous section.

Another common complication in projecting new admission to primary education in developing countries is an irregular development of the intake rate in the years following the major drive towards UPE. In Kenya, this would start from 1974 with the elimination of school fees for the first 4 grades and finally for all grades in 1979, and with the introduction of a free school mild programme. The consequence in terms of new entrants and intake rates is shown in Table 2.7. Based on the results given in the last two columns of this table, Figure 8 illustrates the development of the intake rates for boys and girls between 1970 and 1981. Following a period of fairly slow growth between 1970 and 1973, the rates incrased sharply, registering an intake rate of 1.213 for boys and 1.093 for girls in 1977. The level of new admissions continued to rise until 1981 when the intake for boys reached 1.247 and that of girls 1.171. The total intake rate for boys and girls was 1.209, which means that the total number of new entrants exceeded the size of the population aged 6 years by some 21%. Clearly, there has been a rising trend in the intake rate over the period covered.

98

Table 2.7 : New Entrants, Population of Admission A œ an

1 1 Year 1 1

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981

Source :

Apparent Intake Rates, by Se*. W O - i m Kenya

1 New Entrants | Population Aged 6 years I 1 1 Boys 1 160,329 165,616 191,568 200,314

• • • • • • • • •

299,992 297,489

• • • 330,616 371,336

- 1 Girls | Boys

1 127,122 184,100 130,973 192,500 154,745 200,500 166,458 207,600

215,400 224,100 235,100

268,259 247,400 264,266 258,300

270,200 318,940 283,100 350,097 297,700

New entrants: Calculated from data grade supplied by th Technology.

Population: Derived

• - -Girls |

1 185,100 193,600 197,200 205,800 215,300 225,700 236,700 245,400 257,600 270,600 284,500 298,900

d •

Apparent

Boys

0.871 0.860 0.956 0.965 • • • • • • • • •

1.213 1.152 • • •

1.168 1.247

Intake Rate I 1

I Girls I 1 1

0.687 0.677 0.785 0.809 • • • • • • • • •

1.093 1.026 • • •

1.121 1.171

on enrolment and repeaters by Statistics Unit, Ministry of Education

on the basis of populatj

, Science and

Lon estimates and project :ions prepared by the United Nations Population Division (1980 Assessment).

Note that the UN estimate for 1979 for the population aged 6 years is about 1% higher than that obtained by using the results from the 1979 population census published by the Central Bureau of Statistics.

It is clear from figure 8 that the past development of the intake rate followed a regular trend. The projection of future admission to primary education in Kenya may therefore be based on the past intake rates. In Section II.4.7 we shall suggest sane factors which should be taken into account if the past development of the intake rate does not follow a regular trend and more specifically if the trend cannot be prolonged into the future by means of conventional statistical extrapolation techniques.

For an aggregated analysis of the present type, it is possible to take as a starting point for our projection of new entrants the fact that Kenya's policy objective is to achieve and maintain UPE. According to the five year Development Plan, UPE was targetted to be achieved in the 1979/83 plan period. As shown in Table 2.2, a gross enrolment ratio of 114.8 was achieved in 1980. As the level of repetition if fairly high, this means that the capacity of primary school was not sutficient to enrol all children of primary school age i.e. the age-group 6-12years. It should be kept in mind that to achieve and maintain UPE implies enrolling all children of admission age as well as maintaining them enrolled for the full 7 year duration of primary education.

99

Figure 8: Apparent Intake Rato to Grade 1 of Primary Education. Boys and Girls. Kenya. 1970-1981

1300

t zoo

\ 100

\oco

!00

100

boo

S00

too

- _ _ /

-I l_ -J 1 1_ ^r -> iUO iin i1?V iWt, 197? Hfù i<\?l

Ye».r

SoOfcC . I s_/Je. <' , 7

100

In the case of Kenya, total primary education enrolment has "bulged" twice over the last decade. The first time was in 1974 (observed) when school fees were first eliminated for Grades 1 to 4. In 1978, many of these pupils were in Grade 5 and those who never repeated and did not drop out completed primary school at the end of 1980. The second "bulge" was in 1979 when primary education was made free in all grades. The 1979 primary school admissions could complete their primary education by the end of 1985 again if they do not repeat or dropout. Seen in isolation, there may be a drop in the enrolment ratio in 1986 (confer the illustration given in Section II.4.13 of this report). However, in the case of Kenya, this may be be explained by the fact that the high enrolment ratio experienced over the decade was to cater for the children who were of admission age prior to 1974 and 1979 but did not enter school. As shown in Table 2.7, the apparent intake rate for both boys and girls rose to around 120% in 1981.

The apparent intake rate of more than 100% cannot be maintained indefinitely because this would imply that cumulatively the number of children entering school for the first time will exceed the corresponding school age population. Practically, we would expect the number of over-age pupils enrolling in Grade 1 to be reducing over subsequent years. This would cause the apparent intake rate to fall gradually to 100%. Although for the country as a whole, the apparent intake rate exceeds 100%, it is likely that in North Eastern Province and Turkana, SamDuru and Narok districts of Rift Vally Province, where enrolment ratios are much lower than the national average, the apparent intake rate is also much lower, (probably still less than 100%). Consequently, the process whereby the apparent intake rate for the country drops gradually to 100% is rather complex, since in some districts it may be dropping whereas in other it will be rising. This implies that in the districts which are presently less developed in terms of enrolment ratios and apparent intake rates these ratios and rates may not yet have peaked, and this may extend the time required for them to stabilize at around 100%. Hence the apparent intake rate for the country as a a whole will remain over 100% until these particular districts have caught up with the others.

It is worth noting at this stage a few factors which make it particularly difficult and sometimes costly to provide education for the last 5-10 % of the admission-age-group. To illustrate the consequences of one particular development pattern, Table 2,8 qualifies the implications of gradually reducing the intake rate for boys and girls from their 1981 level to attain 100% in 1987. It should be stressed at the onset that this projection as well (as that to be presented in section II.4.13 on enrolment by grade) is presented here purely as an illustration of how to employ a particular technique.

101

Table 2.8 : Implications of Attaining 100% Intake to Grade 1 of Primary Education by 1987. Kenya.!)

: Year

: Intake rate 2)

: Boys : Girls

: Population aged : 6 years 3)

: Boys : Girls •

-, New Entrants :

: Boys : Girls : » • • • •

1981 1982 1983 1984 1985 1986 1987

1.247 1.206 1.165 1.123 1.083 1.042 1.000

1.171 1.142 1.114 1.085 1.057 1.028 1.000

297,700 313,100 327,300 342,100 357,700 375,200 393,300

298,900 310,300 325,500 341,500 358,400 375,400 389,200

371,336 377,599 381,305 384,178 387,389 390,958 393,300

350,097 354,363 362,607 370,528 378,829 385,911 389,200

1) See explanations in text 2) Obtained by linear interpolation between the 1981 and 1987 values. 3) For source, see note to Table 2.7

Tne results have been obtained by assuming that the intake rates for boys and girls will decrease from their 1981 levels to attain unity in 1987. The values for the intervening years have been obtained by interpolating linearly between the 1981 and 1987 values. Multiplying the rates thus obtained by the population aged 6 years gives the estimates of new entrants shown in the last two columns of Table 2.8.

Tne calculations show that to arrive at a situation in 1987 where the intake rate is 1,000, the number of new entrants would need to increase from 721,433 in 1981 to 782,500 in 1987. This represents an increase of 8% over the 6-year period or an annual rate of increase of about 1%. This low rate of growth is naturally due to the observed high apparent intake rates that Kenya has already attained. As the over-aged primary pupils are phased out gradually over the years, the gross enrolment ratio will tend to fall to 100%. The implications of Kenya's high intake rate will be discussed further in the seminar.

EXERCISE IX :

Using data to be made available during the seminar, participants will : project new entrants for selected provinces in Kenya. :

102

II.4.7 Some Factors-Affecting the Développent of New Entrants

We have examined above, from a purely technical point of view, problems encountered when projecting new entrants. As already explained, it is of crucial importance to determine as accurate as possible the new admissions to Grade 1 as this will influence the enrolment in all subsequent grades in the following years. In general, to project the future development of new entrants for a country which has not yet reached a stage of strictly compulsory education is not an easy task. A number of factors governing the supply of and demand for education have to be taken into account. We shall briefly mention a few such factors below.

First of all, the planner must take into account changes in factors influencing the willingness of parents to enrol their children in school, provided that schools are available, e.g.:

(a) Improvements in the accessibility of schools to the population in rural areas (e.g. building of roads, provision of free school transportation and provision of hostels and boarding facilities);

(b) changes in the costs for parents of keeping their children at school (e.g. changes in fees, provision of free textbooks, school uniforms and school meals).

Secondly, the planner must take into account changes in government regulations as regards the number of children eligible to enter school (e.g. changes in the legal age of admission and changes in regulations which limit the intake of children outside the official admission age-group).

In addition to the above factors governing the number of children who will seek to enter primary education, the planner must take into account factors determining the number of school places available. Among such factors we mention:

(a) the amount, and distribution between regions and sub-groups of the population, of the resources available for building new schools and for training and hiring teachers;

(b) special programmes for increasing the provision of schools to population groups which traditionally have school attendance below the national average. This is quite an important point for countries approaching universal intake. Experience from many countries shows that to enrol the last 5-10% of the children belonging to population groups which, due to their area of residence, ethnic and/ or socio-economic background, have traditionally benefitted less from education than other groups. To serve such groups may require special measures such as boarding schools for nomads and populations living in sparsely populated areas, efforts to reduce the direct as well as the opportunity costs to parents of sending their children to school, adapting the curriculum to the special needs of certain population groups, and so on. In the context of Kenya nomadic groups, such as the Masai and Turkana who rely on their children for herding activities, may need mobile schools.

103

(c) changes in laws and regulations which influence the availability of places for new entrants to primary education (e.g. changes in regulations governing repetition in Grade 1);

(d) changes in the provision of competing types of education. For example, in projecting the new entrants to public schools in a country where children may choose between public and private education, the planner must take into account the future provision of such education.

It should be noted that it is very difficult to give any general rules for how these factors should be taken into account. First of all, the approach would differ a great deal depending on the particular situation which one faces. Secondly, it is very difficult to quantify the relationships between some of the above-mentioned factors and the number of entrants to primary education. These aspects will be discussed further during the seminar.

Naturally, for a country which has already implemented strictly compulsory primary education, the problem of projecting new entrants to this level of education is reduced to one of projecting the size of the population of admission age. However, the factors listed above are still highly relevant for the projection of new entrants to various streams of secondary education and for education at the third level. In the next section we shall briefly review same of the special problems one is likely to encounter when projecting new entrants to secondary education.

II.4.8 Some Special Problems Encountered in Projecting New Entrants to Secondary Education

The methods of projecting new entrants to primary education reviewed in the previous section are, in general, also applicable to secondary education. For example, on the basis of data on enrolment and repeaters in the first grade of secondary education, we may establish a time trend in new entrants to this level. An intake rate to secondary education may be calculated by relating the new entrants in a given school-year to the graduates from primary education at the end of the previous school-year. Projections of this intake rate combined with projections of the number of graduates from primary education will give projections of new entrants to secondary schools.

However, special problems are frequently experienced when projecting the new admission to secondary schools, particularly because pupils may choose between different streams of secondary education and because their choice is often restricted by capacity limits in certain parts of the school systems. Thus, factors of the type discussed at the end of the previous section take special importance when projecting new entrants to secondary schools. We shall briefly illustrate some of these problems below.

As already mentioned above, in most countries, the schooling pattern is determined by a combination of the pupils' demand for education and the supply of school places. There are strong reasons to believe that capacity limits will be of great importance in many developing countries in the years to come, particularly in secondary education. One reason for this is that since enrolment in primary education is rising rapidly in many countries, the number of pupils wanting to enter secondary education may increase considerably. However, since secondary education is relatively costly, many countries may not be able to satisfy the increase in demand. This may in particular be the case in some streams of secondary education which will appear especially attractive from the point of view of future job opportunities.

104

We shall limit our discussion here to illustrating how capacity limits affect the development of new entrants for a country where there are three different streams of secondary education (1,2 and 3), with capacity in the first grade to accept C , C and C new pupils respectively (in addition to

1 2 3 the repeaters). In a given school-year, assume that N , N and N new pupils

1 2 3 would liKe to enter each of the three streams, where:

N > C ,N < C , N < C . 1 1 2 2 3 3

Thus, there is too little capacity in Stream 1 to admit all applicants who have Stream 1 as their first choice, while the capacity in Stream 2 and 3 seems to be larger than required.

As a consequence of the capacity limits, no more than C pupils will 1

be 1 allowed to enter Stream 1. Thus, for this stream there is no need to project the new entrants since they are known to equal the available capacity. However, the existence of capacity limits for Stream 1 will complicate the projection of new entrants to Streams 2 and 3 since same of the pupils barred from entering the stream with restricted admission may have second preference for one of the two unrestricted streams. It may thus easily happen that e.g. Stream 2 may get more applicants than it can accomodate, so that admission control must be introduced even there. As a consequence of this, Stream 3 may get seme "overflow" from Stream 2. In such a situation, the level of intake rate of primary education to the first grade of Stream 1 will be less than in a non-restricted system, while it would be higher for the first grade of Streams 2 and 3. The introduction of admission control may also affect the promotion and repetition rates for other grades.

How the introduction of capacity limits will actually affect the development of new entrants will to a large extent depend upon the selection rules for the restricted stream, and the behaviour of the applicants as well as the behaviour of the applicants who have been rejected admission. We shall briefly discuss each of these three points below.

The selection rules applied for choosing the entrants to secondary education may vary considerably between countries. For example, some countries base the selection on performance in primary education, e.g. on the

105

results of the final exam in the last grade of the cycle, or on special entry exams to the first grade of secondary education. Alternatively, the selection has been based on random drawing, the age of the applicants, or on quotas for each primary school or each region.

The behaviour of applicants in the case of capacity limits depends to some extent on the selection rules. For example, in the case of selection being made on the basis of primary school examination results, some potential entrants to the restricted stream may be so discouraged that they do not apply at all for entry to this stream if they know that their marks are below entry requirements in previous years. These pupils may then apply for entry to streams where they are more sure to be accepted. The application bahaviour may also depend on factors such as the regional distribution of the limited capacity.

An applicant who has been refused admission to the restricted stream in a given year has several choices depending on the particular educational system. For example, he/she may repeat the last grade of primary education to improve his/her results, try to enter an unrestricted stream, drop out temporarily, trying to enter later on, or drop out permanently.

We shall not pursue this example further. It is easily understood from the above discussion that we need statistics on factors such as applicants, new entrants, behaviour of pupils who are refused admission, etc. in order to take into account the effects of capacity limits. Other complications exist as well. For example, in practice pupils often choose not only between alternative streams of education, but also between different individual schools in each stream. Among the reasons for this is that the quality of the school may differ considerably. The graduates of the best schools may have good prospects of being able to enter higher education later on, and may also have good chances in the labour market, while the opposite applies to the graduates from the poorer institutions. For these reasons, a pupil may not prefer all schools in one stream of education to all schools in another. He may, for example, have a good general secondary school as his first preference, a good vocational school as his second, and a poor general secondary school as his third. Obviously, in such a case, one needs a much more complicated model than the one outlined above.

In Kenya, secondary education has expanded very rapidly to cope with the demand for it from primary school graduates over the last two decades. However, it has, admittedly, not been possible for the educational system to cater fully for the educational needs of the population. The high demand for secondary education has facilitated the development of three types of secondary schools in Kenya. First, there are the fully government maintained schools, then there are assisted schools which in most cases are community initiatied (or Harambee schools) and finally, there are private or unaided schools. Out of the 35% primary school graduates who find places in secondary schools, only 12% find places in government maintained schools. The other 23% are admitted in Harambee or private schools. The share of Harambee and private in total secondary school enrolment has been increasing over the last decade and is expected to continue increasing.

106

The Government's fourth national Development Plan 1984-88 gives relatively low priority to the expansion of secondary education (1). It is clearly indicated in the 1984/88 Development Plan that the increase in demand for secondary education is expected to be met by Harambee and private schools while development of physical facilities and all boarding costs will be the responsibility of local communities and parents. It is also indicated that emphasis will be on day schools as they are less expensive, and emphasis of development will shift from physical expansion to the provision of both post-primary and post-secondary levels of greater training opportunities for those who are not able to proceed with further formal education.

It is not the purpose here to review the past and prospective future development of secondary education in Kenya. Our main concern is limited to discussing methods of projecting new entrants. In the case of Kenya, the number of new entrants to the first grade of secondary education (Form I) is determined by the available capacity in this grade. Thus a projection of new entrants must be based on the Government's plans for expanding this capacity rather than on a statistical extrapolation of the intake rate. This rate, measured in terms of the percentage of pupils in Grade 7 in 1980 who transferred to Form 1 in 1981 was 35.3%.

Generally, access to secondary education in Kenya is largely determined by the total number of Form 1 places available in the country. Strictly, it does not depend on the number of schools available in any district of province. The quota system in operation only applies to a handful of national schools whose total intake is insignificant compared to the total intake of the non-national schools. However, in practice, areas with more schools are apt to enrol more students from the local areas resulting in higher gross enrolment ratios from that district compared to others. This is particularly possible in Harambee and private schools.

II.4.9 Projecting Enrolment by Grade Using the Grade Transition Model

Whereas demographic factors condition the future development of new entrants and thus of enrolment in Grade 1, enrolment in subsequent grades is determined by non-demographic factors governing the flow of pupils through the educational system. As illustrated in previous sections of this part of the paper, a large number of the pupils admitted to the first grade of an educational cycle in many developing countries do not complete that cycle within the prescribed minimum period. Some of them drop out before the end of the cycle and seme repeat one or more grades before either dropping out or completing the last grade successfully. Whatever opinion one may have about the actual benefit derived by pupils from the time spent at school before dropping out, or the value or repetition, both these factors have an important influence on the development of the total enrolment in a given cycle and on

(1) See: Republic of Kenya: Development Plan 1984-1988, Nairobi, p. 149-150.

107

the distribution of this total by grade. When estimating future enrolment in a cycle, it is therefore very important to take into account the future development of the promotion, repetition and dropout rates of this cycle.

In mathematical terms the Grade Transition Model may be expressed as:

t+1 (29) E

1

t+1 (30) E

g+1

t+1 (31) N

1

t (32) G =

m

t+1 = N

1

t t = p E

g g

t+i = e

t t g E

m m

+

+

t+1 P a

t t r E 1 1

t t r E g+1 g+1

(g = 2,3, ...., m-1)

where:

t E = enrolment in Grade g, year t g

t N = new entrants to Grade 1, year t 1

t P = number of children of admission age, year t a

t G = number of graduates from the final grade of the cycle, year t m

t e = apparent intake rate

t t p , r = promotion and repetition rates, Grade g, year t g g

t g = graduation rate for Grade m, year t m

m = the final grade of the cycle.

108

To project enrolment by grade using this model we need to project the future developments of the number of new entrants as well as the promotion and repetition rates for each grade. We have already discussed at some length how the new entrants can be projected. In this section we shall review different methods of projecting the transition rates.

In general we may say that there are three different ways of approaching the problem of projecting the future development of the transition rates depending, mainly, on the purpose of the projection exercise, namely:

(i) Using Constant Rates

This approach, for various reasons, is often applied in developing countries. Firstly, it is interesting to know what would be the implications of maintaining constant the rates observed in the last year for which data are available. Secondly, the rates observed may be relatively "acceptable" to the government and/or there may be no plans for introducing measures designed to affect their future development. Thirdly, the data available on repeaters may cover one year only, either because the collection of such data was only recently started, or because the data collected for previous years are not relevant any more, due, for example, to drastic changes in educational policy. Finally, even in cases where data on repeaters are available for several years, the estimated premotion, repetition and drop-out rates may have remained relatively stable in the past. If there are no plans for changes in educational policy, one may assume that this stability will be maintained during the plan perioud. Thus, one may keep constant the rates observed for the last year, or if the past rates show small fluctuations, calculate an average over the last few years.

(ii) Extrapolation of past trends in Transition Rates

Obviously, in real life situations, most transition rates tend to change. This may be due to policy measures, such as introduction of measures designed to reduce repetition and drop-out, introduction of new laws or enforcement of existing ones concerning compulsory school attendance, and so on. It may also be caused by increased public funds to the educational sector, or by changes in demand for education due, for example, to improved living standards, increased employment opportunities for educated manpower, etc.

In sane cases the effects of such policies may lead to gradual changes over time in the transition rates and an educational planner may be interested in deriving the future implications of continuing these trends. Many possible approacnes are available for this, depending on the data availabe, the nature of the trends and mathematical function chosen. (1)

(1) For a discussion of various methods of projecting changes in transition rates, see Chapter V of T. Thonstad, in co-operation with the Division of Statistics on Education, Unesco Office of Statistics: Analysing and Projecting School Enrolment in Developing Countries : A Manual of ot Methodology, Unesco, Paris 1980.

109

(iii) Targets for the Future Development of Transition Rates

Frequently educational plans contain targets for the future development of sane or all of the transition rates. Sometimes these targets are formulated in rather general terms, for example "the repetition and/or drop-out rates will be reduced during the plan-period". Other times they are more specific and quantify the level of the rates to be attained in the final year of the plan or even the development for each of the years covered by the plan. For such targets to be meaningful, the plan should specify which measures will be taken to obtain the desired changes in the rates.

When targets of the above type exist, it is always interesting to quantify their implications in terms of the future development of enrolment. This can easily be done applying the Grade Transition Model.

It is often desiraole to make several projections to derive the implications of different patterns of future development of the transition rates. The final projection selected for the plan may be the result of a mixture of all the three approaches discussed above as regards the future development of the transition rates, i.e. some rates may be left constant, others may be extrapolated, while still others may be based upon targets.

II.4.10 Some Effects of Capacity Limits on Transition Rates (1)

In Section II.4.8 we have already discussed some effects of capacity limits. The purpose of this section is to illustrate briefly how the introduction of (or changes in already existing) capacity limits in one part of the educational system may lead to changes in a number of transition rates.

The most important capacity constraints in developing countries often occur between primary and secondary education. For the purpose of illustration, we shall give an example. Suppose we want to project enrolment in a country where there are no capacity limits in primary education, but where capacity is too low compared to demand in the first cycle of secondary education. (To simplify the example we assume that this first cycle is composed of only one stream). This implies that only a certain proportion of the applicants to the first grade of secondary education can be admitted, i.e. some type of admission control is required. We shall discuss how such limitations affect the observed transition rates. The effects may be more widespread than one might expect, e.g.:

(1) The discussion in this and the following section is partly based the document by T. Thonstad mentioned in footnote (1) on the page 108.

110

(i) The intake rate to the first grade of secondary education will be lower than it would have been had there been no admission control. Tnus, this rate not only reflects the preferences of the pupils for continuing their education beyond primary education. It is also affected by the limited capacity at the second level.

(ii) The repetition rate in the last grade of primary education may be higher than it would have been in an unrestricted system since pupils may repeat in order to try to gain admission to secondary education, or to the best secondary schools, later on. As a matter of fact, extremely high repetition rates are observed in the last grade of primary education in many developing countries, particularly in Atrica, but also in seme countries in Asia and Oceania.

(iii) If the selection mechanism for admission is according to ability, one would expect that the pupils admitted to secondary education would perform better on the average than those who are barred from entering. Thus, the drop-out and repetition rates in secondary education are probably reduced, compared to a situation with free admission. This would, for example, mean that if admission control cuts the number of entrants to secondary education to half of what it would have been in an unrestricted system, the number of graduates may be cut by less than 50 per cent.

How should the existence of such admission control be taken into account in the projections of the transition rates? First of all, if the number of pupils gaining admission to secondary education is constant, this fact should be directly used in the projections. Furthermore, if the number of graduates from primary education is increasing over time, and faster than the intake capacity to the first grade of secondary education, this implies that the intake rate to secondary education will decline over time. Note in this connection that the intake capacity to the first grade in secondary education also depends on the repetition rate in this grade. Any changes in this rate will affect the number of places available to new entrants in cases where the total number of pupils in this grade is fixed.

In the above example we did not mention the fact that in many developing countries, the supply of schools differs considerably between regions, in particular between urban and rural areas. For example, in many countries, the primary schools in rural areas do not provide all the grades at the primary level. This implies that the children, after having completed the highest grade provided by the local school, have to transfer to another school, often

Ill

much further away, if they want to continue their education. Some countries also have two cycles of primary education, and many rural schools only provide the first one. In cases where complete primary schools exist, there is sometimes very low capacity in the upper cycle. Furthermore, secondary schools are often much more scarce in rural than in urban areas.

In cases where the supply of schools differs much between different areas, one should preferably use different transition models for each area. Doing that, one can explore the effects of capacity limits in a meaningful way. Note that when applying regional models, one would have to account for transfers between the regions.

In addition to the effects of capacity limits discussed above, a few other points deserve mentioning. First of all, if there are a large number of pupils seeking, but not obtaining, admission to public schools, this may, after a while, lead to increased supply of private schools. Secondly, it may also lead to political pressures upon the authorities, by parents demanding better educational facilities or their offspring. Thus, it is important to try to evaluate how school budgets may be influenced by the demand for education. Thirdly, educational capacity is rather flexible, and a lack of capacity can often be overcome by reducing the quality of education. For example, teacher-pupil ratios may be reduced, the school facilities may be used in the evenings (double shifts), less teaching material may be spent per pupil, and so on. Furthermore, resources may be shifted from other streams of education, by lowering educational coverage or quality in these areas. Consequently, the capacity in a given grade is, to a large extent, determined by decisions about the above variables (in particular the teacher/pupil ratios).

* * * * * * * * *

In the pupil flow model presented in this paper, the capacity limits of schools are not taken directly into account. The problem here is not however to design a model which takes such limits into account. The real problem is to collect the statistics required to estimate the coefficients of such a model.

II.4.11 Examples of Changes in Educational Policy which may affect the Transition Rates

One of the great advantages of the Grade Transition Model for educational planning is that if we manage to quantify the effect of a particular policy action on the transition rates, this model may be used to quantify the implication of this action on the future development of enrolment and graduation. This in turn makes it possible to examine the effects of given policy changes on the future needs for teachers, on costs, as well as on the supply of qualified labour. This point is of particular relevance to developing countries in an attempt to relate in a better way the structure, content and teaching methods to national needs rather than to foreign models, as well as to take better into account new developments within educational research.

112

Many different types of changes in educational policy are likely to affect the transition rates. To illustrate this point we list below some policy measures which are likely to influence the promotion, repetition, graduation and drop-out rates. We shall distinguish between policy measures having a direct impact on transition rates, and measures having only indirect impact, through their influence on pupil behaviour. The distinction is by no means sharp, but most of the measures listed under points (i) and (ii) below belong to the first group, and most of the rest belong to the second. It should further be noted that, as discussed in Sections II.4.7 and II.4.8, some of these measures may also influence intake to primary and secondary education.

Tne measures may be classified as follows:

(i) Changes in the Structure of the School System, e.g.;

(a) The introduction of new types of course, for example a new stream of secondary education will usually result in changes in the rates describing the transition from primary schools to the streams of secondary education which existed prior ro this changes. An example of this is the introduction of the 8+4+4 system of education in Kenya from 1985.

(b) If a certain course is abolished, the pupils who would otherwise have taken the course may choose other streams of education. One example of this is the present tendency of moving the training of primary school teachers from secondary to higher education. Naturally, the abolition of teacher training at the second level will lead to relatively more students seeking other types of secondary education which will qualify them for entering teacner training later.

(c) If the number of grades in a given cycle of secondary education is changed, or if previous courses are amalgamated into one, several transition rates will be changed.

(d) A common change in the education system of many developing countries is to change the "break-off" point between two cycles, for example, changing a 7 + 4 system to a 8 + 4 system, the first cycle being primary education and the second being the first cycle of secondary education. Such a change might affect several transition rates, and in particular the promotion rate between grades 7 and 8.

(e) Some countries have two cycles of primary education, and are now trying to change into one covering both of the previous cycles. One of the effects of this can be an increase in the promotion rate between the last grade of the lower cycle and the first grade of the higher cycle.

(f) Switches from a system of separated specialized courses to comprehensive education, or vice versa, may have considerable effects upon the transition pattern. For example, there may be changes in the grade at which specialization begins.

113

(g) Changes in the legal age of entry, for example, lowering the admission age for primary education from 6 to 5 years, will, if respected, lead to one new cohort being eligible for entering primary education. If introduced from one school-year to the next, this would imply enrolling two cohorts in the year of change instead of one. Naturally, such a change may be implemented over a longer period, implying that each year during this period the number of new entrants would exceed the population aged 5 years. If, on the other hand, the age of entry were to be raised, during a certain period this would tend to reduce the enrolment in the lowest grades.

(h) Increasing the duration of compulsory education, for example, from 7 to 8 grades, would increase the promotion rate between Grade 7 and 8 and might reduce the repetition rate in Grade 7, while increasing it in Grade 8, which will now be the final grade.

(ii) Changes in the Promotion Policy Within a Given Cycle or Grade

A change from promotion based on tests to automatic promotion has obvious consequences for the transition rates in the grades where the change takes place, and may even affect transition rates in other grades. As introduction of automatic promotion is a policy option considered by many developing countries these days, in the next section we shall briefly review the arguments commonly brought up for and against repetition. That section will also proviae an illustration of how the Grade Transition Model may be used to examine the effects on enrolment and graduation of abolishing repetition.

(iii) Changes in the Policy with Respect to School Costs for the Pupils

Whether school fees exist or not in a given stream of the education system, and their magnitude, obviously affects demand for education. Furthermore, the level of fees in one stream of education may affect demand in other streams (cf. differences in fees between private and public schools). Similarly, whether the pupils must purchase the teaching material themselves or not and whether they receive free meals or not, affects demand. Several studies on wastage stress such factors. (1) Similarly, the existence and size of scholarships is also important. Economic incentives are often used in order to affect school participation by social class, ethnic group, sex, and so on.

(1) See for example references p. 25 in The Problem of Educational Wastage Bulletin of the Unesco Regional Office for Education in Asia, Vol. I, No 2, Marcn 1967.

114

(iv) Changes in Pupil/Teacher Ratios. Improved Teacher Qualifications

Decreases in pupil/teacher ratios may be caused by smaller classes, more teaching hours per pupil or lower teaching loads. All these factors, in particular smaller classes, probably contribute towards reducing drop-out and repetition, since each pupil can receive better attention. However, the effects are somewhat uncertain. The same applies to improvements in teacher qualifications. (1)

(v) Changes in Curricula

Changes in curricula to relate the content of the education provided less to foreign models and more to the national needs, is a priority target for many developing countries. Such changes will generally influence the transition rates but the effects are often very difficult to assess in quantitative terms.

(vi) Changes in Teaching Methods

Tne new trends towards changes in teaching methods, e.g. grouping of pupils into groups of varying size according to the specific needs of pupils and subject, use of teacher assistants, use of educational television and radio and so on may affect transition rates. Again, the effects of such changes are uncertain and difficult to assess in quantitative terms.

(vii) Changes in the Language of Instruction

Many developing countries have a large number of languages of which, at best, only a few are used as medium of instruction. Many countries are, for various reasons, still using the language of the former colonial power as medium of instruction at all levels of education. Some studies on wastage indicate that if the instruction in the first grades at the primary level is not given in the mother tongue, the chance of drop-out and repetition is higher. In higher grades some pupils may prefer instruction in the language most frequently used in secondary and higher education and not necessarily in their mother tongue. The high priority currently given in many developing countries to the provision of education in the mother tongue may hence lead to changes in transition rates.

(viii) Changes in the Location Pattern of Schools

Several studies on wastage demonstrate the importance of distance from the home of the child for his/her educational attendance. In many developing countries only schools covering the first few grades are available in many villages in rural areas. This problem has already been mentioned in Section II.4.10.

(1) For a review of research results with regard to the effects of class size see: W. D. Haddad : Educational Effects of Class Size, World Bank Staff Working Paper No 280, Washington June 1978.

115

(ix) Changes in the Time-Pattern of Attendance

Changes in the required pattern of school attendance obviously influence transition rates. School regulations may require attendance every workday or only a few days a week, schools may have day classes, evening classes or a shift system, and may or may not have schooling during agricultural harvest seasons. Because the children in many developing countries participate in the farm or business of their parents, a proper choice of the required attendance pattern may increase school attendace and reduce drop-out rates.

* * * * * * *

In principle, all of the policy changes mentioned above may influence the transition rates of an educational flow model. To try to estimate these influences is therefore very important for the projection of the changes in enrolment due to the policy changes. Also, for computing the resource needs resulting from the policy measures, such projections are indispensable. But it must be admitted that it is often very difficult to estimate the effects on transition rates of policy changes. As as example, in the next section we shall discuss possiole effects of introducing automatic promotion.

II.4.12 An Example of How the Grade Transition Model can be used to Examine Effects of Policy Changes; Introduction of Automatic Promotion

In most developing countries a considerable amount of repetition takes place in primary as well as in secondary education. (1) Usually, repetition is high because a certain level of attainment is required in order to be promoted to the next grade, i.e. a system of attainment promotion is applied. Some countries have however introduced automatic promotion between some or all grades of a cycle, implying that pupils having spent one year in a grade are automatically promoted to the next. We have already reviewed in Section II.3.4 (in connection with the discussion of the indicators of wastage in education) some of the arguments for and against repetition as a means of helping slow learners. In this section the purpose is to show how one can project the effects on transition rates and enrolment of such a policy.

Tne first point to be noted in this connection is that there are several variants of automatic promotion and different versions of the Grade Transition Model should be used for projecting enrolment in each case. Below we shall distinguish between three different definitions of automatic promotion.

(i) Automatic Promotion Combined with Compulsory Attendance

Tnis type of automatic promotion between Grades g and g+1 implies that (a) repetition is not allowed in Grade g, and (b) attendance is strictly compulsory, so that there is no drop-out from Grade g. Under these conditions the repetition and drop-out rates for Grade g are both zero, implying that the promotion rate equals unity, see Section II.2.6.

It automatic promotion of this type is applied to all grades of a six-grade primary education system, we can project enrolment by using a very simplified version of the Grade Transition Model. Using the symbols of Section II.4.9, this gives for a six-grade primary cycle:

116

t+1 E =

1

t+1 E

g+1

t G

6

t+1 N

1

t = E

g

t = E

6

(33) E = E (g - 1 , , 5)

Introduction of automatic promotion of this type in a number of subsequent grades will, in the short run, have positive as well as negative effects upon enrolment in these grades. Take as an example Grade 3. Due to the introduction of automatic promotion in Grade 2, Grade 3 will receive more entrants from Grade 2 than in the case when pupils repeated Grade 2. On the other hand, Grade 3 will lose seme pupils because those who would otherwise have repeated are now promoted to Grade 4.

It automatic promotion of the above type is applied to all grades of primary education, a larger proportion than before of each cohort of entrants will reacn a given grade, including the final grade of primary education. Thus, if there is limited capacity in the next cycle of the system, the promotion rate from primary to secondary school may have to be reduced (see our discussion of this aspect in Section II.4.10). Furthermore, since the average attainment level of the graduates from primary education may be lower than in a system based on attainment promotion, there may be tendencies towards increased repetition and drop-out in secondary education (if automatic promotion is not practiced there as well).

(ii) Automatic Promotion Without Compulsory Attendance

Tnis is less strict an interpretation of automatic promotion than than given under point (i) above. It implies that (a) repetition is not allowed and (b) pupils are automatically allowed to enter the next grade, but are not forced to do so. This means that the repetition rate is zero, but some pupils may for various reasons drop out even though they are permitted to proceed to the next grade.

In this case, the form of the Grade Transition Model which can be used for projections of enrolment is slightly more complicated than in case (i) above, but simpler than in the case with repetition. For a six-grade primary education system with automatic promotion in all grades, we have:

t+1 t+1 E = N 1 1

t+1 t t (34) E = p E (g = 1, .....5)

g+1 g g

t t t G = g E 6 6 6

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It one wishes to estimate the effects upon future enrolment of introducing such a system, the crucial point is to find out what happens to the pupils who woiua otherwise have repeated the grade, i.e. whether they proceed to the next grade or drop out.

(iii) Both promotion and attendance are voluntary

This is the least strict of the three interpretations of automatic promotion discussed in this section. It implies that (a) nobody is forced to repeat but may choose to do so, and (b) nobody is forced to stay on in school. In this case we need the same type of Grade Transition Model for Projections as when there is attainment promotion, see equations (20)-(32) in section II.4.9. However, the transition rates will change since, contrary to the case of attainment promotion, all who have completed a grade will be allowed to enter the next grade.

* * * * * * * *

Tne above concludes our illustration of how the Grade Transition Model may be used to examine the effects of introducing automatic promotion. To conclude this section we emphasise that the transition from a system with attainment promotion to a system with automatic promotion will usually take place gradually. Furthermore, the practices may not necessarily correspond to the rules and intentions. For example, even in a system where repetition is generally ruled out, a pupil who has been absent during a large part of a school-year may nevertheless be allowed or required to repeat the grade. In some cases, various disadvantages of automatic promotion become apparent and after a while there may be pressures from the schools wanting to reintroduce the possibility of repeating grades. Such reversals of policy have been observed in some countries (e.g. Costa Rica, Egypt, Singapore and Venezuela).

Finally, it should be mentioned that a system of automatic promotion may eventually be replaced by continuous progress instruction, by which each child proceeds at his own pace. With such a system the concept of "grade" as a principle of organization or grouping of pupils is no longer relevant. The term can still refer to the level of achievement reached by an individual but not to the class group he is placed in. Indeed, the individual pupils need no longer be placed in a school class in the traditional sense of the word. Pupils will be grouped together in various ways for various purposes and much basic learning will be given through individually prescribed study assignments. For a school system arranged in this way, the projection models discussed in this document are not directly applicable.

II.4.13 Projecting Enrolment by Grade for Kenya

Returning now to the problem of projecting enrolment by grade by means of the Grade Transition Model, Figure 9 illustrates the various computational steps one needs to take.

The boxes in the top row of the flow chart show the enrolment in the base year for this projection, i.e. 1981. The figures refer to both sexes together. Normally, it is preferable to make projections separately for boys and girls. However, in the case of primary education in Kenya, the intake and transition rates are very similar for the two sexes. We have therefore, for the purpose of this illustration, chosen to make a combined projection.

118

The projections of new entrants shown in the column on the left-hand side are taken from Table 2.8. In order to project the enrolment by grade for years after 1981, assumptions had to be made with respect to the future development of the flow rates. The level of repetition as recorded in official statistics is high in Kenya. It is likely that this rate may decrease in the future. The level of dropout is quite high in Grades 1, 4 and 6. Drop-out is caused by a complex set of factors which operate internally as well as externally to the school system. The extent to which these rates can be reduced significantly during the next few years will depend largely on the resources available to the primary school system as well as on the parents' possioilities and interest in maintaining their children at school.

Since the projections to be presented here are mere illustrations of how to apply a certain technique, and as there are no obvious reasons why the transition rates would change significantly during the next few years, we shall assume that the rates will remain constant at their 1980 level. As can be seen from Table 2.9, the transition rates have fluctuated considerably between 1977 and 1980. Figure 10 has been computed on the basis of the average transition rates of the years 1977 and 1978 to level out these fluctuations.

The projection exercises include the following three steps:

(i) enter the data for the base year (normally the latest year for which statistics are available, in this case 1981) in the top row of the flow chart;

(ii) enter the projected number of new entrants in the column in front of the boxes for Grade 1. In our case, the projected numbers of new entrants are taken from Table 2.8;

(iii) apply the flow rates given in Table 2.9 to the figures given under points (i) and (ii). For example, the enrolment in Grade 2 in 1982 is found by adding the number of pupils promoted frem Grade 1 in 1981 and the number of pupils repeating Grade 2 from the same year. Those promoted equal the enrolment in Grade 1, i.e. 844,508 x 0.680 = 574,265. The number of repeaters equals the enrolment in Grade 2 in 1981 multiplied by the repetition rate for this grade, i.e. 704,999 x 0.123 = 86,715. Thus, the projected number of pupils enrolled in Grade 2 in 1982 equals 574,265 + 86,715 = 660,980.

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Figure 9 : An Illustration of the ffle of tfte

<?ra<fe Transition Model

for Projecting Primary School Enrolment in Renva.

Both Sexes (Alternative

AÏ see explanations in text)

II rs

111

120

Table 2.9 Rates of Promotion. Repetition and Dropout by Grade in Primary Education in Kenya; Both Sexes. 1977-1980.

Grades : Promotion : Repetition : Dropout :

: '77 : '78 : '79 : '80 :'77 : '78 :'79 :'80 :'77 : 78 : 79 :'80 :

.749

.871

.855

.«05

.823

.803

.864

.882

.960

.959

.880

.874

.802

.847

.580

.718

.727

.703

.700

.630

.686

.680

.769

.824

.810

.854

.721

.867

.062

.057

.056

.055

.065

.082

.136

.111

.107

.105

.100

.092

.127

.153

.263

.269

.259

.262

.253

.313

.314

.136

.123

.128

.130

.130

.158

.133

.189

.072

.089

.140

.112

.115 -

.007 -.067 -.064

.020

.034

.071 -

.157

.013

.014

.035

.047

.057 -

.184

.108

.048

.060

.016

.121 -

1) Figures on promotion at Grade 7 include dropouts.

Source; Calculated on the basis of data made available by the Statistics Unit ot the Ministry of Education, Science and Technology.

Following the same approach we may project the enrolment in the remaining grades in 1982, except for Grade 1 where we add the number of new entrants to the projected number of repeaters. When the enrolment has been projected in this way for all grades in 1982, we repeat the same procedure for 1983 and so on for the remaining years of the projection period.

Tne projection method will be explained further at the seminar. Before ending this section we should however, like to point out once again the important role in the projection of new entrants plays in determining total enrolment. Figure 9 shows clearly that the longer the period covered by the projection, the more important is this role. For example, in the final year included in this example (i.e. 1987) the enrolments in Grades 1 to 5 depend almost entirely on the projected development of new entrants during the period 1982-1987.

Columns (3) and (4) of Table 2.10 show the implications of the projections given in Figure 9 in terms of total enrolment and gross enrolment ratio for primary education. The figures for total enrolment are obtained by adding up, year by year, the enrolment by grade shown in Figure 9. The gross enrolment ratio is derived by dividing the figure for total enrolment thus obtained by the number of children aged 6-12 years given in the second column. The projections shown in Figure 9 have been referred to as "Alternative A". As explained above, this alternative is based on constant promotion, repetition and dropout rates (as observed in 1980), and a linear decrease in the apparent intake rate, from its 1981 observed value of 120.9% to 100% in 1987, see Table 2.8. We note that this would imply a decline in enrolment between 1981 and 1987, when the enrolment ratio would correspond to only 89.4% of the population of primary school age.

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Alternative A thus implies that the gross enrolment ratio in Kenya will fall between 1981 and 1987. This is explained by the fact that the enrolment "bulge" caused by the very high intake in 1974 leaves primary education in 1985.

Table

m • • •

: Year :

• - - •

(1) 1981 1982 1983 1984 1985 1986 1987

2.10 : Alternative Projection of Primary Enrolment and

Enrolment Ratip for Kenya

Population aged

1) 6-12 years

(2) 3,588r000 3,762,300 3,943,600 4,131,500 4,326,800 4,538,100 4,754,000

,1981-1987.

2) : Alternative A

• • • • : Enrolment : • •

(3) 3,981,162 4,038,027 4,095,462 4,155,263 4,208,986 4,235,279 4,249,441

Gross Enrol­ment Ratio

(4) 111.0 107.3 103.9 100.6 97.3 93.3 89.4

3) Alternative B

• • Enrolment :

•

(5) 3,981,162 4,082,370 4,173,467 4,279,058 4,417,397 4,528,163 4,618.745

Gross Enrol ment Ratio

(6) 111.0 108.5 105.8 103.6 102.1 99.8 97.2

Source : United Nations Population Estimates and Projection (1980 assessment).

1) Derived by applying Sprague Multipliers to the united Nations Population Projections (1980 Assessment).

2) Taken from Figure 9. Alternative A is based on constant transition rates as observed in 1980 (see Table 2.9) and a linear decrease in the apparent intake rate, from the 1981 observed value of 120.9% to 100% in 1987, see Table 2.8.

3) Alternative B is based on the average transition rates for 1977 and 1978 and the assumption that the intake rate will decrease from its 1981 level of 120.9% to 100% in 1982. See figure 10 and explanation in the text.

Columns (5) and (6) of Table 2.10 show the enrolment and enrolment ratios resulting from a projection where the transition rates remain constant at the average of their 1977 and 1978 levels, but where the intake rate is assumed to decrease from its 1981 level of 120.9% to 100% already in 1982. This projection has been labelled Alternative B. We note that under this alternative the enrolment ratio would decline from 111.0% to in 1981 to 97.2% in 1987, and as long as dropout rates are higher than zero, UPE will not be attained. Tne main reason is naturally that UPE means admitting all children to school and retaining them there for the complete 7-year duration of the primary cycle. As shown in Section II.3,2, the 1980 promotion, repetition and dropout rates imply that only about 49% of those entering primary education in that year will reach Grade 7. In short, to reach UPE will require efforts to increase the holding power of the Kenyan primary schools.

122

Figure 10 t An

Illustration of the use of t

he grade transition model for

Projecting Primary School Enrolment in Kenya. Both sexes.

(Alternative B)

r-.. O

en CO

r* t> *

423

m

r-* m

.12

JS "• c

' *"

4^ -•

o"

it

123

1) II.4.14 Projecting Enrolment by Grade using the Grade Ratio Model

As already explained, to employ the Grade Transition Model requires data on enrolment and repeaters by grade. In this section we shall present the data on enrolment by grade only. The model is generally referred to as the Grad& Ratio Model or the Grade Retention Model and may be expressed as follows:

(35) E t+1 î 1

t+1 (36) E

g+1

t t r E + 1 1

t t k E g g

t+i N

(g = i,. *m)

wnere

= enrolment in Grade g in year t,

t+1 N = new entrants to Grade 1 in year t+1, 1

= repetition rate in Grade 1 in year t

= grade ratios i.e. ratio between enrolment in Grade g+1 in year t+1 and enrolment in Grade g in year t

m = the final grade of the cycle

Equation (35) gives enrolment in the first grade of the cycle in the same manner as in the Grade Transition Model. This procedure requires data on repetition in Grade 1. As lack of data on repeaters by grade is often the main reason for using this simplified model, such data may not be available for Grade 1 either. This may make it necessary to resort to more approximate methods for projecting enrolment in the first grade of the cycle. One way would be to directly project Grade 1 enrolment based on past trends, not distinguishing between new entrants and repeaters. This would naturally be a

(1) This section is based on Fredriksen: "The Use of Flow Models for Projecting the School Enrolment in Developing Countries", in Methods of Projecting School Enrolment in Developing Countries, CSR-E-19, Unesco Office of Statistics, Paris 1976.

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less satistacotry approach, particularly in the long run, as the future development of the new entrants should be related to the development of the population of admission age. Confer in this connection the projection of new entrants for Kenya in Section II.4.6. In that example, the projected development of the population of admission age played a crucial role in determining the future development of the new entrants. It is therefore often preferaoie to use whatever information is available to estimate the repeaters in Grade 1 and hence use equation (35) to project Grade 1 enrolment. If possiDie, sampie surveys should be undertaken to arrive at estimates of Grade 1 repetition. New entrants may then be projected employing one of the methods reviewed in Section II.4.b.

Tne enrolments in each grade higher than Grade 1 are expressed as a coefficient (the grade ratio) multiplied by the enrolment in the grade below in the previous year. Much of the weakness of using this model is related to the interpretation and projection of the future development of these ratios. To facilitate the discussion of this aspects, it is useful to derive the relationship between the grade ratio for a given grade and year and the promotion and repetition rates (used in the Grade Transition Model) for the same year. This can be done by comparing the formulae for enrolment in a given grade obtained by the two different models. We shall use Grade 2 as an example. Employing the Grade Transition Model, the enrolment in this grade mat be expressed as, see equation (30):

t+1 t t t t (37) E = p E + r E

2 1 1 2 2

i.e. it equals the number of pupils promoted from Grade 1 plus the repeaters.

Putting the right-hand sides of equations (36) and (37) equal to each other we obtain:

t t t t t t (38) kE = p E + r E ,

11 11 2 2

t Dividing by E on both sides of this equation gives:

1

t E

t t t 2 (39) k = p + r _ :

1 1 2 t E 1

Equation (39) shows that if the repetition rate is zero, the ratio between the enrolment in two successive grades in two successive years will equal the corresponding promotion rate. In this case, the projection of the grade ratio for future years is facilitated since we know that its maximum value is 1, provided the repetition rate remains equal to zero in the future too. If, however, the repetition rates are far from negligible, the grade ratio may be consiaerabiy larger than the corresponding promotion rate, and it may exceed unity. This complicates considerably the projection of the future development of this ratio.

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Equation (39) also shows that the effect of the repetition rate upon the grade ratio depends on the ratio between the enrolment in two successive grades. If this latter ratio is large, this pulls in the direction of a higher grade ratio, thus increasing the difference between the promotion rate and the grade ratio for a given grade.

It should be noted that the Grade Patio Model is not suited to analyzing implications of changes in educational policy, since the most important parameters, depending on educational policy (promotion, repetition and dropout rates), are not included explicitly in the model. This is a serious weakness.

Tne reader should note that the equations of the Grade Ratio Model referring to all grades higher than Grade 1 are based on the same principles as the Apparent Cohort Method used for Estimating dropout and survival by grade in Section II.3.4. In that section we interpreted the grade ratio as the survival rate between two successive grades, the decrease in enrolment between these two grades in two successive years being taken as dropout. It should be noted in this connection that the shortcomings of the Grade Ratio Model when used in Projecting enrolment are of a different nature to those encountered in Section II.3.4 when estimating the survival between grades of a cohort. In the latter case we imply that the difference between unity and the grade ratio represents enrolment projections. Thus, the model may still yield acceptaole projections even when it is not found acceptable for estimating dropout. This aspect will be discussed further at the seminar.

EXERCISE x

Based on the results derived from Exercises IV and IX, the participants will project the enrolment by grade in primary education for each of the regions covered in Exercise IV.

II.4.15 Concluding Remarks on Part II

In this part of the paper we have discussed the use of flow models for projecting school enrolment by grade. Before leaving this topics the following four points should be stressed:

(i) Althougn the discussion in this part has mainly been limited to primary education, models of this type are equally useful for analyzing the flows of pupils in secondary and higher education, provided the required data on repeaters and transfer between different types of education and fields of study are available.

(ii) It is of great importance to the education planner that he should know how a separate change in any of the factors such as intake, promotion and repetition rates will affect future enrolment and output. When the effects of separate influences are known, the planner may attempt to manipulate them in order to achieve the objectives of educational policy.

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Tnus enrolment projections should always present several alternative possible futures, each based on a particular set of assumptions. There is, of course, an infinite set of different combinations of varying assumptions. The particular sets chosen will be those which, in the planner's judgement, seem most realisteic and useful in the light of alll availaole information. A comprehensive analysis of enrolment in elementary education, for example, would further investigate at least the following:

(a) the effects of differing projections of population

(b) the effects of utilising age-specific intake rates rather than the apparent intake rate,

(c) the effects of differing assumptions about the future development ot intake, promotion and repetition rates. In this connection the importance of collecting annual data on repetition by grade cannot be overstressed,

(d) the distribution of enrolment by regional, provincial or even smaller administrative areas, and, very important, by sex.

(iii) The quality of a projection depends ultimately on the quality or the data on which it is based. In presenting the models above, we have in several cases pointed out gaps in the data available particularly as regards the lack of data on repeaters. An advantage ot flow models, however, is that they point to the priorities in future improvements in data collection and analysis.

(iv) Finally, more sophisticated mathematical and statistical techniques for the development of flow models exist. They cannot, however, be included in an introductory paper such as this. In any case, the effective use of more advanced models cannot be expected in the absence of better data. An efficient national system of educational and demographic data collection is, therefore, of highest priority.

As already mentioned in the introduction to this part of the paper, projections of the future number of pupils enrolled often constitute the starting point for educational planning as they provide the basis for estimating resource needs, and as they may indicate to what extent targets for the development of education systems are likely to be met. Projections of this type are particularly suitable for detecting problems, constraints and inconsistencies inherent in given policies. They do not pretend to indicate the most probaole or desirable future development. On the contrary, the continuation of past trends may lead to results judged highly undesirable by the responsiole authorities. In such a case, conditional projections may serve as a warning signal for the autorities, by indicating a need for policy, decisions which would change prevailing trends. It follows frcm this that if, as a consequence of government intervention to change prevailing trends the actual results differ frcm the projections, this does not mean the projections were wrong. Their main function was to indicate a need to change the trends by showing that the implications of their continuation would be in contradiction to stated national educational objective.

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In this part of the paper we have presented sane models for making the type of projections described above and in Section II.2.4, we have listed certain advantages of using mathematical models for the preparation of such projections as opposed to less formal modes of reasoning such as the purely verbal one. However, this does not imply that mathematical models present only advantages and it may be appropriate to end this part of the paper by a word of warning with regard to their applicability.

Firstly, it should be noted that there are many issues of educational policy which do not at all lend themselves to quantification and analysis by means of mathematical models. This point may be illustrated by mentioning the fact that a model of this nature of course cannot answer the question whether or not to teach e.g. religion at school or whether or not to use the vernacular language as the medium of instruction. At best these models might provide a tiny piece of the total information required to make such decisions in as much as they may be used to shed some light on the costs of different choices.

Secondly, there are other issues where our present knowledge of the learning process is too limited to make it possible to formulate and quantify mathematical models. As an example we mention our discussion in Section II.3.4 of the effects of grade repetition on pupils' school achievements.

Thirdly, even in cases where models can be and are applied, they are merely simplified representations of reality and if these approximations are not good enough the mathematical structures of the models may not approximate reality sufficiently. Moreover, the data available to estimate the parameters of these relationships may not be sufficiently reliable.

For the above and other reasons, results derived from mathematical models should not be used uncritically, but should be employed together with other evidence and judgments. Also, an indispensable prerequisite for successful use of such models is a thorougn knowledge of the structure and functioning of the educational system to which the model is being applied. All too often mathematical models are presented in a way which does not sufficiently emphasize their role as possiole providers of information which, together with other data, may assist policy makers and planners in making informed decisions.

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PART III : TOE PROJECTION OF TEACHER SUPPLY AND DEMAND

SECTION 1: CHARACTERISTICS OF THE TEACHING STOCK •

III.1.1 Introduction

In order to assess the future needs of teaching manpower, a preliminary analysis of the current teaching force (size, composition and distribution) and the way in which teachers are deployed should be made. This is because in the short and medium terms the bulk of future teacher supply will consist of teachers continuing in service from the present, or base, year. The number of additional teachers required will thus consist of the difference between the total future size of the teaching force, on the one hand, and the numbers of present teachers continuing in service on the other. The importance of knowing the composition of the stock of teachers stems both from the fact that this may be deemed unsatisfactory in some respects (balance in respect of sex, subject specialisation, qualification, nationality, etc.), so that future policies on teacher supply should be directed to righting the situation; and from the fact that teachers with different characteristics may have varying propensities to continue in service, so that in projecting future teacher supply, allowance should be made for differential wastage rates. The actual deployment of teachers is directly related to estimates of future need, since shortages of teachers may be reduced or intensified by changing the way in which teachers are used in schools. This last point relates directly to the question of pupil/teacher ratios.

Once future teacher stocks have been projected according to explicit assumptions, the planner may compare these stocks with estimated teacher requirements for the education of the projected future students. A variety of possiDie policies may be adopted to ensure that the required teachers will in fact be available when needed. Among such policies, perhaps the most obvious and important are those concerned with programmes for training new teachers. But the teacner demand-supply balance can also be affected in a number of other ways, througn policies on reducing teacher wastage, resorting to alternative supplies of teachers, altering class sizes or teaching loads in the schools and so on.

Tne characteristics of the stock of teachers in terms of age, sex, qualification, locality, years of service and other variables are often availaoie, even where data more explicitly concerned with flows of teachers are not. Ideally, in order to obtain an understanding of the dynamics of the situation (that is, how the stock alters through time), statistics concerning movements of teaching personnel should be continously collected. Such movements would include both those internal to the stock (promotion, changes of institution, etc.), and external (concerning entry into, and exit from the teacning stock). Estimates of future stocks could then be made by adding and substracting future flows from the evolving stock.

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ni.1.2 DescEjpttop of the Teaching stogk; in Kenya

The pupil/teacher ratio is often considered an important indicator of the quality of the education provided, the basic assumption being that a low ratio means small classes, enaoling the teachers to pay more attention to individual pupils. The relationship betwen the level of the pupil/teacher ratio and the quality of the education provided is, however, far from being straightforward. Firstly, as discussed in Section III.2.3, the same pupil/teacher ratio may correspond to different class sizes, depending on teaching load and the average numoer of hours per week the pupils receive instruction.

Secondly, the effect of instructional group size on the quality of education is far from obvious. Although a number of studies have been conducted to determine the relationship between class size and pupil achievement as measured by a variety of standardized tests, the research evidence in this area is far from being conclusive (1) An important factor in this connection is, of course, whether the benefits derived from smaller classes justify the additional costs. Small classes in themselves do not guarantee better teaching through more individualized programmes. It seems that more important than class size is what the teacher does with the opportunities the size of the class offers for learning. The scope of effective ways of teaching in large classes, using modern teaching techniques and aids, has not been exhausted.

Thirdly, althougn the pupil/teacher ratio within a given country may vary consiaeraoiy between different regions, one often finds what one may call "compensating mechanisms" at work, with urban areas on average being able to attract better qualified teachers but having larger class sizes and the outlying areas having poorer teachers but smaller classes. However, notwithstanding the above arguments for not giving too much importance to the size of the pupil/teacher ratio, it still remains that this is an important indicator.

Table 3.1 shows the number of pupils and teachers as well as the pupil/teacher ratios for primary and general secondary education during the period 1970-1981. As regards primary education, we note that the enrolment growth during the drive towards UPE between 1975 and 1979 was parallelled by some growth in the number of teachers. Thus, while enrolment increased by 38% during this four-year period, the number of teachers increased by 29%.

We note that the overall growth of the number teachers in Kenya has been slower than the growth in the number of pupils. This has resulted into a rising trend in the pupil/teacher ratio as shown in Table 3.1. The pupil/ teacher ratio in primary schools has been worsening and the introduction of the 8-4-4 education system is likely to aggravate the situation. It is expected that the 16 existing primary school teacher training colleges will increase their intake and at the same time strengthen their inservice programmes for untrained teachers.

(1) For a summary of the results of research studies in this area see: W. D. Haddad: Educat-jona-;»- Effects of Class Size» World Bank Staff Working Paper No 280, Washington June 1978.

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Compared to other African countries, the Kenyan pupil/teacher ratio is just about the African average, which was about 38 pupils per teacher in 1981. However, as many as 12 African countries had ratios exceeding 50.

In general secondary education, the growth in the number of teachers has been slower than the growth in the number of students resulting in a rise in the student/teacher ratio from 19.7 in 1963 to 27.9 in 1981 (1). The current efforts being made by the government to expand the existing teacher training colleges and open new ones to train diploma teachers will gradually reduce the student/teacher ratio. Furthermore, the intention of the Government of bonding trained teachers for some period will reduce the high rate of wastage rate of graduate teachers leaving the profession.

Table 3.1 : Pupils, Teachers and Pupil/Teacher Ratios in Primary and General Secondary Education.

Kenya. 1970-1981

Pupils Teachers : Pupil/teacher ratio

: General : : General : : General Primary : Secondary : Primary : Secondary : Primary : Secondary Education : Education : Education : Education : Education : Education

1970 1975 1976 1977 1978 1979 1980 1981

Source

1,427,589 2,881,155 2,894,617 2,9/4,849 2,994,894 3,698,246 3,926,629 3,981,162

: Statisti

126,855 226,835 280,388 313,977 354,452 376,782 407,322 455,598

86,107 89,074 89,764 92,046 92,762 102,489 110,911

5,881 9,189

11,438 12,696 14,286 14,901 15,916 16,706

• • 34 33 33 33 40 38 36

22 25 25 25 25 25 26 27

Statistics Unit, Ministry of Education, Science and Technology.

(b) Geographical Distribution of Teachers

The pupil/teacher ratios shown in Table 3.1 are national averages and may mask considerable differences between provinces, districts and schools. For a national study of supply and demand of teachers, it is indispensable to carry out a detailed study of the distribution of teachers in administrative regions in order to find out whether national imbalances are reflected at the local

(1) Republic of Kenya Nairobi, p. 37.

Development Plan 1984-1988, Government Printer,

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level or whether, as sometimes happens, national level sufficiency conceals local shortcomings. Even where there is no numerical deficit at the provincial level, it may well be that the qualitative composition of the teacning force in some remote districts is much inferior to the national average, and that this situation merits intervention by the autorities. As a matter of fact, such data have to be interpreted with great care. It is not always clear for example whether a small stock of teachers in a particular province is the cause of low enrolment, or the result of it. Do the authorities respond to a demand for schooling by providing schooling, or is the provision of schooling the "prime mover" and the level of enrolment simply the reflection of a prior administrative decision? One might think that this coma be checked by examining the pupil/teacher ratio to discover whether schools and classes are full. But one has to bear in mind that pupil/teacher ratios are quite largely dependent on population densities. It does not necessarily follow that provinces with 40 pupils per teacher are being treated less favourably than those with 30. As already mentioned, one often finds certain "compensating mechanisms": at work, with urban areas on average being able to attract better qualified teachers, but often having larger classes, and some outlying areas having less well qualified teachers, but smaller classes.

To illustrate possible geographical disparities in the distribution of teachers in Kenya, Table 3.2 shows the pupil/teacher ratio and enrolment per class in public primary education in 1979, by Province,. The table shows that there were quite large differences between Provinces, the ratio ranging from 26 pupils per teacher in North Eastern to 45 in Nyanza Province. Enrolment per class ranges from 31 pupils per class in North Eastern Province to about 41 in Nairobi.

Table 3.2 : Pupil/Teacher Ratio in Primary Schools. Kenya 1979.

Province Pupils per Teacher

Enrolment per Class

Central Coast Eastern North-Eastern Rift Valley Nyanza Western Nairobi

38.9 36.5 37.4 26.0 40.1 45.2 40.9 32.7

39.7 33.9 35.8 31.1 37.2 37.9 38.7 40.5

TOTAL 39.9 37.6

Source : Ministry of Education, Annual Report, 1979 Kenya.

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(c) Teacher Qualifications

The qualifications of the teacher are, of course, a very important indicator of the quality of the education provided. As pointed out above, the training of primary school teachers in Kenya has not kept up with the pressing demand for them in the recent years following the tremendous growth in primary school enrolment. The current overriding concern is to increase the number of trained teachers. At the same time, efforts are being made to re-structure the education system and develop a programme which can produce mature school leavers with skills to enable them to enter modern employment without further training.

Table 3.3 provides information on the qualifications held by primary school teacners in 1980 and 1981. The table shows that in 1980 70% of the teacners were trained while 30% were untrained. In 1981, the respective figures were: 66% trained and 34% untrained. The reduction in the percentage of trained teachers could be caused by the recruitment of more untrained teachers, retirement, or resignation of trained teachers. In the two years, a majority of the trained teacher were p 2's while a large number of the untrained teachers were KCE graduates.

Table 3.3 : Percentage Distribution of Teachers in Primary Education in Kenya by Qualification. 1980 and 19"81.

1980 1981

(%) (%T TRAINED Graduate 0.1 0.1 Approved

SI 2.6 2.6 PI 24.1 23.6 P2 26.1 24.6 P3 15.2 14.4 P4 1.4 1.0

Other 0.8 Total 7 0 3 66^3

UNTRAINED Graduate 0.03 K.A.C.E. 0.6 0.7 K.C.E. 19.9 23.3 K.J.S.E. 7.5 8.0 C.P.E. 1.5 1.5 Other 0.2 0.2

Total 29.7 33.7

TOTAL 100.0 100.0

Source; Central Bureau of Statistics, Economic Survey 1983, Ministry of Economic Planning and Development.

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In secondary education in Kenya in 1979, a majority of the teachers (51.7%) were professionally qualified, of whom 50% were graduates and 37.3% were Si teachers, (see tabl 3.4). About 62% of the unqualified teachers in secondary schools were untrained "A" level school leavers.

d) Age structure of the teaching force

A very important characteristic of the teaching stock is its age structure since depletion of the stock through death, retirement (and even resignation) is highly dependant on the age of the teachers. The future planning of teacher supply must take these causes of loss of teachers into account. The age-structure also has financial implications. For example, the retirement rate has obvious implications for the level of future pension payments. Moreover, as the salary a teacher receives often depends on his/her age and teacning experience, the age structure of the teaching force also affects the costs of education.

Table 3.4 : Percentage Distribution of Teachers in Secondary Education by

Kenva. 1979

Level of Qualified Qualification (%)

PI 3.9 SI 37.3

Approved (1) 4.1 Graduate 50.0 EAACE EACE Others 4.7

Total 100.0

Not Qualified (%)

10.7 62.4 24.5 2.4

100.0

(1) An approved teacher has completed the equivalent of a University Education.

Source: Central Bureau of Statistics, Statistical Abstract, 1982. Republic of Kenya, Ministry of Education Annual Report, 1979.

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A young teaching force is fairly common to developing countries and is due partly to the young age structure of their populations and partly to the recent expansion of their educational systems, with many young, newly qualified teachers entering the teaching force. In countries with a longer history of relatively well-developed educational systems, the age structure of the teaching stock is considerably different, older teachers forming a much higher proportion of the total. As explained above, the significance lies in the calculation of flows out of the stock through death, retirement in a young teaching force such as that of Kenya will be relatively insignificant for a number of years to come.

e) Length of Service

One rather indirect indication of the age structure of the teaching force is length of teaching experience of serving teachers. Length of teaching experience is normally closely associated with age, but not necessarily completely so, since some education systems make provision for women, for example, to return to the classroom after several years' absence bringing up children: these teachers might be well above overage age for teachers generally, but below average in terms of experience. Length of teacher experience is sometimes taken, along with qualifications, as an indicator of the quality of instruction in schools.

f) Percentage Female Teachers

The distribution of the teaching stock by sex may be important for a number of reasons. For example, female teachers in certain age-groups may withdraw from the teaching force for a period of time in connection with child-bearing and -rearing. Moreover, in countries or areas where mixed education is not practised, the sex-distribution of the teaching force is obviously important. Also, in seme countries female teachers do not, for a variety of reasons, seek appointments in certain rural areas.

In Kenya, female teaching accounted for 23% of all the number of teachers in secondary schools in 1979. In 1981, the percentage of female teachers in Africa as a whole in secondary education was 30% for primary education and 28% for secondary. In the industrialized countries and in Latin America, female teachers account on average for about 3/4 of the teaching force for primary education and for almost 1/2 of the teaching force for secondary education.

(g) Language of Instruction

In a large number of developing countries instruction, particualrly at the first level of education, is provided in a number of languages. In such cases it is naturally very important to have statistics showing the language(s) in which teachers can give instruction. The high priority currently given in many countries to the provision of education in the mother tongue illustrates the importance of this type of information as the present distribution of teachers by language of instruction will affect future recruitment to teacher-training institutions.

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SECTION 2 : PROJECTION OF TEACHER REQUIREMENTS

111.2.1 Introduction

After having projected the number of pupils enrolled in future years, the next step is generally to project the resources required to sustain this enrolment. For primary education, the teacher is by far the most important such resource, accounting generally for 80-90% of the total recurrent expenditures at this level of education.

Several methods may be used for deriving projections of teacher requiments, depending mainly on the data available. The simplest, and maybe most employed method in developing countries, is based on assumptions or targets for the future pupil/teacher ratio. We shall discuss this technique briefly below and illustrate it further during the seminar. A more sophisticated method consists of studying the factors determining this ratio, i.e. class size, teaching load and average number of hours' instruction received by the pupils. Section III.2.3 below presents this method which will be illustrated further by examples during the seminar.

Having projected the number of teachers required to sustain a given number of pupils, the next step is to determine the output needed from teacher training institutuions to meet this requirement. This is the subject of Section III.2.4.

111.2.2 Method Based on the Number of Pupils and the Pupil/Teacher Ratio

It the only available data refer to the projected enrolment and the future pupil/teacher ratio (which may simply be a policy target), then the number of teachers required is obtained by the following simple formula:

P (49) Teachers required (T) = _

R

where T = number of full-time equivalent teachers required (1)

P = total projected number of pupils

R = pupil/teacher ratio, i.e. the average number of pupils per teacher.

A projection of teacher requirements in a given year is now obtained by inserting the projected value of P for this year in this equation along with an estimate for the pupil/teacher ratio for the same year.

(1) Not all teachers are necessarily full-time. It is useful, therefore, to establish as a unit of measurement of teaching input the "full-time equivalent teacher". Two half-time teachers (having equal qualifications) may thus be aggregated as one full-time equivalent teacher.

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It shouia be emphasized however, that the introduction of new teaching ipproaches may, in the future, make calculations of the need for teachers »sed on this method less appropriate. This is because the concept of a "correct pupil/teacher ratio loses much of its meaning when the ratio ceases :o be synonymous with class size. Modern education systems allow much greater Ereedom to vary the size of the teaching group to meet the particular needs of 3ifferent pupils, or curricular subjects, or teaching methods. Moreover, a Low pupil/teacher ratio may simply reflect limited class contact hours for teacners, rather than smaller teaching groups. Given these consideration, there is an increasing realisation on the part of educational administrators that, on its own, the level of the pupil/teacher ratio may not indicate very much about the quality of instruction in the schools and hence forms a rather weak basis for estimating future teacher needs.

I EXERCISE XI I

: Based on the enrolment projections to be made during the exercises included : : in Part II, the participants will make projections of teacher requirements : : under different hypotheses for the development of the pupil/teacher ratio. :

III.2.3 Method Based on the Number of Pupils per Class, Hours Taught by Teachers and Hours Pupils are in Contact with Teachers

The data necessary for this method are the following:

(a) the number of students enrolled by grade;

(b) the average number of students per instructional group over the weekly timetable (with due weighting for the time spent in groups of different sizes);

(c) the average number of weekly hours per student in contact with teachers;

(d) the average number of weekly hours per teacher in contact with instructional groups.

Wider (c) and (d) above one may of course substitute "timetable periods" per week where teacher loads are expressed in this form rather than in hours.

It should be noted that where a system has different curricular branches or streams, or where different grades of teachers have varying teaching loads, it may be necessary to take weighted averages if the aggregate system is under review. Alternatively, it may be necessary to prepare separate disaggregated estimates for each sub-system or sub-group of students and teachers, and total the figures at the end of the exercise.

In order to make the initial calculation of full-time equivalent teachers, the following formula may be utilized:

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H x P (41) Teachers required (T) =

G x L

where T = number of full-time equivalent teachers required

P = total projected number of students

H = average number of weekly hours per student in contact with teachers (contact hours)

G = average number of students per instructional group (class size)

L = average number of weekly hours per full-time teacher (teaching load).

It can be seen that the number of teachers required is directly proportional to the number of pupils and the average number of weekly hours per student spent in contact with teachers. The requirement is inversely proportional to the number of pupils per class and the weekly hours taught on average by teachers. Thus the educational planner, by making various assumptions about future values of the four variables on the right hand side of formula (41), may obtain a set of alternative projections of future teacher requirements. This formula is, therefore, very useful for examining how the number of teachers required depends on alternative combinations of these four variables. It also illustrates why the pupil/teacher ratio is frequently used as an indicator of class size, particularly in primary education where the average number of weekly hours per student in contact with teachers (H) generally corresponds quite closely to the teaching load of the teachers (L). It can be seen from formula (41) that, in the case where H = L, the pupil/teacher ratio equals the class size.

The use of an approach such as that outlined above is particularly important when teaching jobs are differentiated to quite a large extent and many of them can be perfomed only by teachers with certain characteristics. For example, in some countries, it is not acceptable for girls to be taught by male teachers and teacher demand has, therefore, to be calculated separately for males and females. In other countries, several languages of instruction exist and an overall demand-supply balance may conceal some severe imbalances in respect to the languages in which the teachers are capable of teaching. The most obvious way in which teacher markets are subdivided is, however, in terms of teaching subject. This is particularly the case in secondary and higher education where knowledge and skills are rather specialised and where the individual teacher's expertise is normally limited to one ot two subjects. At these levels of education, a projection based on pupil/teacher ratios is too crude and it is desirable to apply an approach such as that given by formula (41). Illustrations of how to use this approach in practice will be given during the seminar.

I EXERCISE XII I

: If, at the time of the seminar, data can be obtained on H, G and L, the use : : ot equation (41) will be demonstrated here. :

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III.2.4 Projecting the Demand for New Teachers

The question now arises: How should the demand for new teachers be calculated? The following four steps may be taken to compute the required output of new teachers from teacher training institutions:

Step 1;

Projection of the number of teachers needed for each of the years of the plan period: This projection may be based on one of the two methods presented above. As already explained, it is frequently not sufficient to project only the total requirement; a disaggregation by factors such as subject specialisation language of instruction and sex may also be necessary.

Step 2:

Proiection of the development of the present teaching force: Using data concerning the teacher stock, the number of teachers presently employed who will remain in their jobs in the future may be projected. In order to do this, estimates must be made of the number (or proportion) of teachers who will leave the profession permanently or temporarily through:

- death, - retirement, - replacement of unqualified by qualified teachers, - resignation, movement to other occupations, etc., - temporary secondments, study leave, in-service courses, etc., - transfer to administrative work or to other level of education, or other sub-systems (e.g. private schools),

- other causes.

Ideally a data system would be developed that enabled one to keep track of losses due to each of these causes of outflow and also identified return flows and types of inflow other than new recruits from teacher education and training (e.g. returning qualified teachers from approved absence, re-entry from other occupations, transfers from other level or types of education, recruitment from abroad, etc.). Most systems, however, do not record flow in this detail and so annual loss has to be calculated on a net basis, at the aggregate level. In other words, instead of recording separately each type of outflow and inflow and calculating from these gross inflow and gross outflow figures, one takes a crude measure of the net loss, which is the excess of all types of outflow over all types of inflow (excepting new entrants from teacher training). One can express this as an apparent teacher retention rate which may be derived as the number of teachers available at the beginning of a school-year (before new recruitments are made) divided by the number of teachers available the previous school-year, i.e.:

Teachers in year t+1 - new recruitment at start of year t+1

Teachers in year t •

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For example, if this ratio is calculated to equal 0.90 for a given school-year, this means that the size of the teaching force at the beginning of this school-year (before new recruitments are made) corresponds to 90% of the size of the teaching force in the previous school-year. However, this does not necessarily mean that 10% of the teaching force left the profession. Firstly, some left only temporarily (e.g. study leave, in-service training) and will return later. Secondly, some of those who left temporarily in earlier years may have returned, implying that the "gross" loss is larger than 10%.

Step 3;

Projection of the need for new recruitments; Subtracting the results obtained under Step 2 above (i.e. teachers remaining in the teaching force at the beginning of a given year) from the results obtained under Step 1 (i.e. total number of teachers required in the same year) yields a projection of the number of new recruitments required. These "entry to the teaching stock" figures can then be converted into "college output" figures.

Step 4;

Projection of new intake to teacher training institutions; The need for newly trained teachers calculated under Step 3 may now be converted into projections of the required intake to teacher training institutions in future years. These account factors such as dropout and repetition rates of teachers undergoing training and the length of the teacher training courses. (1)

Naturally, the above four steps are simplifications of the complete policy-analysis which would (data permitting) have to be carried out in a real situation. A number of practical complications would present themselves, including at least the following:

(a) the steps outlined do not consider the distribution of teachers by subject area, a factor particularly significant in secondary education. The above method aims at an aggregate balance of the supply of and demand for teachers, but such a balance can be consistent with marked imbalances within particular subjects. Only refined and diasggregated projection methods (making greater data demands) can offer a solution to this. A similar problem arises when teachers need to be projected according to language of instruction;

Illustrations of how to employ this model for this purpose are given in T. Thonstad; Analyzing and Projecting School Enrolment in Developing Countries; A Manual of Methodology, op. cit., Chapter VT. A more comprehensive discussion of the issues involved in planning teacher demand and supply is given in P. Williams: Planning Teacher Demand and Supply, Fundamentals of Educational Planning No 27, HEP, Unesco, Paris 1979.

(1)

i

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(b) the outlined steps also fail to analyse the distribution of teachers by geographical locality. In view of existing regional disparities in most developing countries it would be important to carry out a more disaggregated analysis;

(c) no distinction was made by sex. In view of the low partipation of females in the teaching force in some developing countires, this may be important, particularly if increasing the enrolment ratios of girls should require a greater supply of female teachers;

(d) finally, the above discussion was limited to the demand for new teachers and to initial or pre-service training. However, in many countries, particularly in the Third World, the need for in-service training, i.e. training of teachers already in the teaching force, is very important. The purpose of such training is to up-grade the qualifications of unqualified teachers and to give persons who possess the required formal qualifications for the post they are presently holding a chance to qualify for higher posts or simply to up-date their knowledge.

As illustrated by the above discussion, a full analysis of teacher demand and supply requires quite sophisticated and up-to-date statistics. One of the advantages of the simple analytical models presented in this section is the indication they give as regards which data should be a priority in future efforts to improve the statistics on teachers.

In conclusion, two main issues deserve re-emphasis. New approaches to teaching methods, new curricula and other reforms in the general educational system must all fundamentally affect the future requirements for teachers. Crude models cannot readily take such developments into account.

Secondly, any fully acceptable analysis for policy purposes must include the costs of training and employing teachers. The opportunity costs of training a teacher to a high level of qualification are very considerable. This must raise issues such as whether teachers need have such lengthy period of training as they have in some countries; whether the desire for lower pupil/teacher ratios can be justified by scientifically proven research; and whether teachers do any tasks which could equally well be perfomed by less highly paid, lesser trained personnel. The cost of employing the teachers who have been trained has also to be taken into account. We shall return to these issues in Part IV where we consider the costs and financing of education.

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PART IV: ANALYSIS OF EDUCATIONAL EXPENDITURES AND OF EDUCATIONAL POSTS

SECTION 1: ASSESMENT OF NATIONAL EDUCATIONAL EXPENDITURE

IV.l.i Introduction

Educational planners must be closely concerned with the financing of education, and the size and distribution of educational expenditure. It is finance which mobilises the real resources needed to carry out educational plans, and so the budgetary process is enextricably bound up with plan formulation and implementation. Moreover, since resources are scarce there is competition for resources both between education and other sectors of expenditure like health or industrial investment; and also within education itself, between levels of the system, different purposes of spending, such as teacher training or curriculum development, different regions and so on. This lays on the educational administrator and planner the duty to try and ensure that expenditure patterns represent the best way of meeting national objectives. A further reason for very close concern with educational finance is that the incidence of educational costs and benefits is a highly important political question. Who pays for education, and who receives the benefits in terms of school attendance and opportunities for higher subsequent incomes? Since appointment to jobs in most societies is becoming increasingly dependent on educational qualifications, the distribution of educational costs and benefits is becoming an ever more important determinant of the distribution of influence and wealth in society at large.

At the present seminar we can only review very briefly some of the problems encountered in this field.

IV.1.2 Definitional Problems

In assessing the total national outlays on education, an initial problem which arises is to define educational expenditure. The choices one makes are not so important. But it is desirable that definitions of what is included in national educational expenditure are clear, particularly when one country is compared with another, or when one period of time is being compared with another.

One must first arrive at a definition of the scope of education for the purposes of such analysis. Will it include just formal schooling or does it extend to all kinds of structured learning wherever it takes place? Should vocational training organised by employers be included for example? What about adult literacy classes or the work of agricultural extension officers?

t How much of the activity of cultural agencies - museums, libraries, etc... -is to be regarded as education? what about research? It is clear that we have here some fundamental choices in either defining our concerns narrowly, in terms just of school and colleges, or more broadly to embrace additionally

* a wide range of training, cultural, research and information activities.

A second set of problems, concerns definitions of what expenditures even within 'education* are truly 'educational'. In order to support school attendance, the authorities may have to be involved in the provision of non-educational services, which might otherwise fall to the expense of

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households. For example, pupils may be fed in schoools or colleges, they may be housed in boarding hostels. They may be transported free or at subsidised rates, and perhaps given free medical care and attention, poor students may be given free clothing, or uniform allowances. For comparative purposes it is important to know whether such items are classified under education or under other expenditure headings. And if universities, for example, are undertaking research, it is necessary to know whether research costs are included in the education budget or not.

Thirdly, there are problems arising from accounting practice. Are teachers1 pensions to be counted as expenditure on education? Is allowance for imputed rent made in respect of educational buildings or, once built, are they regarded as free apart from the expense of maintaining them? What is the practice on depreciation of educational equipment?

IV.l.J Source of Educational Finance

As a preliminary to any assesment of total national educational effort in financial terms, it is helprui to consider how education is paid for, because this will give guidance in tracking down the different elements in educational expenditure that make up the total national outlay on education.

Basically those who provide educational services draw resources from five main sources:

i) The public authorities.

ii) Religious and other charitable bodies.

iii) The clients of the education system (pupils and parents).

iv) Income generated by education institutions themselves.

v) Subsidisation by institutions' other activities.

From such a listing it becomes immediately clear that unless all educational effort is channelled through the government budget, an analysis of Government outlays alone will not reveal the full extent of national resources devoted to education.

Let us briefly review in turn the sources of finance listed above.

Tne public authorities draw their resources mainly from taxation, borrowing from the public (issue of bonds and loans, operation of saving * schemes, etc..) and from foreign aid. Education is normally financed from general revenue, but some countries meet part of their expenditure by raising specific earmarked educational taxes. Foreign aid may come either in the form of general support for Government programmes, or may be tied to particular « projects. In the latter case it may not necessarily pass through the Ministry of Education's budget, and may have taken separate account of when attempts are made to aggregate expenditure on a nation's education.

Religious and other charitable bodies may either run schools themselves, or they may give grants to support schools or to enable individual students to attend them. If such private donations are made to public schoools, it is possiDie that they will be entered in Government accounts at the national level. But more often these bodies are organising or supporting private educational efforts outside the Government sector. The resources involved may be substantial.

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The clients of the education system may help to support it through payment of tuition or other fees. There are arguments both for and against financing education by directly charging the pupil or his family, which are however beyond ther scope of this paper. The choice a country makes will largely reflect the history of the evolution of its education system, and its social and political philosophy. It is worth noting that the financing of schools should be distinguished from their management; in some countries one finds private fee-paying in publicly run schools, and in some there is government financial support for schools under private management. It should be noted that if fee payments are made to a public school and retained by it to meet its operating expenditure, these sums will be additional to sums budgeted by Government.

Income generated by educational institutions themselves would include all kinds of self-help activities on the part of schools and colleges. This income might arise from selling of farm or craft products, cultural performances to raise money, contributions in labour or in cash for the construction of buildings or purchase of equipment. Alternatively, education institutions may own property or other financial assets which yield income. Again, the analyst of educational expenditures needs to be reminded of these resources, the spending of which represents part of the total national educational effort, but which do not as a rule pass through the government budget.

Subsidisation by institutions' other activities would apply particularly in the case of economic enterprises which run vocational training programmes. Expenditure on training provided through Government departments may be identifiable in the Government budget; but training by para-statal organisations or private industry may be equally, or more important in developing vocational skills.

IV.1.4 Public Expenditures on Education in Kenya

Table 4.1 shows Government expenditures on education as compared to total Government expenditure and to GNP. The figures cover the period 1970 to 1982. The table shows that in 1982, Kenya devoted 16.5% of the total Government expenditures to education. In the same year the part of the budget allocated to education corresponded to 6.5% of the nation's Gross National Product. The other figures given in the table will be commented on below.

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IV.1.5 ALTERNATIVE WAYS OF DISAGGREGATING EXPENDITURES

The educational administrator or planner is interested not only in the total size of national educational expenditure, but also in its composition and distribution. There are at least four different types of expenditure breakdown that will be of interest for financial analysis of educational expenditure:

i) By expending agency and administrative programme.

ii) By type of expenditure.

iii) By level and specialisation of school.

iv) By population group.

Naturally analysis under these four categories will be more meaningful if cross-tabulations are possible (spending agency and area, level and type, etc.) or if trend analysis is feasible througn having data under one heading for several successive years. We shall below briefly comment upon each of these four points.

(i) Analysis by Spending Agency and Administrative PEpgrapps,

Tnis type of analysis is most common since it reflects the way in which funds are actually made available througi different agencies and programmes. It thus corresponds to the classification used in budgetary appropriations and so has direct administrative uses.

Table 4.1 further shows that in 1982, the Ministry of Education had at its disposal about 20% of the total Government recurrent budget. The capital expenditure on education in the same year was about 5.6% of the total Government Capital expenditure.

(ii) Analysis by Type of Expenditures

A broad distinction is normally made in accounting between capital items and current items of expenditure. As a general rule of thumb one can say that capital items are those which have a long life and yield services to the consumer over a period of years, whilst current items are those which are consumed in one year or less. All personal services are regarded as current items, and materials such as paper and chalk, etc., would also be current items. Building and heavy equipment with a life of several years would be capital items. More difficult to classify are items like textbooks or footballs which may last more than one year, but nevertheless wear out quite quickly.

Capital expenditure may conveniently be broken down into: _ Acquisition of land and development of sites.

- Construction of buildings for teaching, administrative, recreational and sometimes residential purposes.

- Laying on of services (water, electricity, etc..) to such sites and buildings.

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- Purchase and installation of fixed installations and permanent equipment including vehicles.

- Other miscellaneous items.

Current expenditures include:

- Emoluments of various kinds (salaries, allowances insurance and superannuation payments, etc....). s

- Travel and transport of personnel and subsistence allowances.

- Goods and materials used in the teaching process, or by the < the administration.

- Purchase of services - water, electricity or gas, sewerage, telephones, postal services, etc...

- Repair and maintenance of buildings.

_ Rents.

- Depreciation allowance on capital.

- Interest charges.

- Transfer payments such as scholarships, grants, etc....

_ Other miscellaneous items.

Table 4.1 shows that in 1982, recurrent expenditures on education were 3,906 million shillings as compared to 402 million for capital expenditures. Thus, about 91% of the total Government expenditures on education was on current items including personal services. The share of education and training in total Government recurrent expenditures in recent years has been declining from 27.7% in 1975 to 20.5% in 1982. In recent years capital expenditures on education have been accounting for a considerably larger proportion of the Government's total capital expenditures than in 1970 or 1975.

(iii) Analysis by Level and Specialisation of School

Analysis by level and specialisation is particularly important when drawing up plans for the future development of education, and assessing the s resources that will be needed. Tertiary education tends to be more expensive per student than secondary, which in turn is more costly than primary. Similarly, applied and scientific subjects involving practical work are more expensive than ordinary classroom subjects. The reasons for this gradation of , unit costs are not difficult to identify.

In general terms the higher levels of education are more expensive per student than the lower levels because:

- Teachers are better qualified and more highly paid.

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- In many countries teachers are in direct contact with students for fewer hours per week; in other words there are more teachers per class.

- Class sizes may themselves be smaller.

- Higher institutions have more clerical, administrative and support staff.

- In many countries higher institutions have an element of residential attendance by students, since the institutions are fewer and further from students' homes.

- The standard of accomodation is higher both in terms of quantity, (reflecting the fact that older pupils require more physical space), and in quality.

- The higher up the education pyramid one goes, the greater the element of practical work or vocational specialisation; this tends to be more expensive.

Applied subjects are generally more expensive than general classroom subjects because:

- Teaching groups tend to be smaller either because of supervision requirements (teachers can only demonstrate practical skills or supervise handling of dangerous or expensive substances or tools if groups are small) or because specialist options are not fully subscribed.

- Teachers may be (but are not in practice always) more highly paid, reflecting the fact that they could alternatively sell their skills to industry and commerce.

- Buildings and equipment costs are higher - more space needed per pupil and more expensive equipment and tools.

- A good deal of consumable materials is used up in practical work.

The percentage distribution of Ministry of Education recurrent expenditures by educational sub-sector are shown in Table 4.3.

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Table 4.3 : Percentage Distribution of the Ministry of Education Recurrent Expenditure by Educational Sub-Sector

in 1975/76 and 1981/82

Sub-Sector

General Administration and Planning Pre-Primary Education Primary Education Secondary Education Technical Education Teacher Training Special Schools Polytechnic Education Higher Education

Source :

Miscellaneous

TOTAL

Central Bureau of Statistics,

1975/76

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Economic Survey,

1981/82

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100.0

1983.

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The share of general administration, teacher training, polytechnic education and higher education registered a marginal increase in the two years covered by the table, while the share of the rest of the sub-sectors either remained almost at the same level or decreased somewhat.

(iv) Analysis by Population Group

In the development of national cohesion, governments are naturally concerned to ensure that all segments of the population claim their fair share of national resources. In view of the decisive role education often plays in determining an individual's employment and income prospects, an equitable distribution of educational services is, of course, of particular importance. Depending on national conditions, we may need information on the distribution of educational expenditures by geographical region, religious and ethnic groups, different categories of handicapped pupils, different income groups, by sex, etc.

For a number of historical reasons there may be an inheritance of inequalities in the extent to which different population groups benefit from education. For example, education is traditionally more developed in urban than in rural areas, males generally find it easier to obtain education than females, high income groups can more easily afford to pay school fees than low income groups, etc.

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Inequalities in the distribution of educational services are a difficult policy issue in developed as well as in developing countries. It is not even obvious how the term "an equitable distribution of educational services" used above, or the more common term "equal educational opportunities", should be interpreted, The call for equal educational treatment, in terms of equal participation, and equal quality

( of the education received, is based on a democratic sentiment that all people have the right to equal treatment. What is meant by "equal treatment" is, however, not obvious. For example, no one wishes to treat a blind child in the same way as a cripple, in fact, appropriate

> educational provision would imply unequal treatment on the basis of unequal needs.

However, almost regardless of how the term "equal educational opportunities" is defined, statistical data on the distribution of education expenditures by factors such as sex, ethnic group, socio-economic group and region, at all levels of education, are of crucial importance for analyzing a society's distribution of the benefits accrued from education among its members.

SECTION 2 : THE ANALYSIS OF EDOCATIONBL POSTS IV.2.1 Distinction Between "Costs" and "Expenditures"

The word "cost" is usually defined in the context of cost analyses as the measure or equivalent in monetary terms of the sacrifice made to acquire specific goods or services. Although the term is similar to "expenditure" in connotation, not all expenditures result in costs and not all costs are related to current expenditure. The distinction is more significant in commercial enterprises than in non-profit making organizations such as the public school system. Still, even for public schools there are some items of expenditure which are not costs, for example, purchases of investments or some permanent assets, and there are costs such as those related to the use of previously acquired assets or the accrual of future liabilities which are not related to current expenditure.

IV.2.2 Purpose of Cost Analysis

The usual purpose of cost analysis is to provide insight into the ways in which the resources available to an organization have been devoted to various activities of this organization. In this context it seems reasonable to assume that all expenditure incurred by the organization has been incurred as the result of a conscious decision, past or present, and that by a careful evaluation of the effect of intended effect of the expenditure, it is possible to relate each cost element to one or more of the activities or functions of the organization and thus by a process of further analysis and aggregation to obtain a total cost for each activity or programme. The final objective of cost analysis is hence to contribute to greater efficiency in the allocation of educational resources. This means either to maximise educational output resulting from given inputs; or, alternatively, to minimise the required inputs for a given output.

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This paper has already discussed the central difficulty facing efficiency analysis in education: the definition and measurement of output. One must accept that although attempts to define outputs more clearly must and will continue, it is doubtful whether a completely quantified description of all the outputs of an education system will ever be attainable. What is more immediately practicable however is to seek ways of reducing the costs of producing each unit of output in the case of outputs which are most easily measurable - for example months of student attendance in school (since the experience of school may be regarded as an output of the system as well as an input towards higher intellectual achievement), number of course graduâtes, number of students reaching a prescribed level of competence. The search for cost savings has immediate practical utility in all education systems.

IV.2.3 The Concepts of "Joint Costs" and "Opportunity Costs"

In practice, considerable difficulty is often experienced in making cost analyses. One such difficulty is the prevalence of "joint costs", i.e. costs which are incurred jointly for two or more purposes and which cannot be readily attributed to each of the purposes or objects involved. It is sometimes possible to find a reasonable basis for the apportionment of such "joint costs" but there are many cases where it is necesary to fall back on seme relatively arbitrary formula. The frequency with which such arbitrary allocations have to be made and the significance of the amounts involved obviously has a very direct influence on the validity of the overall results of an analysis.

A further limitation of cost analysis results from the frequent exclusion of all expenditure or costs related to the acquisition of capital assets -land, buildings, and equipment -except to the very limited extent that expenditure for such purposes may have been included in the current operating accounts for the year under review.

The validity of the results derived from cost analysis is also limited by the frequent omission of all "imputed costs" or "opportunity costs".

The notion of "opportunity cost" is a fundamental one in economic analysis. The opportunity cost of a service, or of any factor of production (in this context, of any input into the educational productive process), is its value in its best alternative use. Where goods and services are produced and exchanged in competitive markets, their prices will reflect their opportunity costs. If, for example, a service were priced below its value in its best alternative use, it would be bid away from its current activity into that in which it was more valuable. Competing bidders for the service would ensure that its price to its present user would rise until it was equal to its price in alternative uses.

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However, of course, in no country are educational goods and services wholly provided under freely competitive market conditions. Indeed a market in education may be explicitly banned by legislation, or if not, prices (fees) may be closely controlled. The efficiency analyst, in these circumstances, cannot rely on observed market prices for the appropriate estimation of costs. He will need to make estimates of the real

( opportunity costs involved, e.g. in employing teachers. These estimates are known, in the technical economic literature, as 'shadow' prices. Methods of calculating shadow prices cannot appropriately be discussed here. But the central question is simple: what is the value of a resource

? (an input) in its best alternative use? For this is the only proper measure of its true cost. It may be, for example, that a government employs, as a teacher, an individual who would otherwise be unemployed. In such a case, in stark constrast with the financial cost to government, the opportunity cost to the economy would be zero as no output would be foregone elsewhere through his public employment. The appropriate cost therefore to use in a real resource analysis (as opposed to a financial, accounting analysis) would be zero.

Thus sometimes the financial costs of employing inputs (e.g. teachers) differ sharply from their opportunity costs to the economy or to the individual. The difference between expenditures and real costs becomes clearest when we consider what is perhaps the major input to education systems, which is student time. If a student were not at school, what would he be doing? If the answer is that he would be engaged in productive activity, then the value of the output lost through his school attendance is part of the total opportunity costs of education. It is, of course, a part which never appears in the financial accounts. But it is a real part nevertheless.

This underlines the important point that when we speak of 'cost* we ought also to specify 'cost to whom1 . The student's time does not enter into the Ministry of Education budget, unless the student has to be paid an allowance to attend: consequently the student's time is 'free' to the Ministry of Education. But it is not free to the student and his family, if that time could otherwise be used to boost the individual's or the family's income: this is one reason why poor families cannot release their children from the farm or shop or from child minding to attend school. Nor is it 'free' to the economy if production is lost. (The same point can of course be made about 'free' education which may be cost-free in a financial sense to individuals, but certainly not to the government or the

; national economy as a whole).

Education budgets nearly always conceal the real cost of using education buildings. If buildings are rented the 'cost' appears in the

i budget. If the buildings are owned by government, the cost is ignored, even though the buildings might be let out for rent (which is thus foregone) or the capital locked up in schools might have been invested in a profit-making business.

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IV.2.4 Costing Educational Plans

The estimation of the costs of educational plans is a wide topic which cannot be fully discussed here. Only a few of the central issues can be mentioned.

Generally, such estimations start from a calculation of unit costs. Costs - both recurrent and capital - may be analysed from past data on the basis of costs per pupil, per teacher, per school, etc. This should be done separately for each level in view of the wide differences in cost between levels. In estimating costs per pupil, care must be taken to ensure that:

a) all the costs incurred in educating a particular group have been recknoned, and account has been taken of the politically important question of which groups such costs fall upon;

b) if only the financial costs are considered, their relationship with respect to opportunity costs is clearly understood by the decision makers;

c) a clear distinction is made between average costs and marginal costs.

The distinction between average and marginal costs is of fundamental importance in decision making. The marginal cost of educating an extra individual may differ very considerably from the average cost per pupil incurred in educating the group he joins. In efficient decision making, it is of course the comparison of the extra, or marginal, costs (inputs) with the marginal benefits (outputs) of the programme that should form the basis of the choices made.

Having calculated past unit costs, the planner must make explicit assumptions about their future development. As the salaries of teachers generally play such a major role in total recurrent costs their likely future trend will obviously be of paramount importance to the planner. He will bear in mind that it is not only educational expansion or revisions of salary scales that may tend to inflate the teacher salary element in costs. If there are teacher upgrading programmes or policies to replace inadequate teachers, this may increase the average teacher salary. Similarly, if the average age of teachers is slowly rising, then more teachers will be higher up in the pay scales, (a phenomenon sometimes known as 'incremental creep'). Again, if there is any tendency to shorten teacher hours (without shortening the length of the school day, week or year) or to reduce class size, this will raise average teacher cost per pupil. Of all the different causes of a higher teacher salary bill the most important in the majority of countries - rising student numbers apart - is the fact that newly recruited teachers are better qualified than their predecessors and so are entitled to higher pay. A sort of 'qualification inflation' is at work.

Close analysis of future enrolment (i.e. future number of units) and future unit costs should be carried out in such a way as to distinguish the different elements causing future rises in the educational budget. The planner will quickly realise that some of these increases (e.g. annual

153

increments for teachers) cannot be avoided, while in other areas - such as the level of scholarships, or rate of expansion of universities - there may be room for the policy maker to choose. The margin of choice is nearly always less than the size of the education budget might seem to indicate, for the first call on resources will always be the pupils already in the system whose progression to the next grade or course must be allowed for, and the teachers already employed. But it is only a careful cost analysis, aimed at identifying cost trends and the scope for economies, that will reveal

( opportunities for policy changes to improve and extend the systems.

Once future levels of enrolment and future cost per student have been calculated, it is relatively simple to make cost projections for the major

' parts of the education budget. Some items such as curriculum development or the educational broadcasting service Cannot easily be estimated on any unit cost basis and will have not separately estimated. In just the same ways parts of the capital budget may be calculated on a unit basis if standardised buildings are used, or if a standard provision (so many square metres, or so many dollars per pupil) is made; while other buildings may have to be individually costed.

IV.2.5 Concluding Remarks on Part IV

The object of Part IV has been to highlight some aspects of expenditure and cost analysis in the field of education. The purpose of the discussion has been limited to drawing the reader's attention to certain important issues in this area. The importance of specifying the defining terms was stressed and a number of different ways of analysing educational expenditure were examined.

The important distinction between financial expenditure and real costs was made. Finally, some of the processes and issues involved in calculating educational costs were briefly surveyed.

Countries all over the world are faced with the dilemma of a widening gap between resources and requirements. Therefore, educational plannners in the future will need to give even more attention than in the past to increasing the outputs from the educational system (in both quantitative and qualitative terms) from the resources already available. To cope with this situation, educational planners and administrators will need the help of improved analytical tools and of fuller information about what is actually going on in their educational systems. In providing training in methods of collecting, analyzing and projecting education and population statistics, it is hoped that the present seminar has contributed towards this end.

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154

ANNEX I : The Education System in Kenya d9S3i 1)

Expected ages at 1 January

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Table 3: Primary School Enrolment Ratios by District and Province, 1975-1980

Taita Kilifi Tana River Lamu Kwale Mombasa

Coast

Machakos Kitui Embu Heru Marsabit Isiolo

Eastern

Garissa Wajir Mandera

North-Eastern

Nairobi

Nyandarua Kirinyaga Nyeri Muranga Kiambu

Central

Nakuru Kericho Nandi Iaikipia Kajiado Narok Baringo Elgeyo Marakwet Uasin Gishu Turkana Samburu Trans Nzoia West Pokot

Rift Valley

Kisumu Kisii South Nyanza Siaya

Nyanza

Busia Bungoma Kakamega

Western

1975

(%) 89 51 55 105 61 59 61

126 92 98 86 29 46 101

12 7 6 8

75

106 104 106 109 97 105

84 68 95 109 62 48 82 73 70 9 18 100 43 70

85 113 75 95 93

95 104 108 105

1976

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121 93 99 77 28 56 98

11 7 7 8

73

102 98 104 108 121 103

89 79 95 105 65 45 83 74 71 8 19 98 45 74

71 105 61 91 83

89 101 112 122

1977

(%) 82 49 48 114 56 53 57

122 94 101 82 29 44 99

12 14 8 11

73

85 97 104 106 99 101

89 88 93 116 69 46 97 72 75 N/A 19 101 53 77

69 92 67 89 80

89 104 105 102

1978

(%) 85 48 43 101 54 54 56

120 98 99 83 31 46 99

10 13 8 10

74

93 97

102 105 97 100

91 81 98 125 69 51 80 71 73 9 20 101 63 76

67 79 58 78 70

82 101 87 90

1979

(%) 89 65 45 105 67 55 65

126 112 103 95 33 56 109

13 13 10 12

74

97 100 101 106 , 98 102

103 89 99 138 73 60 93 83 85 10 23 138 68 92

87 113 93 108 101

116 118 106 111

1980

(%) 91 68 56 117 71 56 68

123 110 103 94 33 57 108

16 12 12 13

74

93 99 101 110 101 102

124 89 95 155 78 67 93 84 93 19 30 147 98 98

93 82 90 106 97

106 120 104 100

KENYA . 88 86 85 81 96 96

Source: Statistics Unit, Ministry of Education, Science and Technology.

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