EFFECT OF PEER MEDIATED INSTRUCTION ON THE ACADEMIC ACHIEVEMENT OF STUDENTS IN ALGEBRA.PDF

8/16/2019 EFFECT OF PEER MEDIATED INSTRUCTION ON THE ACADEMIC ACHIEVEMENT OF STUDENTS IN ALGEBRA.PDF

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EFFECT OF PEER MEDIATED INSTRUCTION ON ACADEMIC ACHIEVEMENT OF STUDENTS IN

ALGEBRA

BY

EKE, HENRYPG/08/09/152014B.Sc (Ed) Maths, UNN

Dissertation Submitted to the Postgraduate Schoolin Partial Fulfillment of the Requirements for the

Award of Degree of Master in Education (M. Ed) inMathematics of the Delta State University, Abraka.

DEPARTMENT OF SCIENCE EDUCATIONDELTA STATE UNIVERSITY, ABRAKA

JULY, 2012.


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APPROVAL PAGE

This dissertation has been approved by the Department of

Science Education, Delta State University, Abraka, for the

award of the M.ED Degree in mathematics.

BY

___________________________ _______________________Dr. U. L. Ezenweani DateSupervisor

__________________________ _______________________Prof. Emperor Kpangban DateHead of Department

___________________________ _______________________Prof. P.O. Ikoya DateDean of Faculty

___________________________ _______________________Dr. P. O. Ajaja DateInternal Examiner

__________________________ _______________________Prof. U. N. V. Agwagah DateExternal Examiner


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DEDICATION

This work is especially dedicated to my beloved wife Mrs.

Roseline Eke and our children – Mercy, Joy and Miracle.


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ACKNOWLEDGEMENTS

This work could not have been successful without the help

of the almighty God who granted me great favor before

everybody I came in contact with throughout this program of

study. To God be the Glory.

I wish to express my gratitude to my able and dynamic

supervisor, Dr U.L. Ezenweani for his patience, guidance and

direction throughout this work. My gratitude also goes to Dr

P.O. Ajaja for his valuable contributions, useful criticism and

corrections which led to the success of this work. I equally owe

a lot of thanks to my lecturers at Delta State University,

Abraka. Few names however deserve special mention. They are

Professors N.S. Okoye, Emperor Kpangban and E.A. Iniomesa.

Others are Dr T.E. Agboghoruma, Dr Mrs. M.O. Mokobia, Dr

(Mrs.) R.J. Musa, and Dr (Mrs.) J.I Adjekpovu

I wish to appreciate the Executive Chairman, Post Primary

Education Board Asaba for granting me study leave with pay for

this fulltime program of study.


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I also wish to thank the principals, staff, students and

particularly the research assistants of the schools used for the

study for their concern and cooperation throughout the period

of the field work in their schools.

I also acknowledge with thanks the member of Christ Air

Force Ministry, Kwale for their prayers that successfully saw me

through this program of study. I shall not fail to remember my

friends Mr. Oghobe Anthony, Pastor Ofumaduadike Mike and

Pastor Malagu Festus for their constant prayers and

encouragement throughout the period of my study. Finally, I

appreciate my dear wife, Mrs. Roseline Eke for her prayers and

financial contributions. I equally appreciate my children, Mercy

Joy and Miracle who accepted my continuous absence, missed

my company and for most part of the duration of this study.

Eke, Henry


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TABLE OF CONTENTS

Certification - - - - - - - - iii

Approval Page - - - - - - - - iv

Dedication - - - - - - - - v

Acknowledgements - - - - - - - vi

Table of Contents - - - - - - - viii

List of Tables - - - - - - - - xi

List of Figures - - - - - - - - xiii

Abstract - - - - - - - - - xiv

CHAPTER ONE: INTRODUCTION

Background of the Study - - - - - - 1

Statement of Problem - - - - - - 11

Research Questions - - - - - - - 12

Research Hypotheses - - - - - - 13

Purpose of the Study - - - - - - 14

Significance of the Study - - - 15

Scope and Delimitation of the Study - - - 16

Limitations of the Study - - - - - - 16

Operational Definition of Terms - - - - - 17


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CHAPTER TWO: REVIEW OF RELATED LITERATURE

Theoretical Framework of the study - - - - 19

Peer Mediated Instruction - - - - - - 24

Teaching of Algebra in Nigerian Schools - - - 31

Application of Peer Mediated Instruction in

Teaching Algebra - - - - - - - 39

Empirical Studies on Achievement of Students in

Algebra - - - - - - - - 42

Appraisal of the Review - - - - - - 46

CHAPTER THREE: RESEARCH METHODS AND PROCEDURE

Design of the Study - - - - - - - 49

Population of the Study - - - - - - 51

Sample and Sampling Procedure - - - - 51

Research Instrument - - - - - - 52

Treatment Procedure - - - - - - 55

Method of Data Analysis - - - - - - 57


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CHAPTER FOUR: ANALYSIS OF RESULTS AND DISCUSSION

Discussion of Research Questions - - - - 58

Testing of Research Hypotheses - - - - 63

Discussion of Results - - - - - - - - - - 78

CHAPTER FIVE: SUMMARY CONCLUSION AND

RECOMMENDATION

Summary of the Study - - - - - - 84

Conclusion - - - - - - - - - - - 88

Contributions to Knowledge - - - - - - 90

Recommendations - - - - 90

Suggestions for Further Studies- - - - - 91

References - - - - - - - - 93

Appendix A: Lesson notes for Teachers - - - 101

Appendix B: Algebra Achievement Test (AAT) - - 114

Appendix C: Reliability Coefficient of AAT - - - 124

Appendix D: Test of Assumption of Homogeneity of

Regression - - - - - - - - 127


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Appendix E: Pre-test and Post Test Data Collected from Algebra

Achievement Test - - - - - - 130

LIST OF TABLES

Table I: Variable Matrix Design for Algebra Achievement

Of School Location by Gender - - - - - - 50

Table II: Test Blue print for SS1 Algebra Achievement

Test - - - - - - - - - - 54

Table III: Post-test mean achievement scores of

PMI and self directed study groups in Algebra - - - - 58

Table IV: Post-test Mean Achievement Scores and Standard

Deviation of Urban and Rural PMI students in Algebra - - 59

Table V: Post-test Mean Achievement Scores and Standard

Deviation of Male and Female PMI Students in Algebra - 60

Table VI: Post-test Mean Achievement scores and standard

deviation of subjects by method and gender - - - 61

Table VII: Post-test Mean Achievement Scores and standard

deviation of subjects by method and school location - - 62


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Table VIII: One-Way Analysis of Covariance (ANCOVA) of

Posttest scores of Students exposed to peer- mediated

instruction and those exposed to self directed study - 63

Table IX: Estimated Marginal Means of the Experimental and

control groups - - - - - - - - - - 64

Table X: One-Way ANCOVA table of posttest mean

achievement scores of Urban and Rural PMI Students - - 66

Table XI: Estimated Marginal Means of urban and rural PMI

Students - - - - -- - - - - - - 67

Table XII: One-Way ANCOVA of posttest mean achievement

scores of male and female PMI Students - - - - 69

Table XIII: Estimated Marginal Means of male and female PMI

students - - - - - - - - - - - - 69

Table XIV: Two-Way ANCOVA table of subjects scores in AAT

showing interaction of method and Gender - - - 72

Table XV: Estimated Marginal Means showing the interaction of

Teaching Methods and Gender - - - - - 73

Table XVI: Two-Way ANCOVA Table of subjects scores in AAT

showing interaction of method and school location - - 75


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Table XVII: Estimated Marginal Means showing the interaction

of Teaching Methods and School Location - - - 76

Table XVIII: ANCOVA Test for Homogeneity of Regression - 127

LIST OF FIGURES

Figure 1: Estimated marginal means of algebra test score for the

two teaching methods - - - - - - - - 65

Figure 2: Estimated marginal means of algebra test score for

urban and rural PMI students - - - - - - 68

Figure 3: Estimated marginal means of algebra test score for

male and female PMI students - - - - - 71

Figure 4: Estimated marginal means of algebra test score

showing the interaction of teaching methods and Gender - 74

Figure 5: Estimated marginal means of algebra test score

showing the interaction of teaching methods and school

location - - - - - - - - - - - 77

Figure 6: Graph showing the linear relationship between the

covariate and the dependent variable - - - - 129


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ABSTRACT

This study investigated the effects of peer mediated instruction (PMI) on the

academic achievement of students in algebra in Delta North Senatorial

District of Delta State. This study was necessitated by the poor achievement

of senior secondary school students in mathematics. Five research questions

and five null hypotheses were formulated to guide the study. The study

employed a non equivalent control group quasi experimental design. A sample

of 192 SSI students drawn from six mixed senior Secondary schools was used

for the study. Data was collected using a 30 – item Algebra Achievement Test

drawn from WAEC past questions. The Kuder-Richardson 20 formula was

used to establish the reliability coefficient which was found to be 0.71. Data

was analyzed using mean, standard deviation and analysis of Covariance

(ANCOVA) at a significant α - level of 0.05. The findings of the study show

that the use of PMI is found to be more effective than the self directed studygroup. The results also show that there was no significant difference between

the achievement of both the male and female and urban and rural students

exposed to PMI technique. The results also confirm that while there was no

significant interaction effect between methods by Gender there was a

significant interaction effect between methods by School Location. Based on

the findings, it was recommended that teachers should apply PMI technique

as an effective strategy in teaching algebra in senior secondary schools.


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CHAPTER ONE

INTRODUCTION

Background of the Study

The National Policy on Education (FRN, 1998) and

revised (2004) made Mathematics so important that every

child must study it for six years in primary school, three years

in Junior Secondary School and three years in Senior

Secondary School. Mathematics is a subject that affects all

aspects of human life in different degrees. The socio economic,

political, geographical scientific and technological aspect of

man is centered on numbers (Malik, Ngban and Ibu, 2009).

In Nigeria, mathematics taught in schools include:

Arithmetic, Geometry, Trigonometry, Algebra and Statistics.

Ukeje (1997) remarked that “without mathematics there is no

science, without science there is no modern technology and

without modern technology there is no modern society”. This

statement implies that mathematics is a strong factor to

societal building and development. Its indispensability is often

encountered in the contribution of mathematics contents in

the studies of science and technology courses mostly at the


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higher level of education. Mathematics occupies a central

place in the scientific and technological development of any

nation. Yet the teaching and learning of the subject, at the

secondary school does not reflect the commitment and

seriousness that teachers and students ought to show in the

teaching learning process. The performance of students in

mathematics has proved that the teaching of the subject is

below expectation. No wonder teachers parents and

government are worried about the situation. Available data at

the WAEC office in Ghana for May/June Senior Secondary

Certificate Examination (SSCE) conducted in Nigeria between

2004 and 2006 revealed that only 32% - 42% of the candidates

passed mathematics at credit level.

Numerous complaints such as one by Elekwa (1996)

over the poor level of students’ achievement in mathematics in

our secondary schools aroused my concern and interest to

look into some ways of ameliorating the problem of poor

performance.

According to Adeleke (2007) the performance of students

in mathematics at the senior secondary school level in Nigeria


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is not encouraging despite the importance attached to it both

as an academic discipline and as knowledge that everybody

needs in the society as stipulated in the national policy on

education (FRN, 2004). The need to curb this problem of poor

performance in mathematics and to make a case for effective

approaches for its teaching has led to various policies,

programmes and decisions aimed at achieving the goals of

mathematics education. The most comprehensive of this is the

National Policy on Education (NPE) which recommended that

the teaching of mathematics at the primary and secondary

schools should be compulsory.

Obioma (1989) observed that secondary school students

in Nigeria are known to demonstrate low attainments in

mathematics examinations. This has made some students to

develop fear and dislike for mathematics. One particular area

where students have problems is Algebra. WAEC (2004)

reported candidates’ weakness in algebraic expression and

word problems. Thus algebra has been known to be a major

stumbling block in the learning of mathematics. Problems with

algebra can be ascribed to the use of traditional teaching


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method and their effects on the learners have bearing on the

performance of students in mathematics examinations

(Kieran, 1992). In the traditional methods of teaching algebra,

students are exposed to rote learning and mastering of

algorithms where mathematical operations are taught through

procedures that lead the students to the correct answer. This

approach does not encourage mathematical reasoning, so

when students are presented with problems that require

conceptualization they become frustrated and develop

mathematical phobia. The classroom teacher has in most

cases borne the responsibility of students’ poor performance in

mathematics examinations. Obioha (1987) and Njoku (1993)

for instance, are of the opinion that teacher’s instructional

methods and strategies have often affected the poor

performances of students and indeed the classroom

procedure. One of the biggest misconceptions about the

teaching and learning of mathematics is the belief that there is

only one method for determining the solution of problems.

This situation will remain as long as instruction remains

uniform for all students irrespective of individual difference.


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teacher guidance will normally depend on how much he knows

of the learner, his ability to diagnose the problem of the

learner and intervene appropriately and on time too. Thus

effective teaching must aim at helping the learner to take the

best of what his environment can afford as learning

experiences.

The teaching of mathematics has been that of the teacher

initiating knowledge while students sit as passive recipient of

knowledge. This has resulted in the downward performance of

students (Ado, 2008). Defur (2002) observed that the low

performance of students in examinations can be traced to

teachers inability to deliver effective instruction. This suggests

that the major objectives of teaching mathematics are not

being achieved with the method in use; hence there is need for

teaching strategies that will create varieties of activities which

involve active participation of the learner, induce the spirit of

cooperation, competition and inquiry under the guidance of

the teacher. These have led to the development of various

teaching techniques to make learning more suitable to the

learner. These techniques include the Individualized


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Prescribed Instruction (IPI), Computer Assisted Instruction

(CAI) and Mastery Learning. All these techniques emphasize

on task learning. It is against this background that the effect

of peer mediated instruction (PMI) on the academic

achievement of students in algebra is being investigated.

The PMI is a teaching technique aimed at helping students

acquire the best learning experiences which they failed to

attain as a result of poor learning environment. The PMI is

based on Vygostky’s social development theory. This theory is

one of the foundations of constructivism. In the constructivism

theory, the learner interprets, organizes and uses information

from the environment and uses the knowledge gained from

these actions to acquire skills and knowledge. During peer

interaction, students speak at a level that other students

understand, challenge each other and try to reconcile

contradictions, take feedback from other students seriously

and accept communication and corrections from other

students (Damon, 1984). All these play a role in effectiveness

of collaborative work. The act of explaining plays essential role

in the process of resolving cognitive conflict which entail a


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series of interaction in which students explain their view

points to each other. Students benefit from receiving

explanation from peers who have more knowledge, better

understanding or a different perspective. They benefit from

explanations that help them clarify, correct, elaborate or

solidify their own understanding. In the context of teaching

role, most researchers found that giving explanations relates

positively to achievement (Webb, 1989 and Pallinscar, 1998).

That is when a student gives explanation in other to help

someone else. This action also benefits her understanding and

achievement. This implies that the role of PMI in context of

learning is significant. Peers are known to respond to

themselves faster than they do to adults and this will help the

children to learn new materials in academic situations

(Essuman, Nwaogu and Nwachukwu, 1990) thus students

gain more knowledge through the private studies, discussions

and tutorials which follows instructions.

For the purpose of this study, peer mediated instruction

(PMI) is an educational programme in which students act as

teachers to other students. When one critically observes the


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secondary schools, one will clearly see that students put in

much of their learning time and efforts on their own during

mathematics examinations. A close observation will also show

that some of them teach other students. PMI is an

instructional strategy that consists of pairing students

together to learn an academic task. This pairing of students

can be based on the same or differing ability and/or age range.

Bender (1992) defined PMI as an instructional method

that assists in the development of both academic and social

skills among children with learning disabilities. These children

may participate on one to one peer tutoring in which one child

teaches the skill to a recipient. At a particular time, one

member of the group directs the learning activities that guide

or teach the other. The learning that takes place under this

condition is what is considered as peer mediated learning.

This study seeks to identify the effect of PMI on the

achievement of students in algebra as it relates to gender

(male and female) and school location (Urban and rural). The

issue of gender has become relevant in the study because the

schools in the study area are mixed secondary schools.


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Gender as a variable is widely believed to have influenced the

achievement of students in mathematics examinations.

Evidence from researches reveals that gender is a significant

factor in secondary school mathematics achievement (Obioma

& Ohuche, 1980). Fennema and Carpenter (1981) observed

that there is no significant difference in the performance of

boys and girls in mathematics before the age of 11. This

difference becomes significant in favor of the boys after the age

of 11. Research evidence (Agwagah and Ezeugo, 2000; Harbor

Peters 1993) also revealed that there is difference in the

achievement of students in mathematics scores in favor of

boys. Thus this study seeks to investigate the effect of PMI on

the achievement of boys and girls in algebra. The school

location as another variable is relevant in the study since

many secondary schools are located in both the urban and

rural areas. The urban-rural influence on mathematics

learning as in any other subject is expected because of the

psycho-social influence it may have on teachers and students.

Emma (1989) noted that students in the urban environment

are exposed to the presence of material properties, electronic


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and high technology products which are likely to stimulate the

students intelligently. This suggests that students in urban

areas will perform better than their rural counterparts in

mathematics examinations. In discussing the influence of

school location on the achievement of students in

mathematics, Maliki, Ngban and Ibu (2009) noted that

students in the rural areas, against all odds, perform better

than their urban counterparts. Thus, this study will seek to

investigate the effect of PMI on the academic achievement of

urban and rural based students in algebra.

Statement of Problem

This problem was identified due to the continuous low

achievement by students in the senior secondary school

mathematics examination. WAEC Chief Examiners Report in

the past few years points to students’ poor performance in

mathematics. The Chief Examiners observed that candidates

had problems in simplifying algebraic expression and solving

word problems. Furthermore, students’ poor performances in

mathematics examinations suggest that the instructional

methods used by teachers are ineffective. This incidence of


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ineffective mathematics instruction in our senior secondary

schools necessitated the need for an alternative approach

which has the potential for effective teaching and learning of

algebra. One such approach is the use of PMI in algebra

learning. The statement of problem therefore is; will the

application of PMI in mathematics instruction enhance

students’ achievement in algebra?

Research Questions

To guide this study, the following questions were raised.

i.

What are the mean achievement scores of students

exposed to PMI and those exposed to self directed study

in algebra?

ii.

What are the mean achievement scores of urban and

rural students exposed to PMI in algebra?

iii. What are the mean achievement scores of male and

female students exposed to PMI in algebra?

iv.

What is the effect on the interaction of method by gender

in both students exposed to PMI and those exposed to

self directed study in their posttest mean achievement

scores in algebra?


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v. What is the effect on the interaction of method by school

location in both students exposed to PMI and those

exposed to self directed study in their posttest mean

achievement scores in algebra?

Research Hypotheses

From the research questions raised above the following

null hypothesis were formulated and tested at a significant α

level of 0.05.

HO1: There is no significant difference in the mean

achievement scores of students exposed to (PMI) and the

self directed study group in algebra.


achievement scores of urban PMI students and their

rural counterparts in algebra.


achievement scores of male PMI students and their

female counterparts in algebra.

HO4: There is no significant interaction effect between method

and gender on students mean achievement scores in

algebra in both PMI and self directed study group.


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HO5: There is no significant interaction effect between method

and school location on students mean achievement

scores in algebra in both PMI and self directed study

group.

Purpose of the Study

The major purpose of this study was to investigate the

effect of peer mediated instruction on the academic

achievement of students in SS1 algebra. Specifically, the study

sought to:

i.

Find out if the PMI students will perform better than the

self directed study group in algebra.

ii.

Find out if there is a significant difference in the mean

achievement scores of male and female PMI students in

algebra.

iii. Compare the achievement of urban and rural PMI

students in algebra.

iv.

To find out if the interaction of method by gender and

method by school location influence students’ mean

achievement scores in algebra.


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Significance of the Study

The findings of this study may help school owners with

relevant information on PMI which would enable them to

incorporate the technique into their school curriculum.

Educational researchers would equally benefit from the

findings in this study since the study may highlight gaps in

instructional methods especially in terms of time constraints

in teaching mathematics. Information provided by this study

may also help to generate and sustain a continuous research

in area of improving mathematics teaching in senior secondary

schools.

The findings in this study may also enable teachers to

apply PMI in classroom since it can accommodate a classroom

of diverse learners including students with learning disabilities

(Access Centre, 2004). PMI is easy to implement by the teacher

since it does not cost him anything to obtain maximum

benefit.


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The findings in this study may also help students to

understand and appreciate that interaction with their peer

would bring about social standing among them.

Curriculum planners may also benefit from the findings

since awareness would be created on the essence of PMI in the

learning of mathematics in schools.

Scope and Delimitation of the Study

This study was limited in scope to finding out the effect of

PMI on academic achievement of students in algebra. The

aspect of algebra that was focused on was quadratic

equations. The choice of this topic was based on the repeated

reports from the WAEC Chief examiner’s report that students

could not solve simple algebraic equations correctly.

The study covers SS 1 students in public mixed secondary

schools in Delta North Senatorial district of Delta State.

Limitations of the Study

Generally the findings of the study may be affected by the

following factors.

Some of the students in the sampled schools were

frequently chased away from classes by the school authorities


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during PMI sessions for not participating in evening sports

activities. This irregularity in attending classes may have

affected the performance of students in the study.

Research assistants used for the study were trained and

tested; this does not guarantee them to produce the desired

effect on the subjects during the treatment.

In spite of these limitations, the findings strongly indicate

that PMI approach made a difference in the achievement of

students in algebra.

Operational Definition of Terms

To assist the comprehension of this study, a list of terms

utilized is provided.

1.

Peer: These are students in the same class undergoing

the same learning experiences.

2. Peer Mediated Instruction (PMI): This is an

instructional strategy in which a peer through a structured

arrangement interacts or mediates with another peer in other

to promote learning.

3.

Achievement: This is a measure of the overall performance

of a learner in a test.


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4. Peer Tutor: This is a student who was used in instructing

his/her classmates.

5. Peer Tutee: A low achieving student who receives instruction

from his/her classmates.

6. Subjects: These are students who were used in the study.

7. PMI students: Students who were exposed to peer mediated

Instruction.


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CHAPTER TWO

REVIEW OF RELATED LITERATURE

This chapter presents the review of related literature

under the following headings.

1) Theoretical Framework of the study

2)

Peer mediated instruction

3)

The teaching of Algebra in Nigerian schools.

4)

Application of peer mediation in teaching of Algebra.

5)

Empirical studies on achievement of students in

mathematics.

6) Appraisal of the review

Theoretical Framework of the study

Vygotsky (1978) formulated the theory of peer mediation

otherwise called Vygotsky’s social development theory which is

one of the foundations of constructivism. The constructivist

theory and social development theory of Vygotsky reinforce the

impact of learners’ participation in peer interactions. Thus,

learners’ activities are always bounded in a social context and

involve learners’ use of language and interpretative abilities.

The learners in this case interpret and organize information


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from the environment and use the knowledge they gain from

these activities to acquire skills and knowledge. Ascherman

(2001) remarked that as children discover a world that is full

of meaning through interactions with their peers, they help to

shape and share in their own developmental experiences.

Ascherman further noted that in determining the nature and

part of development in the learner, it is essential to determine

the social environment where the development occurs. The

development in the learner does not occur in isolation but

rather it is formed by the interconnection of social

relationships and interaction between them. Thus, as learners

coordinate ideas, they are able to contribute to their present

understanding of the situation and information that is related

to it cognitively and socially.

Vygotsky (1978) argued that cognitive development not

only takes place with social support from others in an

interaction, but also involves the development tools for

mediating intellectual activity. Hence social interactions play

an important role in cognitive development.


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“Every function in the child’s (Cultural) development appears

twice, first on the social level and later on the individual level;

between people (interpsychology) and then inside the child

(intrapsychology)” (Vygotsky, 1978). Vygotsky’s psychological

model emphasized the role of dialogue in mediated cognitive

growth and suggested that learners were able to perform in

collaboration with one another, what they have not mastered

independently. The constant dialogue between the learners as

they discuss and negotiate helps strengthen their language

and mathematical skills. Moore (1991) described dialogue as

the interaction between the teacher and learner, when one

gives instruction and the other responds. Corsaro and Rizzo

(1988) emphasized that learners interaction with their

playmates affect their development. This occurs through the

constant dialogue, negotiation and construction of experiences

between the learners within their interactions. The learners

are able to do this at a level between them that is different

from interactions with adults.

Vygotsky (1978) remarked that there are certain areas in

learners’ interaction that specifically contribute to a higher


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level of cognitive understanding; one such area is the zone of

proximal development (ZPD). Vygotsky defined the zone of

proximal development as the distance between the actual

development level as determined by individual problem solving

and the level of potential development as determined through

problem solving under adult guidance or collaboration with

more capable peers.

The ZPD defines the functions that have not yet matured

in the learner, but are in the maturation process. Without the

learner interacting and communicating, their zone of proximal

development would not be affected (Aschermann, 2001).

Tharpe and Gallimore (1988), while discussing Vygotsky’s

theory emphasized the need for education to move towards a

more collaborative role between students and teachers. They

remarked that teaching must be redefined as “assisted

performance” where teachers assist the learner by providing

structure and assistance in their work. This assisted

performance occurs between the learner when they participate

in experiences together by providing information to each other

thereby increasing their understanding of the activity or


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concept. This is related to Vygotsky’s term of working with the

zone of proximal development. When teaching is structured

under the concept of assisted performance, it works within the

zone points where the learners’ performance requires

assistance. The learner can move through the ZPD by a more

capable person or by practicing a skill on their own while in

the process of mastering it. The more capable person can

either be an adult or a peer.

Tharpe and Gallimore (1988) noted that in any

educational settings, peer models are more important sources

of assisted performance. This is similar with Vygotsky’’s view

of the learner developing within their social world and the

importance of peer interactions and fostering higher levels of

cognitive development.

The researcher considered this theory to be more

appropriate for this study because it stressed on the use of

peers in teaching concepts that have been learnt. This study

involves peers interaction with other peers through discussion

which will help them have a proper understanding of whatever

they are taught.


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Peer Mediated Instruction

Peer mediated instruction has played an important role

in education and has probably existed in one form or other

since the beginning of civilization. The first systematic

approach to peer tutoring is credited to Andrew Bell in late

18th Century. Bell realized that using monitors to teach other

children was a significant discovery than to cut cost by using

unorthodox and sandy teaching practices (Brendan, 2000).

Another important player in peer tutoring is Joseph Lancaster.

According to Brendan, Lancaster opened a school in London,

England in 1801 where he was responsible for about 350

students. Since there was no way he could teach this number

at the same time and maintain order, he decided that boys

who know little were qualified to teach those who knew less.

The numerous instances of peers teaching peers and the

generally accepted value of tutoring involving two peers have

lent great practical support to the elaboration of the idea of

peer mediated instruction as an effective program in

facilitating the learning of algebra in our secondary schools.

Elekwa (1996) remarked that in most of our secondary


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children work together on an academic activity, with one child

providing assistance and instructional feedback to the other.

For Hall and Stegila (2003) peer mediated instruction and

intervention is an alternative classroom arrangement in which

students take an instructional role with classmates or other

students. Several approaches have been developed, some

support students working in pairs and other allow students to

work in small cooperative learning groups. For this instruction

to be effective, students must be taught instructional roles to

be systematic, to elicit responses and provide feedback

(Tontaleya, 2007). The effectiveness of PMI requires a high

degree of attention devoted to supervision of students learning

activities. Hall and Stegila (2003) supported the use of these

approaches as alternative practice activities; however, they do

not condone the use of peers for providing instruction in new

instructional content.

Hall (2002) explained four features of PMI as follows:

Students are taught roles by their teacher. During this

phase the teacher shows students how to help peers and


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provides the format in which a concise and clear peer

mediated learning can take place.

Students provide instruction to other students. In this

phase once the teacher has determined that students

have mastered the skills necessary for success, students

are allowed to provide instruction to other students.

Students are not allowed to present new concepts, they

merely reiterate key concepts that have already been

explained, identified and addressed by the teacher. The

students are merely used to assist peers and further their

understanding of concepts.

Teachers monitor and facilitate. During this process, the

teacher monitors and facilitates pupils’ progress. The

teacher ensures that students are receiving appropriate

redirection by peers. Thus both students will act as tutor

and tutee. Generally, these students will be required to

become experts in certain task and then they must

demonstrate this proficiency to the teacher and tutee.

Academic and social goals. The goal of PMI is to build

academic and social skills. Instruction of this type


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enables each peer partner to enhance each other’s

understanding of the concept and to develop critical

thinking skills. Thus, students learn and discuss

academic goals and understand that learning is a social

cognitive activity.

The PMI is implemented through various designs. This

study will focus on two widely researched form or model of

PMI. The cooperative learning model and the peer mediated

instruction and intervention Dyads model.

In the cooperative learning model, the teacher groups

students, and the students share knowledge and ideas within

the group (Hall and Stegila, 2003). The cooperative learning

model is accomplished through team cooperative learning and

group and regroups models. Team cooperative learning is

achieved when students remain in the same group through an

entire lesson (Johnson and Johnson, 1986). Team cooperative

learning is divided into three subunits; students teams

achievement divisions, cooperative integrated reading and

comprehension and teams games tournaments.


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have the opportunity to develop interpersonal skills, while the

older students learn how to facilitate learning, the younger

student who is disabled is provided with the opportunity to

practice and obtain mastery with the academic material.

In Class Wide Peer Tutoring (CWPT) students are all in

the same class and are being taught the same material. The

students are instructed on how they can assist each other in

the role of the tutor and tutee. Nobel (2005) remarked that

during the practice phase of the system, students are taught

how to present material to their partner, praise correct

responses and provide error correction for incorrect responses.

In this model, students swap roles so that each will have a

chance to serve as tutor and tutee (Hall and Stegila, 2003).

Nobel (2005) remarked that CWPT has been used primarily to

teach discrete skills or concepts, such as vocabulary words,

math facts, or spelling word. Concepts with more than one

acceptable response or responses that require elaboration

would be difficult to practice with CWPT. The academic skills to

be tutored are usually chosen by classroom teacher.


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The cross-age tutoring model is commonly used outside

the general classroom environment. Cross-age tutoring

approach joins students of different ages, with older students

assuming the role of tutor and younger students assuming the

role of tutee (Hall and Stegila, 2003). Maher (1984) observed

that the younger and older students benefit socially from the

tutoring environment and learn the academic content.

Teaching of Algebra in Nigerian Schools

Wikipedia Encyclopedia (2010) defined algebra as a

branch of mathematics concerned with the study of rules of

operation and relations and the construction and concepts

arising from them, including terms, polynomials, equations

and algebraic structures. For Kieran and Yerushalmy (2004)

algebra is seen as a generalization of numeric and geometric

patterns and the law governing them; while Sfard (1994)

discussed algebra as a generalized arithmetic consisting of

“operation and structural phases”. The operation algebra can

be summed up as being tied to arithmetic operation while the

structural algebra can be seen in solving an equation with

variables on both sides.


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Historically, algebra can be traced to ancient Babylonians

who developed an advanced arithmetic system with which they

were able to do calculations in an algorithmic fashion. The

Babylonians developed formulas to calculate solutions for

problems typically solved today by using linear equations,

quadratic equations and indeterminate linear equations (Struit

and Dirk, 1987).

Since the introduction of formal education in Nigeria,

mathematics has gone through several developments, from the

era of formal arithmetic, algebra, geometry, trigonometry and

the likes through the period of traditional and modern

mathematics controversy to the present day general

mathematics (Aguele and Usman, 2007). At the secondary

school level in Nigeria, the mathematics curricula consisted of

arithmetic, geometry, algebra, trigonometry, and statistics.

The method of teaching the subject consisted of computational

drills, algebraic manipulations and some exposure to

deductive method of logical reasoning. The teachers’ main

objective was to prepare students to pass examinations but

this idea has resulted in teachers and students being


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compelled to work to restricted examination syllabus with

definite bias to passing examinations (Elekwa, 1996).

The traditional method of teaching algebra in our schools

has been identified as being ineffective and is one of the major

factors responsible for the students’ low achievement in

mathematics in public examinations. Osibodu (1988)

attributed this to the pattern in which answers to the previous

day homework are first given, and then teacher-directed

explanations are used to present materials for the new lesson.

This widespread discontent over the state of mathematics

teaching and learning in our schools prompted the Federal

Ministry of Education and her agencies to organize

conferences, set up task forces and committees to study the

problems and issues militating against effective mathematics

instruction in our schools. These problems as reported by the

Nigerian Educational Research and Development Council

(NERDC) Task force on mathematics (1977) include:

The growing increase in school population with attendant

problems of corresponding increase in the range of

interest, abilities and levels of intelligence.


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Language evaluation and management problems.

Inadequate number quality of teachers required to carry

through mathematics curriculum.

Adepoju (1991) remarked that mathematics curriculum

was adequate and the real problem in the teaching of

mathematics remains the provision of mathematics teachers

in the right quantity and quality. The teaching and learning of

algebra has been seen as a source of difficulty. The situation

in Nigeria reveals problems similar to researches carried out in

various parts of the world. These problems can be ascribed to

external factors like the teaching approach, poor image and

also to the intrinsic difficulties of the topic. Teachers,

mathematicians and mathematics educators consider algebra

to be one of the most important areas in senior secondary

school mathematics curricula. In spite of the importance

placed on it, many students find it difficult to comprehend.

The problem of students’ linguistic abilities places serious

constraints on actual algebra teaching. Oviedo (2005) observed

that students linguistic ability play an important role in their

learning and conceptual processing of academic subjects. For


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example, the task of solving word problems relies on students’

comprehension abilities, so that faulty solutions to word

problems may be traced to incorrect text comprehension and

inability to access relevant background knowledge. Harbor-

Peters and Agwagah (1993) remarked that students perform

badly in word problems because of their inability to

comprehend the problems. They argued that if a student has a

problem with reading, he cannot even read or understand a

mathematical problem and so cannot solve it. Oviedo (2005)

further stated that in many instances individuals who seem to

lack adequate computational skills in solving word problems

demonstrate these skills when problems are presented in

numeric form. Research has shown that most of the

difficulties with word problems arise from mismatch between

text comprehension, situation comprehension and problem

solving procedures.

Another problem observed by teachers in the teaching of

algebra is that grown-ups often have negative image of

algebra, and many students can make no sense of it. In other

words, algebra is seen as a very rigid abstract branch of


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mathematics having no relationship with the real world.

Ezenweani (2006) noted that the society has preconceived that

mathematics is a very difficult subject and that only gifted

individuals can excel in its study. This notion has been

transferred to the children about algebra. This is however a

wide speculation that exposing students to the beauty,

elegance and order inherent in mathematics may uplift,

generate and arouse their interest, change their attitude

towards mathematics thereby improving achievement

(Kurumeh, 2007). Kurumeh and Chiawa (2009) noted that the

highest failure rates in all public examinations right from

common entrance examination into the Junior Secondary

School to University matriculation examination is because

students are afraid of mathematics and are not interested in

studying it since they believe that mathematics is difficult to

understand.

Apart from the need for more trained teachers for algebra

instruction in schools, there is a problem of correcting certain

deficiencies in the existing approaches. Most of the

approaches used in instruction could be carried over from the


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way algebra or mathematics teachers had themselves been

taught. Ezenweani (2006) observed some problems inherent in

the study of mathematics to include the abstract nature of its

concepts and their abstraction by the teachers without

experimentation. As a result, mathematical concepts appear

vague to the learner. Thus students cannot understand simple

algebraic concept such as variables, expression and

equivalence. In this regard, the use of teacher centered

approaches with minimal interaction between students and

teachers are particularly inappropriate to algebra teaching.

Agwagah (2000) noted that one such variable which affects the

students in the learning of algebra is the teacher. She further

remarked that teachers’ inability to use instructional materials

in the teaching of algebra could arise from the fact that they

are not familiar with the instructional materials that may be

used in teaching the concept. Alternative teaching styles are

clearly demonstrated in seminar and meetings for upgrading

professional teaching skills.

Yoloye (Cited in Elekwa, 1996) on how many and how

well these identified approaches are being used in our


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secondary schools showed that not enough time is being spent

on these approaches, hence the low level of achievement in

mathematics examinations by a larger segment of learners.

In finding ways of teaching algebra that allow students to

learn with understanding Kaput (2000) outlined the following

as the needed changes from what we already know about

algebra and learning.

Beginning early (in part by building on students’ informal

knowledge).

Integrate the learning of algebra with the learning of

other subject matter. (By extending and applying

mathematical knowledge).

Include the several different forms of algebraic thinking

(by applying mathematical knowledge).

Building on students’ natural occurring linguistics and

cognitive powers. (Encourage them on what they learn

and articulate what they know).

Encourage active learning (and the construction of

relationship) that puts premium on sense making and

understanding.


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Application of Peer Mediated Instruction in Teaching

Algebra

Various forms of PMI have been conducted in a great

range of settings over the years. Most of the researches

conducted were on non educational and educational

environment with positive outcome on each (Hall and Stegila,

2003). Forms of peer mediated instruction and intervention

are reported to be the instructional method of choice for

preventing and alleviating many of the social problems related

to children, adolescents and young adults (Johnson, Johnson

& Stanne, 2000). Fuch, Fuchs, Mathes and Martiniez (2002)

also remarked that socialization experiences that occur during

peer tutoring can benefit both the tutor and tutee by

motivating students to learn and increasing their social

standing among peer.

For successful implementation of PMI in the teaching of

algebra, the Access Centre (2004) identified the following

process of implementing a peer tutoring lesson.


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The teacher trains students on the process of peer

tutoring and strategies for fulfilling their role of tutor or

tutee.

The teacher assigns partners.

Students retrieve their tutoring materials prepared by the

teacher.

Students followed a highly structured tutoring procedure

in which tutors present materials previously covered by

the teacher, and provide feedback to the tutee.

Students switch roles after the teachers signal. The tutee

becomes the tutor.

The teacher circulates around the room monitoring and

providing feedback.

On the application of PMI in teaching of mathematics,

Access Centre (2004) illustrates peer tutoring as a discussion

of vocabulary words, symbols, numbers and their relationship.

The combination of visual representation, communication of

the process, and description of math concept, a student with

disabilities will benefit from the peer tutoring process.


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The PMI can be applied in a number of ways in the

teaching of algebra. Before PMI sessions, the teacher should

clearly specify task to the students, and assigning students to

their tutoring pairs. The Access Centre (2004) remarked that

students must be taught methods for seeking help, such as

directing, asking for help and continuing to ask for help until

they understand. The pairs should be made to understand

each other’s learning needs and the background to specific

task. The students should be taught how they can explain to

their partner, how they can find answers rather than giving

the answer.

The assigning of partners is based on the level of ability

of the content area for tutoring. Sheldon (2001) observed that

matching of pairs of course depends on compatibility of the

tutor and tutee. In other words, in assigning partners the

teacher should consider the personality and the academic

difficulties of the students. For example, using PMI to reinforce

an algebra lesson involving reading, understanding and

forming of equation from a word problem will work best with a


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cross-age tutoring model or pairing a highly skilled tutor with

a lower-skilled tutee.

In peer tutoring script, students are given a task like

“Solve for x” for an equation like “ax + by = c”. Students go

through two phases, a preparation phase and a collaboration

phase (Walken, Rummel, McLearn and Keodinger, 2007). In

the preparation phase, the peer tutors are given the

opportunity to practice with the material ahead of time, by

solving the problems given to them by the teacher. During the

collaboration phase students are grouped in pairs and are

allowed to collaborate with the problems, taking turns being

peer tutors and peer tutees.

Empirical Studies on Achievement of Students in Algebra

Many studies have been carried out to measure the

achievement of students in mathematics. Mubark (2005)

defined mathematics achievement as a measure of overall

performance across all mathematical abilities typically found

in comprehensive school test, as compared with mathematical

thinking which measures the specific mathematical abilities


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such as geometrical abilities ability to generalize, logical

abilities etc.

Educational research over the years has examined

gender difference as it affects the achievement of students in

algebra. Agwagah and Ezeugo (2000) conducted a study to

determine the effect of concept mapping on students’

achievement in algebra. Data was collected from 387 SS II

students using the algebra achievement test. The result of

their study to determine the differential effect of concept

mapping on the achievement of boys and girls in algebra with

particular reference to quadratic equations and inequalities

reveals that gender was a significant factor on students’

achievement in algebra. The study shows that male students

achieved significantly better than their female counterparts in

algebra content. In a similar study, Harbor-Peters (1993) in

her study on students gender by teacher gender interaction in

SS 3 students achievement in mathematics, observed that the

male performed significantly better than their female

counterpart. In contrast to the above study Obioma and

Ohuche (1980) in their study of gender difference in


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mathematics on secondary school students’ performance

found that female students performed better than male

students.

A number of studies have been carried out in Nigeria on

the effect of school location on the academic achievement of

the child. Emma (1989) observed that the dichotomy between

urban and rural community is a reality. He explained that

urban-rural environment can be identified with social class

differences. He further stated that high standards of living and

presence of material properties, electronics and high

technology products in the home are likely to stimulate

intelligently. These he concluded are all available in urban

areas. From the above study one would feel that it will be

difficult for a student in the rural environment to perform

equally well academically as his counterparts in the urban

environment, since the rural students would not have the

same amount of teachers’ attention as their urban

counterparts. A study carried out by Maliki, Ngban and Ibu

(2009) on whether location of school influences performance in

mathematics test reveals that students from rural school,


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was done to the other two groups without pretest. All were

exposed to six weeks course unit, at the end of which

test/examination results were complied and data collected.

The result confirmed that the PMI group performed better than

the control group.

Appraisal of the Review

The review of related literature in this chapter clearly

shows that mathematics is very important for the development

of a modern society (Ukeje, 1997). The teaching and learning

of mathematics in senior secondary school has shown that

enough time is not being spent by teachers on the identified

teaching methods. This has led to the notion that teaching is

inadequate in our schools and hence the poor performance of

students in public examinations. The performance of students

in mathematics has proved that teaching and learning are

below expectation (WAEC, 2006). Several efforts were made to

study the problems and issues militating against effective

mathematics teaching and learning in Nigeria. These problems

include the inability of teachers to use instructional materials

(Agwagah, 2000) and teachers’ methodology (Elekwa, 1996).


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The reviewed literature indicated that few researches

have been conducted using PMI technique in the teaching and

learning of mathematics. For example, Bienesmith (1991)

focused his study on the acquisition of basic additional facts

in children with learning disabilities. In discussing school

location, Greenwood, Delquadri and Hall (1984) observed that

students’ academic behavior occurred less in inner-city 4th

grade classroom than the suburban schools. Thus many

researchers claim that rural based students performed better

than their urban counterparts.

The literature reveals that most of the work reviewed

were carried out in foreign countries and were very significant

to the achievement of students in mathematics. It appears

that there is no known study to this researcher yet on the

effect of PMI on students’ achievement in algebra in Nigeria.

The only known study carried out in Nigeria was that of

Elekwa (1996) which was on the effect of PMI on students’

performance in mathematics. The absence of known studies in

algebra in Nigeria motivated the researcher into carrying out


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this present study to empirically determine the effect of PMI on

the achievement of students in SS 1 algebra.


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CHAPTER THREE

RESEARCH METHOD AND PROCEDURE

This chapter presents the method and describes the

procedure used by the researcher in this study. These include:

the design of the study, population of the study, sample and

sampling procedure, research instrument, validity and

reliability of the instrument, treatment procedure and method

of data analysis.

Design of the Study

This study adopted the quasi-experimental design. In

quasi-experimental design, there is no random assignment of

subjects, rather intact classes are used. The quasi-

experimental design adopted is the pretest-posttest non-

equivalent control group design. There are both experimental

and control groups. The variables focused upon are PMI as the

independent variables, gender and school location as

moderator variable while achievement was used as the

dependent variable. The choice of this design is to ensure that

normal class activities are not disrupted. This design can be

represented diagrammatically as:


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A O1 x O2

B O3 O4

Where

Experimental group A: O1 = Pretesting

x = Treatment

O2 = Post-testing

Control group B: O3 = Pre-testing

O4 = Post-testing

Table I Variable matrix design for Algebra achievement of schoollocation by Gender

School Location

Gender Urban Rural

Male A

B

O1 x O2 O1 x O2

O3 O4 O3 O4

Female A

B

O1 x O2 O1 x O2

O3 O4 O3 O4

Source: Author


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Population of the Study

The population of the study comprised all the 6,646

senior secondary one (SS 1) students in the 92 public mixed

senior secondary schools within Delta North Senatorial

District in the 2010/2011 academic session. The figure (6,646)

was obtained from the Research and Statistics Department of

the Zonal Offices of Post Primary Education Board in Asaba,

Agbor and Kwale. The choice of SS 1 students was to ensure

that students to be used in the study have already been

exposed to elementary algebra in their junior secondary school

mathematics curriculum.

Sample and Sampling Procedure

The sample for this study consists of 192 senior

secondary one (SS 1) students in six (6) mixed secondary

schools drawn from the ninety two (92) public mixed

secondary schools in Delta North Senatorial District in the

2010/2011 academic session. The choice of mixed secondary

schools is due to the fact that single sex schools are not

located in the rural areas of Delta North Senatorial District.

The use of mixed secondary schools was to take effective


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control of the sex variable of the study. In each of the sampled

schools one intact class was drawn for the study using

balloting with replacement technique. This gives a total of 6

intact classes that were drawn for the study. Intact classes

were used for this study because initial equivalence may not

have been achieved for the subjects in the two groups.

Delta North Senatorial District was stratified into three

namely Agbor Educational Zone, Asaba Educational Zone and

Kwale Educational Zone. In each stratum, the researcher

purposively sampled two schools, one from urban and one

from rural area in agreement with one other variables of the

study that is school location. In each stratum one school was

assigned to experimental group and the other to control group,

so that for the three educational zones, 3 schools were

assigned to the experimental while the other 3 were assigned

to the control group through a simple random sampling

technique.

Research Instrument

The instrument that was used for collecting data is the

algebra achievement test (AAT) drawn from past WAEC


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questions. The instrument comprises 30 objective test items.

The AAT was used for both pretest and posttest of the study.

The instrument was based on the table of specification for this

study as shown in Table II below. The test blue print was

based on the revised WAEC mathematics syllabus. The test

blue print indicates the cognitive levels of knowledge,

comprehension and application were represented by the test

items of the instrument. The knowledge area has 18

questions, comprehension has 9 questions and application

has 3 questions. Lesson notes were developed by the

researcher based on the topics to be treated from WAEC

general mathematics syllabus. The lesson notes developed by

the researcher were used by the research assistants. These

lesson notes were validated by three experts from the

Department of Science Education, Delta State University,

Abraka. See sample of lesson notes in Appendix A.


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Table II

Test Blue print for SS1 Algebra Achievement Test

Topic/Content Content

Weight

Knowledge

60%

Comprehension

30%

Application

10%

No of

question

lgebraic

Simplification

and

Substitution

30% 5 3 1 9

Quadratic

Equations

30% 5 3 1 9

Equations and

formula

30% 5 3 1 9

Quadratic

graphs

10% 3 - - 3

Total - 18 9 3 30


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Validity of the Instrument

The algebra achievement test used in this study was

drawn from past WAEC questions. It comprises 30 algebra

objective test item. See Appendix B.

Reliability of the Instrument

The instrument was trial tested on a sample of one class

of SS 1 in Ogume Grammar School, Ogume, Ndokwa West

L.G.A. This school was excluded from the final study. An

estimate of internal consistency was established using Kuder-

Richardson (K.R.-20) formula. The reliability coefficient was

0.71. This was considered high enough for the study. See

Appendix C.

Treatment Procedure

At the beginning of the treatment the researcher

administered the pretest of the AAT to both the experimental

group and the control group. To control for test effect, the

subjects were instructed to provide their pre-test answers in

their pretest question papers during the pretest in order not to

allow them anticipate the same question when post test was to

be administered. The objectives of the lesson were formulated


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from the general scheme of work by the researcher. These were

presented to the research assistants to guide him in teaching

the classes both for the experimental and control groups

without making the subjects aware of the objectives as this

was not his usual practice. During treatment, the teaching

was conducted in all SS 1 classes of the various schools used

for the study. The subjects in the experimental group were

briefed on the purpose of the system. After pretest, the

research assistants in the respective schools started adhering

to the lesson notes developed for this purpose by the

researcher. To control for threats for experimental bias during

the study, subjects were taught by their regular mathematics

teachers so that the researcher was not personally involved in

administering the research process.

Each class has five (5) periods of forty five (45) minutes

on their time table. The research assistants could only take

three periods out of the 5 periods required for mathematics

lesson, thus making an allowance for the research assistants

to use the other two (2) periods a week for PMI session.


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In the experimental group, a test was administered to the

subjects at the end of the third period each week. Subjects

that performed poorly in the test were asked to choose

partners from those that performed better. Those subjects that

performed better were to act as peer tutors during the PMI

sessions. During this period, the peer tutors instructed the

peer tutees on what they learnt during that weeks’ lesson. The

research assistants supervised the subjects during PMI

sessions, also the researcher with the help of the research

assistants ensured that they observed the subjects in the

control group as they did their remedial reading on their own

without the peer’s assistance. This treatment lasted for six (6)

weeks. At the end of the treatment a posttest of the AAT was

administered to the subjects in the sampled schools.

Method of Data Analysis

In analyzing the data obtained for the study, the research

questions were answered using mean score and standard

deviation. On the other hand the hypotheses were tested using

Analysis of Covariance (ANCOVA) at significance α-level of

0.05.


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CHAPTER FOUR

ANALYSIS OF RESULTS AND DISCUSSION

This chapter deals with analysis and discussion of

results of the experiment. The results are presented in tables

based on the five research questions and five hypotheses that

guided the study.

Discussion of Research Questions

Research Question One:

What are the mean achievement scores of students

exposed to PMI and those exposed to self directed study in

algebra?

Table III

Post test mean achievement scores of PMI and SelfDirected Study groups in Algebra. Teachingmethod

Mean Std deviation N

Peer mediatedinstructionSelf directedstudy Total

19.51

12.13

15.82

2.984

2.906

4.726

96

96

192

The results in Table III reveal that the PMI subjects had a

mean score of 19.51 and standard deviation 2.984 while the

self directed study group had a mean score of 12.13 and


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standard deviation of 2.906. The scores in Table III also

reveals that the PMI group had a higher post test mean

achievement score than the control group, thus indicating that

the PMI approach is more effective than the self directed study

in the teaching of algebra in senior secondary school level.

Research Question Two:

What are the mean achievement scores of urban and

rural PMI students in algebra?

Table IVPost test mean achievement scores and standarddeviation of Urban and Rural PMI students in Algebra.Location Mean Std deviation NUrbanRural Total

19.7019.1319.51

3.0792.7912.984

643296

The results in Table IV reveal that the urban PMI

subjects obtained a higher mean achievement score of 19.70

and standard deviation of 3.079 while their rural counterparts

had a mean score of 19.13 and standard deviation of 2.791.

This implies that the urban PMI students performed better

than their rural PMI students in SS1 algebra.


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Research Question Three

What are the mean achievement scores of male and female

PMI students in algebra?

Table VPost test mean achievement scores and standarddeviation of Male and Female PMI students in Algebra.Gender Mean Std deviation NMaleFemale Total

19.9818.9019.51

2.7443.1992.984

544296

The results in Table V shows that the male PMI students

obtained a mean achievement score of 19.98 and standard

deviation 2.744 while the female PMI students had a mean

score of 18.90 and standard deviation 3.199. This indicates

that the female PMI students performed better than their male

counterparts in algebra.

Research Question Four

What is the effect on the interaction of method by gender

in both students exposed to PMI and those exposed to self

directed study in their posttest mean achievement scores in

algebra?


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Table VIPost test mean achievement score and standard deviationof subjects by Method and Gender.

G e n d e r

Method

Group Peer mediatedinstruction

Self directedstudy

Mean S.D Mean S.D.

Male 19.98 2.744 12.38 2.765Female 18.90 3.199 11.78 3.086

The summary of the results in Table VI indicates that the

male PMI students had higher mean achievement scores of

19.98 with standard deviation 2.744 than the male students

in the control group who had a mean score of 12.38 with

standard deviation 2.765 while the female PMI students

obtained a higher mean score of 18.90 with standard deviation

3.199 than their female counterparts in the control group who

had their mean achievement score of 11.78 with standard

deviation 3.086. However, comparing the mean achievement

scores of male and female PMI group, it was observed that the

male subjects had a higher mean achievement score of 19.98

while their female counterparts had a lower mean score of

18.90.


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Research Question Five

What is the effect on the interaction of method by school

location in both students exposed to PMI and those exposed to

self directed study in their posttest mean achievement scores

in algebra?

Table VIIPost test mean achievement scores and standarddeviation of subjects by Method and School location

S c h o o l

L o c a t i o n

Method

Group Peer mediatedinstruction

Self directedstudy

Mean S.D Mean S.D.Urban 19.70 3.079 13.88 2.661Rural 19.13 2.791 11.25 2.631

Table VII reveals that the urban PM1 group had a higher

mean achievement score of 19.70 with a standard deviation

3.079 than the urban control group with mean achievement

scores of 13.88 and standard deviation 2.661, while the rural

PMI students obtained a higher mean score of 19.13 and

standard deviation 2.791 than their rural counterparts in the

control group who had a mean score of 11.25 and standard

deviation 2.631. Comparing the mean achievement scores of


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urban and rural PMI group, it was observed that the urban

subjects obtained a higher mean achievement score of 19.70

while their rural counterparts had a lower mean score of

19.13.

Testing of Research Hypotheses

Hypothesis One

There is no significant difference in the mean

achievement scores of students exposed to (PMI) and the self

directed study group in algebra.

Table VIIIOne-Way Analysis of Covariance (ANCOVA) of Posttestscores of Students exposed to Peer- mediated instructionand those exposed to Self directed studySource Type III

Sum ofSquares

df Mean

Square

F Sig

atp


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Table IXEstimated Marginal Means of the Experimental andControl groups

Teaching Methods Mean StdError

95% ConfidenceintervalLowerBound

UpperBound

Peer mediatedInstructionSelf Directed Study

19.313a

12.323a

.243

.243

18.834

11.844

19.791

12.801

a.

Covariates appearing in the model are evaluated at the

following values: pretest = 8.37.

Table VIII shows that F (1,189) = 412.179, p


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Hypothesis Two:

There is no significant difference in the mean

achievement scores of urban PMI students and their rural

counterparts in algebra.

Table XOne-Way ANCOVA table of posttest mean achievementscores of Urban and Rural PMI Students Source Type III

Sum ofSquares

df MeanSquare

F Sig at

p


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Table XIEstimated Marginal Means of Urban and Rural PMIStudents

SchoolLocation Mean

Std.Error

95% Confidence Interval

LowerBound

UpperBound

Urban 19.572a .319 18.937 20.206

Rural 19.388a .453 18.489 20.287

a. Covariates appearing in the model are evaluated at the

following values: pretest = 8.66.

From Table X above, the calculated F (1, 93) = .109.

The calculated p = .742 is greater than the declared α- level of

0.05. The researcher upholds the null hypothesis two and

concludes that there is no significant difference in the mean

achievement scores of urban PMI subjects and their rural

c

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EFFECT OF PEER MEDIATED INSTRUCTION ON THE ACADEMIC ACHIEVEMENT OF STUDENTS IN ALGEBRA.PDF