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## ABSTRACT

The study was undertaken to investigate the “Effects of Class Size and Ability levels on Students‟ Performance in Mathematics among Junior Secondary School Students in Kaduna Metropolis” to proffer solutions to the problem of poor performance in Mathematics. The study made use of experimental design in which three secondary schools were used with a sample of one hundred and fifty (150) students, ninety (90) students from school I representing large class, forty (40) students from school 2 representing medium class and, twenty (20) students for a small class size. Mathematics Achievement Test (MAT) was used for the students while observation schedule was used for the Mathematics teachers. Three (3) research questions were generated to guide the investigation. Also, three (3) hypotheses were postulated and tested at 0.05 level using Analysis of Variance (ANOVA), T-test and descriptive statistics (Mean and Standard Deviation). The findings revealed that students‟ performance in Mathematics improved as class size decreased. There was no significant difference in the performance of male and female students irrespective of the class size. The findings also revealed that students in mathematics performed better when taught by teachers who have high qualification and teaching experience. Based on the research findings, it was recommended that stipulated maximum class size of 20-40 in Nigerian schools, be observed, government is to ensure adequate employment of dedicated and qualified Mathematics teachers to teach the subject and tutorial should be encouraged where by students with high ability levels take it upon themselves to instruct their colleagues with low ability levels in Mathematics.

## TABLE OF CONTENTS

Title page————————————————————————————————————i

Declaration———————————————————————————————————ii

Certification——————————————————————————————————-iii

Dedication———————————————————————————————————-iv

Acknowledgement————————————————————————————————-v

Table of contents————————————————————————————————–vi

List of tables——————————————————————————————————-xi

List of appendix————————————————————————————————–xii

Abstract———————————————————————————————————–xiii

CHAPTER ONE

INTRODUCTION

1.1 Background to the study———————————————————————————1

1.2 Statement of the Problem——————————————————————————–3

1.3 Objectives of the study———————————————————————————–4

1.4 Research Questions—————————————————————————————4

1.5 Hypotheses————————————————————————————————-5

1.6 Significance of the study———————————————————————————5

1.7 Basic Assumptions—————————————————————————————-6

1.8 Scope of the Study—————————————————————————————-7

1.9 Operational Definition of Terms————————————————————————7

vii

CHAPTER TWO

REVIEW OF RELATED LITERATURE

2.1 Introduction————————————————————————————————9

2.2 Theoretical framework———————————————————————————–9

2.3 The Concept of Class Size—————————————————————————–19

2.4 Academic Achievements in Mathematics————————————————————27

2.5 Ability Levels and Effects of Class Size on Students’ Performance——————————29

2.5.1 Types of Academic Achievers————————————————————————-32

2.5.1.1 Low Achievers——————————————————————————————-32

2.5.1.2 Average Achievers————————————————————————————–33

2.5.1.3 High Achievers——————————————————————————————33

2.6 Gender and Mathematics Achievement————————————————————–42

2.7 Influence of Teachers’ Qualifications on Students’ Performance in Mathematics————–43

2.8 Empirical Studies—————————————————————————————-46

2.9 Implication of the Review of Literature to the Present Study————————————-51

2.10 Summary————————————————————————————————-55

CHAPTER THREE

METHODOLOGY

3.1 Introduction———————————————————————————————-57

3.2 Research Design—————————————————————————————–57

3.3 Population of the study———————————————————————————57

3.4 Sample and Sampling Techniques——————————————————————–58

3.5 Instrumentation——————————————————————————————59

3.6 Description of instrument——————————————————————————59

viii

3.7 Checklist / Observation Schedule———————————————————————60

3.8 Validity of the instruments—————————————————————————-62.

3.9 Pilot Study————————————————————————————————62

3.10 Reliability of the Instrument—————————————————————————63

3.11 Procedure for data collection————————————————————————–63

3.12 Method of data analysis——————————————————————————–63

CHAPTER FOUR

DATA PRESENTATION AND ANALYSIS

4.1 Introduction———————————————————————————————-64

4.2 Respondent: Biodata————————————————————————————64

4.3 Analysis of Research Questions———————————————————————-64

4.4 Hypotheses Testing————————————————————————————-68

4.5 Descriptive Statistic————————————————————————————-71

4.6 Major Findings——————————————————————————————-73

4.7 Discussions———————————————————————————————–74

CHAPTER FIVE

SUMMARY, CONCLUSION AND RECOMMENDATIONS

5.1 Summary————————————————————————————————-77

5.2 Conclusion———————————————————————————————–78

5.3 Recommendations—————————————————————————————78

5.5 Suggestions for Further Study————————————————————————-79

References————————————————————————————————81

Appendix————————————————————————————————-95

## CHAPTER ONE

INTRODUCTION

1.1 Background to the study

Mathematics has always been regarded as the language of science. It is an important

discipline in the training of logical reasoning and it is an important instrument used in

attaining practical goals. Concepts in mathematics are useful in solving problems in applied

engineering (Andre, 1985). Mathematics has an important role to play in the task of national

development. It is an instrument for effecting economical, social, political, scientific and

technological changes. In order to achieve these goals of education, the teachers are required

to perform their duties efficiently, need to be given controllable and adequate class size of 35

students to teach for effective learning in mathematics, (Balogun, 2002). The history of

development of knowledge and much of the development in science and technology has been

greatly facilitated by applications of mathematical knowledge and procedures.

The role mathematics plays in the realization of scientific skill is well known that any

society that is serious in its quest to develop its technology, must be serious in the teaching

and learning of mathematics. Mathematics is always overlooked by many students even

when they know that they need it for solution to problems in area of science. They claim that

if it was possible not to take mathematics at all, they would have preferred it but would

continue their study of science. Hence they put up negative attitude towards the learning of

mathematics which consequently appears to affect their performance in the sciences. Because

students have already conditioned their minds on the impossibility of learning mathematics,

they therefore fail to get a grasp of the subject matter, no matter how hard they persevere

(Uhumuavbi and Umoru, 2005). The researcher is of the view that something has to be done

to change students‟ negative attitude towards the learning of mathematics. There is need to

arouse the interest of students towards the learning of mathematics.

2

This study attempts to expose some of the numerous problems facing mathematics

that prevents the effective teaching and learning of mathematics in Nigerian secondary

schools. The issue of class size is one important area of this study as it relates to

teaching/learning of mathematics in junior secondary school level. Alio (2003) attributes

students’ development of negative attitude towards mathematics teachers to what is called

“idiosyncrasy” of mathematics instruction. The usual way some mathematics teachers

approach the teaching of mathematics contributes to the students’ development of negative

attitudes to both the subject and the teachers. Effective and good mathematics performance

cannot be possible when students’ attitude towards the teachers and the subject is negative.

The need for development of science and technology in this nation will not be

successfully achieved without solving the problem of poor performance in mathematics

(Betiku, 2002). According to Onu (2003), the usefulness, power and place of mathematics in

the field of human endeavor continue to be recognized. In trying to develop science and

technology in a nation, mathematics is the key. It is seriously needed to gain access into the

world of scientific knowledge and understanding. The importance of mathematics is not a

doubt, that is why in the first ordinance enacted by Fredrick Lord Luggard (1914), enforcing

western education, Arithmetic, writing and reading were the three areas in which the pioneers

of formal education in Nigeria were trained. The need to identify suitable class size by which

students, especially with medium and low ability can be made to receive teachers’ attention to

grasp the content of the subject easily and intelligibly is the focus of this study.

Education (FRN, 2007) recommended an average class size of 30. Anikweze (2004)

recommends teachers/pupils ratio to be 1:35 in order to be more effective to, cope with an

over-crowded classroom in our schools. The present study considers class size as the total

number of students in a class at a given time to a teacher. That is students/teacher ratio of 20

students to a teacher, which constitutes a small class size; 40 students to a teacher as average

3

class and 90 students to a teacher as a large class. These are to be tested in this study to see

the effectiveness. The National Policy on Education (FRN, 2007) recommends an average

class size of 40 students to a teacher, but hardly is this attained in Nigerian schools. Duyilemi

(2004) observed that in most Nigerian schools what exists in the class ranges from 50 to a

large number of 120 students to a teacher in many secondary schools. Oakes (1992) and

Lynch (1994) defined ability grouping as dividing students into separate classes of high,

average and low achievers, that is classifying students according to their academic

performance. This can best deal with individual differences in the classroom. Feldhusen

(1992) noted that students of lower and average ability often flourish or become better

students when the high ability level students are present and leading to competition. High

ability or gifted students are needed in all classrooms in order to stimulate, motivate and

inspire other students. Salau (1996) concluded that the achievement profile of high achievers

declines as the class size becomes larger. This means that increase in class size tends to

reduce the performance of students generally, despite the level.

The researcher is of the view that the use of heterogeneous class could be of more

advantage since low and average groups would gain more knowledge from their interactions

and sharing with the high achievers whether the class is large or small. The major objective

of this study is to determine the adequacy and effectiveness of class size and ability levels on

the academic achievement of different group of students in mathematics, when taught with

mathematics concepts in junior secondary schools in Kaduna metropolis. This is with the

view to establishing what might be considered appropriate class size that will promote

teaching and learning in schools. This is then the rationale for this study.

1.2 Statement of the Problem

The objective of secondary school education is to produce high quality students who

would be able to face the challenges of the society and prepare them for higher education.

4

Today, our secondary education is faced with high population of students since the inception

of Universal Primary Education in Nigeria. Consequently, there has been high percentage of

student‟s failure in Mathematics.

Many studies have been conducted to find out the causes of this poor performance in

Mathematics among secondary school students (Korau, 1988). Reasons ranging from quality

of teachers, lack of utilization of instructional materials as a result of shortage of funds, lack

of workshops and seminars for Mathematics teachers, over-crowded classrooms, lack of

Mathematics textbooks, lack of Mathematics laboratory to mention a few have been

advanced. On the part of the students themselves, reasons given range from lack of interest,

poor attitude to learning, and effects of peer groups influence and many others (Kemiyele,

1993). These variables make teaching/learning of Mathematics in secondary schools difficult

for government to achieve the main stated objectives

1.3 Objectives of the study

The objectives of this study are to:

i. Investigate the relationship between class size and varying ability levels and students‟

performance in Mathematics in junior secondary schools.

ii. Determine the effects of class size and ability levels on gender-related difference in

the performance of students in Mathematics in junior secondary schools.

iii. Determine the relationship between teachers‟ qualification and students performance

in Mathematics in Junior secondary schools.

1.4 Research Questions

In an attempt to come up with relevant findings in this study, the following questions

were raised to guide and give focus to the study:

i. What is the relationship between class size, ability levels and students performance in

Mathematics in Junior secondary schools?

5

ii. What is the effect of class size on male and female students with different ability

levels and students‟ performance in Mathematics in junior secondary schools?

iii. What is the relationship between teachers‟ qualification and students‟ performance in

Mathematics in Junior Secondary Schools?

1.5 Hypotheses

The following hypotheses were postulated and tested at 0.05 level of significance.

H01: There is no significant relationship between class size and performance of students

exposed to various class sizes and ability levels in mathematics.

H02: Class size does not significantly affect the performance of male and female students

exposed to different class sizes and varying ability levels in mathematics.

H03: Teachers’ qualifications have no significant relationship with the students’

performance in mathematics in secondary schools in Kaduna metropolis.

1.6 Significance of the study

The findings of this study will hopefully provide the following benefits:

It is hoped that this study would contribute in enhancing the standard of

teaching/learning of mathematics in any given class size and the students’ ability levels. This

study would encourage mathematics teachers particularly in junior secondary schools to

acquire skills and appropriate teaching methods so as to encourage interest and

comprehension of the principles and concepts taught in any given class size and varying

ability levels of the students.

Education planners, mathematics educators and curriculum designers would

hopefully benefit from the findings of this study through the evolution of teaching/learning of

mathematics in secondary schools with the aim of improving students’ performance in any

given class size.

This study would provide mathematics teachers with a guide on how to control

6

various class size at any given time in order to improve students’ performance in

mathematics.

Education authorities and state ministry of education would be alerted to the extent to

which various class size effects can contribute to the achievement of various ability levels in

teaching/learning of mathematics in junior secondary schools.

This study would hopefully enable other researchers to identify areas for further

studies in relation to the effects of class size and students’ ability levels for the improvement

of teaching/learning.

The findings would be useful in educational policy making and finding may arouse

instructional educational agencies such as Federal Ministry of Education, Facilities or

Schools of Education, National Teachers’ Institute as well as professional bodies such as

Mathematics Association of Nigeria (MAN), Science Teachers Association of Nigeria

(STAN) to formulate educational policies which would be useful in implementation of

mathematics curriculum.

1.7 Basic Assumptions

This study is guided by the following assumptions:

1. The students used were familiar with the area of staffing, facilities as well as students

enrolment.

2. The selected topics were appropriate for the level of subjects used for the study.

3. Most mathematics teachers in the secondary schools do not know how to cope with

overcrowded class rooms.

4. Teachers are employed to teach mathematics in secondary schools without

considering the effects of class size and ability levels of the students.

5. The teachers cannot give individual attention to the medium (average) and low

achievers in schools where mathematics are overcrowded.

7

1.8 Scope of the Study

This study is basically on the effects of class size and ability levels on students‟

performance in Mathematics among Junior Secondary School Students in Kaduna

Metropolis. The study sought to expose some of the numerous factors responsible for poor

performance in Mathematics. It was therefore restricted in its coverage to all J.J.S. two (2)

students in the Government Secondary Schools in Kaduna Metropolis with total students‟

population of three hundred and two thousand, one hundred and sixty-one (302,161)

students.