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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.
HO2: There is no significant difference in the mean
achievement scores of urban PMI students and their
rural counterparts in algebra.
HO3: There is no significant difference in the mean
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