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UNIVERSITY OF EDUCATION, WINNEBA
INSTITUTE OF EDUCATION
USING A FRACTIONAL BOARD TO TEACH ADDITION OF EQUIVALENT
FRACTIONS IN BASIC FIVE OF AKOTEYKROM NO.1 D/A BASIC SCHOOL
OSEI-OWUSU MICHAEL
JUNE, 2015
UNIVERSITY OF EDUCATION, WINNEBA
INSTITUTE FOR EDUCATIONAL DEVELOPMENT AND EXTENSION
USING A FRACTIONAL BOARD TO TEACH ADDITION OF EQUIVALENT
FRACTIONS IN BASIC FIVE OF AKOTEYKROM NO.1 D/A BASIC SCHOOL
BY
OSEI-OWUSU MICHAEL
(4130363283)
A PROJECT WORK SUBMITTED TO THE INSTITUTE FOR EDUCATIONAL
DEVELOPMENT AND EXTENSION, UNIVERSITY OF EDUCATION, WINNEBA
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF
DEGREE IN BASIC EDUCATION
JUNE, 2015
DECLARATION
Candidate’s Declaration
I hereby declare that this project work is the result of my own original research and that no
part of it has been presented for another Degree in this University or elsewhere.
Candidate’s Signature…………………..Date……………………….
Name: Osei–Owusu Michael
Supervisor’s Declaration
I hereby declare that the preparation and presentation of the project work were supervised in
accordance with the guidelines on supervision of project work laid down by the University of
Education Winneba.
Supervisor’s Signature……………………Date……………………….
Name: Mr. Yaw Andoh Bennin
ABSTRACT
The focus of the study was to design a fractional board to teach addition of equivalent
fractions in basic five of Akoteykrom No1 D/A Basic School. The study revealed that factors
that contribute to poor performance of pupils in Mathematics include:
Inadequate Teaching and learning materials.
Teacher and student’s absenteeism and lateness.
Lack of parental monitoring of pupils progress among other factors.
The instruments used for the study were questionnaire, interview and test. Data from the
various instruments were analysed using frequency, percentages and mean.
After the intervention, it became known that the use of the designed fractional board and the
other strategies like the educational talk had contributed immensely to the performance of
pupils in mathematics.
Recommendations made from the study were that, the Government should provide adequate
textbooks to the schools to facilitate learning and motivation should come from both parents
and teachers to eradicate the misconceptions associated with mathematics.
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ACKNOWLEDGEMENT
I am grateful to my supervisor Mr. Yaw Andoh Bennin for his guidance which made this
project a success. My heartfelt gratitude goes to my dear parents, Mr. Stephen Osei-Owusu
and Mrs.Theresah Osei-Owusu for their spiritual support. I acknowledge Miss Helen
Akweley Mensah and all my siblings for their tremendous help and encouragement during
the writing of this project.
Finally, I pay glowing attribute to the staff of Akoteykrom No1 D/A Basic School for
providing me information needed for the success of the project.
iv
DEDICATION
I dedicate this project to my parents, Mr. Stephen Osei. Owusu and Mrs.Theresah Osei-
Owusu for supporting me morally, financially and prayerfully
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TABLE OF CONTENTS
ABSTRACT
ACKNOWLEDGEMENT
DEDICATION
CHAPTER ONE
Background of the study
Statement of the problem
Purpose of the Study
Research Questions
Significance of the study
Delimitation
Limitation
Organisation of the study
CHAPTER TWO
Review of related literature
CHAPTER THREE
Methodology
Research Design
Population
Samples and sampling
Research instruments
Questionnaire
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Interview
Test
Pre-test
Intervention
Data Analysis
CHAPTER FOUR
Results, Finding and Discussion
CHAPTER FIVE
Summary, Conclusion and recommendation
References
APPENDICES
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CHAPTER ONE
INTRODUCTION
The introductory chapter deals with the background of the study, statement of the problem,
purpose of the study, research questions, significance of the study, delimitation, limitations
and organisation of the study.
Background of the study
Throughout the ages, mathematics has been part of all human activities. These human
mathematical activities are demonstrated right from childhood. Children possess a natural
curiosity and interest in mathematics, and come to school with an understanding of
mathematical concepts and problem solving strategies that they have discovered through the
exploration of the world around them. Mathematics educators are to provide experiences that
will continue to foster students’ understanding and appreciation of mathematics to improve
on their performance.
Mathematics has developed many countries like China, India and the Muslim world since 300
B.C. It has a major role to play in energy, commerce, banking and even informal trade. With
the current energy crises in Ghana, Mathematics has an important role to play. It takes a lot of
engineering and a substantial amount of mathematics to get the petrol from oil reservoir into
your car, or the electricity from renewable sources or fossil fuel power plants to your light
switch.
Skemp, R. (1985) explains mathematics as a way of finding solutions to problems and a way
by which information and our knowledge of shapes and measurement are related to our day-
to day activities. This means our knowledge of the basic articles in mathematics is very
crucial in solving the problems we encounter in our daily activities.
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In Ghana, mathematics is one of the important subjects that are to be learnt by all students
from the basic schools to the higher level of education. In recent times, one cannot gain
admission into either Senior High School or any tertiary institution with a fail in
mathematics. This is the reason why pupils must be helped to develop interest in the learning
of mathematics.
My experience as a mathematics teacher at the basic level for about seven years has made me
identify that most pupils have conceptual problem in dealing with fractions. This is because
most teachers use the traditional method of teaching, which involves teaching without
appropriate teaching and learning materials.
To overcome the challenges, a variety of teaching and learning strategies have been
advocated for use in mathematics classrooms. These include the use of child – centred
methodologies and relational learning model, which does not improve the use of formula on
the pupils.
At the basic level of education, Mereku (2001) asserts that the Ghanaian mathematics teacher
is regarded as a demonstrator of process and transmitter of information and taught largely
through teacher centred approaches. This denies the students the ability to experience and use
manipulative materials. It is no wonder therefore that students’ performances in mathematics
in Ghana is among the lowest in Africa and the world (Kraft, 1994).
The Trends in International Mathematics and Science Study (TIMSS) Report in 2003
recommended that the Teacher Education Universities in Ghana such as University of
Education Winneba (U.E.W) and University of Cape Coast should re- examine the content
and pedagogy of mathematics and science programme to ensure that teachers can teach the
topics included in the Basic Schools Syllabus.
ix
If Ghana is to achieve the millennium development goals and go beyond the status of a
successful knowledge based economy, she must ensure that her youth are equipped with
stronger mathematical skills that include practical problem – solving at the basic and higher
levels of education. Unfortunately, devastating and oppressive problems are being developed
in Akoteykrom, where the researcher teaches currently.
Akoteykrom is a community with only one school. The school is divided into the
kindergarten, primary and Junior High levels. Farming is the main occupation of the people.
Parents mostly engage their wards in farming after they have closed from school. This
deprives the pupils from getting ample time to practise what they are taught at school.
Surprisingly, some girls are seen selling foodstuffs on the streets. They remain on the streets
even till late in the night, as late as 11.pm. As a result, they sleep in class during lessons.
Statement of the problem
The importance of mathematics is not much realised at Akoteykrom N0.1 D/A Basic School.
Pupils’ interest in mathematics is gradually diminishing. They do not contribute in
mathematics lessons. Most of them sleep during mathematics lessons.
The problem of low performance among pupils and their inability to solve problems
involving the addition of equivalent fractions was identified by the researcher in basic five of
the school. Hence the topic, “using a fractional board to teach addition of equivalent fractions
in basic five of Akoteykrom No 1 Basic School.”
Purpose of the study
This project seeks to:
Investigate the cause of low performance of pupils in mathematics in basic five
x
Help pupils overcome difficulties in solving problems involving addition of equivalent
fractions
Find means by which pupils interest in mathematics could be promoted
Research questions
The study was guided by the following research questions:
1. What are the causes of low performance of pupils in mathematics?
2. What are the causes of pupils’ inability to solve problems on addition of equivalent
fractions?
3. What are some of the measures that can be adopted to solve the problem?
4. Could an improvised fractional board be appropriate to facilitate pupils’ understanding of
addition of equivalent fractions?
5. What role can parents play to help pupils improve on their performance in mathematics?
Significance of the study
This research work will promote pupils’ understanding of addition of equivalent fractions and
help them improve on their performance in mathematics. This work will highlight various
means by which pupils’ interest in mathematics could be promoted and sustained. It will
provide information to curriculum planners, teachers, circuit supervisors, course organisers
and parents. It will also serve as a reference material for further research in a related area of
study.
Delimitation
The research was conducted on pupils in basic five of Akoteykrom N0.1 D/A Basic School
only. The population of the pupils is forty. There are other pupils in other classes who have
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similar problems but could not be covered due to the difficulty that would be encountered in
selecting a sample size. Finally the study is based on mathematics and not any other subjects.
Limitation
During the research period, an encounter with some of the parents revealed that they do not
have any idea in mathematics. Some pupils were reluctant to answer some questions for fear
of mistake or being mocked by their friends.
Some mathematics teachers also gave different answers to the question
Organization of the study
The study comprises five chapters. Chapter one deals with the introduction, background of
the study, statement of the problem, purpose of the study, research question, significance of
the study, delimitation and limitation.
Chapter two reviews related literature on the study.
In chapter three, the research design used in the study and methods used in collecting data for
the study are discussed.
Chapter four is composed of analysis of data and the presentation and discussion of the
results of the study.
Chapter five presents the summary, conclusion, recommendation and suggestion for future
research.
xii
CHAPTER TWO
REVIEW OF RELATED LITERATURE
Overview
This part of the research work reviews what has already been written on the topic in terms of
theories, concepts, and empirical evidence. It covers the following topics:
Importance of mathematics
Causes of low performance of pupils in mathematics
Misconception about mathematics
How children learn mathematics
Generating and sustaining pupils’ interest during mathematics lessons
Gender equity in mathematics lessons
Meaning and types of fractions
Importance of mathematics
As Russell, B. (1986) put it, “mathematics is the subject in which we know neither what we
are talking about nor whether what we say is true”. Perhaps, first and foremost, we should
study and find out what it is.
Mathematics is about relationships and structure, even at the most basic level. First you learn
to count and the important relationship is ‘order’. Then you learn to add and multiply.
One of the benefits of studying mathematics is the variety of career opportunities it provides.
A 2009 study showed that the top three best jobs in terms of income and other factors were
suited for mathematics majors.
Another recent survey showed that the top fifteen highest- earning college degrees have a
common mathematical element.
xiii
In actuarial science, mathematics and statistics are applied to finance and insurance, which
include a number of interrelating disciplines such as probability and economics.
Computer science, which is the study of the theoretical foundation of information and
computation also prizes mathematics highly. Cryptography, which is the practise and study of
finding information, is not just meant for spies anymore. It is considered to be a branch of
both mathematics and computer science. Cryptography applications include the security of
ATM cards, computer passwords and finger print sensors, which are currently being used by
computers and smart phones.
Causes of low performance of pupils in mathematics
The performance of pupils in mathematics has been of great concern to most citizens in the
country. Flolu, Dzansi- McPalm and Awoyemi (2007) posit that, performance of pupils in
mathematics at the basic level has not been encouraging. Several factors have generally been
identified as causes of low performance of pupils in mathematics at the basic level of
education in Ghana.
One of the factors that is relevant to consider is teacher attitude and behaviour towards
teaching and learning. According to Ikonta (2008), teachers should be made to realise that
they are the bedrock of any educational system and should therefore show more
responsibility and commitment to their work. A great number of them do not have mastery
over the content of mathematics and therefore skip certain content areas. Etsey (2005) asserts
that skipping content areas in mathematics would affect the performance of pupils in the
subject. Since the curriculum tends to be spiral, failure to teach some areas would lead to
future problems in mathematics.
xiv
Another cause of low performance of pupils in mathematics is teacher qualification.
Agyemang (1993) asserts that a teacher who does not have both academic and professional
qualification would undoubtedly have a negative impact on teaching and learning. However,
if a teacher is academically and professionally qualified but work under unfavourable
working environment, that teacher would be less dedicated than a teacher who is unqualified
but works under favourable working environment.
Motivation is yet another factor that can affect the performance of pupils. According to
Farrant (1968), the relationship between teachers and pupils is often up – side down. Pupils
come to school because they must and teachers teach because they are paid to. Teachers
mourn that their profession is not respected and complain that they are inadequately paid for
the services they render. This often results in a lackadaisical attitude towards work.
In the educational system, the academic performance of students may be dependent, to a large
extent, on the quality of the teacher, his/ her teaching methodologies, the resources available
and class size. These in turn depend on both the educational system and how the teacher is
motivated (Okendu, 2008).
Asamoah (2009) added that a teacher whose needs are not met may be psychologically
unstable and unproductive. On the other hand, a satisfied teacher is stable and therefore
would be more productive. In line with this, Cook (1980) observed that the key to improving
performance is motivation.
Misconception about mathematics
The word “Mathematics” strikes dread in the hearts of many pupils. But why does
mathematics appear so daunting? Several misconceptions in learning mathematics may be
causing unnecessary distress.
xv
One of the misconceptions about mathematics is gender perception. Gender perception is
held by the society that mathematics is a subject for boys. This perception discourages girls
from pursuing mathematics at the higher level.
Armstrong and Prince (1982), found that the view of mathematics as a male domain has
contributed to the enormous decline in the performance of girls.
Notwithstanding, the following perceptions also exist in the minds of people;
Mathematics is different from other subjects and somehow mysterious however,
mathematics is not special. It requires the same basic reading and logical skills that you
would use in other subjects areas.
Mathematics is not needed for the real world. However, research has shown that it is an
integral part of our daily activities.
How children learn mathematics
The book, mathematics for teacher training colleges in Ghana has specified in its content how
children learn mathematics from two theories. These are the Behaviourist and
Developmentalist theories.
The Behaviourists believe that learning takes place through a stimulus response mechanism.
This school of thought believes that re-inforcement and motivation promote effective
learning. As a result, mathematics teachers should reward pupils when they do well in their
lessons. The rewards can be in material form such as pens, pencils, exercise books among
others. It can also be verbal praise like “Good” or “Very well” when they answer questions
correctly. Behaviourists also believe that the learning environment has an impact on the
pupils. The Developmentalist theory on the other hand suggests that understandable learning
does not come as a result of observable behaviour but should be based on the intellectual
development of the learner.
xvi
Piaget, (1987), a major proponent of the Developmentalist theory, identifies four stages of
cognitive development. These stages are the sensory motor stage, pre- operational, concrete
operational and formal operational stages. This means that at each stage, there are a whole lot
of different things to be done by the teacher. At every stage, the teacher has to know what is
supposed to be taught to suit the intellectual ability of his/ her pupils.
Dienes, Z (1985) added that the teachers should also adopt different methods or techniques of
teaching a particular topic.
Skemp, R. (1985) identified two forms of learning. These are the instrumental learning and
relational learning. Under the instrumental learning, children may be able to solve a problem
but may not know how the procedure came about. Under relational learning, pupils know
how the procedure came about.
Generating and sustaining pupils’ interest during Mathematics lessons.
The teacher plays an important role in the development of pupils’ interest in lessons.
One important factor is the use of activity method of teaching. The activity method places the
child in the central focus of the teaching leaning process. In this method, the child is allowed
to discuss interact or take active part in the learning process.
The use of appropriate teaching and learning materials can help sustain pupils’ interest. The
pupils get the opportunity to interact with these materials using their senses thereby making
learning very interesting.
Gender equity in mathematics lessons.
A study conducted by the American Association of University of Women (1992) revealed
that girls are not receiving the same quality of education as boys. Marshal S. T (1982) also
says that girls may read a problem in mathematics and science more easily and more quickly
xvii
than boys, but boys are better at solving the problem. According to Smith, A (1981), there is
a strong, pervasive, traditional and conservative belief among people that mathematics is a
male preserve. Girls are most often regarded as being incapable of learning mathematics at
the higher level. As a result, most girls shy away from studying mathematics at the higher
level.
Maccoby and Jackling (1974) assert that parents allow boys more chance to interact actively
with the physical world, but they talk more to girls. Pranti et al (1983) also posit that girls
who offer mathematics are referred to us witches and are believed to portray supernatural
powers.
Gender equity is an important goal of the exclusionary classroom. Teachers, parents, authors,
publishers, examiners, and curriculum planners should ensure that written materials should be
devoid of gender stereotyping. However, written materials should communicate high
expectation to girls in order to improve upon their performance and also to motivate them
succeed in mathematics.
Meaning and Types of Fractions
A fraction is a part of a whole. It is a way of representing division of a “whole” into “parts”
It has the form: Numerator
Denominator
The numerator is the number of parts chosen and the denominator is the total number of
parts. Example13
, 25 ,
12 , In the fraction
13 , 1 is the numerator and 3 is denominator.
The types of fractions include:
Proper fraction: It has the numerator part being smaller than the denominator. Examples
are 26 ,
47 ,
35
xviii
Improper fraction: Its numerator is greater than its denominator. Examples are 75 ,
94 ,
83
Mixed fraction: It is made of a whole number 32
3 ,546 , 2
25 ,
Equivalent fractions: They are pair of fractions that look different but show the same
amount. To test whether one fraction is equivalent to another, one must express both
fractions in their lowest terms. All the following are equivalent fractions:
13 ,
26 ,
39 ,
39 ,
412,
515 ,
xix
CHAPTER THREE
METHODOLOGY
Overview
This chapter comprises research design, population, sample and sampling procedure, research
instruments, data collection and data analysis procedures.
RESEARCH DESIGN
Gray (1992) explained that research design indicates the nature of the hypothesis and the
variables involved in the study. The research design used in this study was action research.
Action research is concerned with working collaboratively with other people to solve
perceived problems. The fundamental aim of action research is to improve practice rather
than to produce knowledge (Elliot, 1991)
Some of the benefits of action research are as follows:
It promotes teachers’ personal development.
It helps the teacher to understand what actually goes on within the teaching and learning
process
It enables the modern teacher to adapt to appropriate teaching methods that best suit the
child’s development level.
In spite of the various benefits of action research, the under listed weakness has been
identified:
Since action research is collaborative in nature, some participants who may be involved in the
study may not give the necessary or required information for the study.
xx
Population
Population is a group of people of interest to the researcher. It is the target group to whom the
research would like to generalize the result of the study. The population for the study
included basic five pupils of Akoteykrom No1 D/A Basic School. Another group was the
staff including the headmaster of the school. They provided the researcher with some
information to the identified problem.
In basic five of the school, there are seventeen boys and twenty three girls. Some of the
parents of these pupils were also interviewed for adequate information.
Sample and sampling
Sampling is the process of selecting a portion of the population to represent the entire group.
Seven boys and eight girls were sampled and their ages range between 11- 15 years. They
were purposively sampled because of their low performances and negative attitudes towards
mathematics lessons.
Research instruments
The researcher used the following instruments to gather information on the population under
study: questionnaire, interview, pre-test, post- test and intervention.
Questionnaire
Questionnaires were administered to parents. During the process, all stakeholders contributed
immensely to the exercise. Sample of the questionnaire could be found in appendix A.
The researcher retrieved information from the questionnaires distributed to the parents of the
target population.
xxi
Interview
The researcher prepared an interview guide and conducted it face-to- face with all fifteen
pupils under study. The sample of the interview guide can be found in appendix B.
Test
Two tests, pre-test and post-test, were organised for the pupils. The pre-test was conducted to
diagnose their weaknesses. Then after the intervention, the researcher organised a post-test to
find out whether the strategies adopted worked effectively.
Pre-test
The researcher used this test to realise and define the perceived problem. The researcher used
interview and observed the pupils to see how they participated in mathematics lessons. The
test was administered on the topic “addition” of equivalent fractions”. The fifteen pupils were
allowed to solve five questions within a given period of time. Sample of the test can be found
in appendix C
Intervention
It is a series of methods put in place to solve a specific problem. After the problem had been
identified, the researcher developed some strategies to solve the problem. Some measures
such as putting the class into three groups were put in place.
The researcher organised an educational talk for them. This was meant to eliminate any
misconception associated with mathematics and to provide the pupils with career
opportunities in the subject. A lesson was taught with the use of an improvised fractional
board.
xxii
The researcher found it necessary to design the fractional board in such a way that, it would
appeal to the senses of the pupils. For easy handling the researcher used a light weight board
made of wood to construct the factional board.
The board is in a rectangular shape with dimensions 10mm x 25mm. Along the equal
portions. This was done according to the number of parts required at each stage which are the
whole, half, quarter, one-eighth and one –sixteenth .
xxiii
Fig 1.0. The Designed Fractional Board
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116
116
116
116
116
116
116
116
116
116
18
18
18
18
18
18
18
18
14
14
14
14
12
12
1 whole
During the lesson delivery, the researcher allowed the pupils to interact with the fractional board. The researcher asked the pupils how many The
quarters are there in a half. The pupils were allowed to count and they realised that there are two quarters in a half. Thus, 1/4+1/4=1/2.
The children were also allowed to find the number of one-eighths in a half. They counted and realised there are four one-eighths in a half. Thus
1/8+1/8+1/8+1/8=1/2. The children also realised that one of the halves equals two of the one-fourths and also equals four of the one-eighths.
Thus 1/2=2/4=4/8.
24
Post-test
After the display of the designed fractional board and the presentation during the educational talk, pupils were observed in their mathematics.
Afterwards the post-test was organised to ascertain whether the strategies used at the intervention stage had been effective. The test contained the
same questions and the same time was given to the pupils to solve the question. The result and analysis of this test can be found in chapter 4. A
sample of the post- test can be found in appendix D.
Data analysis plan
The data collected through the various instruments were analysed using simple frequency data analysis. The analysis was done using tables,
frequencies, percentages and simple mean.
25
CHAPTER FOUR
RESULTS/ FINDING AND DISCUSSIONS
Overview
This chapter of the project briefly talks about the information gathered after the application of
the various data collection instruments. Pupils were interviewed, questionnaires were
administered to parents/ guardians of the pupils. Data from the various instruments were
analysed using percentages and frequency tables as follows:
The Responses on the questionnaire given to Parents/Guardians on the Causes of Low
Performance of Their Wards.
Table 1:
Does Your Child Go To Bed Early?
Responses No. of parents Percentages (%)
Yes 1 7
No 14 93
Total 15 100
Table 1, which describes whether children go to bed early or not, revealed that 93% of the
children do not go to bed early. 7% of the parents also confessed that their children go to bed
early.
26
Table 2:
Do You Buy Mathematics Books For Your Children?
Responses No. of parents Percentages (%)
Yes 5 33
No 10 67
Total 15 100
From table 2, which is about the issue of parents buying books for their children, they had
this to say: 67% of the parents said they do not buy books for their children. 33% of them
said they buy books for their children.
Table 3:
Do You Encourage Your Wards To Study Mathematics At Home?
Responses No. of parents Percentages (%)
Yes 2 13
No 12 87
Total 15 100
From tables 3, which is about the issue if parents encouraging their children to study
mathematics at home, 87% of the parents said they do not encourage their wards to study
mathematics at home. 13% of them said they encourage their students to study mathematics
at home.
27
Responses of Pupils in an Interview
Table 4:
Do You Enjoy Mathematics Lessons?
Responses No. of pupil’s Percentages (%)
Yes 4 27
No 11 73
Total 15 100
From table 4, which shows whether pupils enjoy mathematics lessons, 73% of the pupils said
‘no’ to the question while 27% of them said ‘yes’ to the question.
Table 5:
Do You Study Mathematics At Home?
Responses No. of pupil’s Percentages (%)
Yes 3 20
No 12 80
Total 15 100
On the question of pupils studying at home, 80% of them said they do not study mathematics
at home while 20% of them said they study mathematics at home.
28
Analysis of Pupils’ Performance in Pre – Test and Post – Test
Table 6:
Pre – Test Results.
Marks(x) No of pupils (f) Percentage (%) fx
0 4 27 0
1 6 40 6
2 1 6 2
3 4 27 12
4 0 0 0
5 0 0 0
Total ∑ f = 15 100 ∑ fx=20
Mean = ∑ f x
∑ f=
2015
=1. 33
Table 6, which indicates pre- test result, clearly shows a relatively low performance of the
pupils in the pre-test. 27% of the pupils scored zero, 6% of them scored 2 marks and 27% of
them scored 3 marks. This is an indication that pupils’ inability to solve problems on addition
of equivalent fractions needed urgent attention.
29
Table 7:
Post–Test Results.
Marks(x) No of pupils (f) Percentage (%) fx
0 0 0 0
1 1 7 1
2 1 7 2
3 2 13 6
4 3 20 12
5 8 53 40
Total ∑ f = 15 100 ∑ fx=20
Mean= ∑ fx
∑ f =
6115 = 4.1
Table 7, which is about post- test results, shows that there had been a great improvement after
the intervention strategies were implemented. 53% of the pupils were able to solve all the
questions correctly, 20% of them scored 4 marks and 13% of them scored 3 marks.
Comparing the mean scores of the pre-test and post-test shows that there had been an increase
in performance, thus from an average mark of 1.33 to 4.1.
30
Summary of Chapter Four
This chapter is simply dedicated to results, analysis and discussion of finding.
The researcher used a descriptive statistical procedure in analysing the data.
The data analysis was based on the responses obtained from the questionnaire, interviews and
tests that were conducted. Analyses were also presented in tabular form using percentages
together with a measure of central tendency, which is the mean.
31
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
Overview
This is the final chapter of the research work and it highlights the summary of the research
work, conclusion of all the data analysis and recommendations for other researchers who may
also take up the challenges to research into pupils’ inability to solve problems on the addition
of equivalent fractions.
Summary
The study was to use a designed fractional board to help basic five pupils of Akotekrom N0.1
D/A basic School solve problems involving addition of equivalent fractions.
During the study, a target group of fifteen pupils, made up of seven boys and eight girls, were
sampled from a population of forty pupils. The researcher used questionnaires, interviews,
and tests as the instruments to collect data for the study.
Among the key findings, the researcher realised that most teachers do not use teaching and
learning materials to teach. In addition, the methods used by them were teacher centred
instead of child-centred. These and other factors were the major causes of pupils’ poor
attitude towards the learning of mathematics.
32
Conclusion
A critical study of the research report and its findings reveals that pupils could learn and do
better in mathematics if:
Teachers use appropriate teaching and learning materials to teach mathematics.
Teachers employ the use of child-centred methods in teaching mathematics.
Both teachers and parents encourage and motivate pupils to develop their interest in
mathematics
Parents provide their wards with the basic needs and stationery such as mathematics
textbooks
Teachers discourage pupils from teasing their colleagues whenever they make mistakes
during the answering of questions.
Recommendations
Based on the findings, the researcher outlined the following recommendations; The
government should provide adequate textbooks to the schools to facilitate learning
Secondly, encouragement and motivation should come from both parents and teachers to
eradicate the misconception that mathematics is difficult. Parents should entreat their wards
to learn mathematics at home and after school.
Finally, teachers should endeavour to use the most appropriate teaching and learning
materials that suit the development level of the pupils. Where the materials are not available,
teachers should improvise where necessary. Also, teachers should use activity methods which
give pupils the opportunity to take active part in lessons.
33
Suggestions for future research.
In view of the findings and suggested recommendations, a follow up research into the causes
of pupils’ inability to solve addition of equivalent fractions will complete the task. It is
therefore suggested that:
A study should be conducted to ascertain why girls tend to perform relatively lower in
mathematics as compared to boys.
A study should be conducted to find out how motivation could be used to encourage
pupils to develop interest in mathematics.
34
REFERENCES
Armstrong and Prince (1982), The relationship of mathematics; Self efficacy, journal of
vocational behaviour, Castle Rock, Colorado: Adler Publising.
Asafo – Adjei, R. (2002), teaching basic school mathematics for colleges of education,
Accra – Ghana: University Press.
Bacnneger and Newcomer (1989), Women and girls in mathematics, London: Oxford
University Press.
Cockcroft, W.H.(1982), Mathematics count, London: Oxford University Press.
Dienes,Z. (1985), Mathematics and Activity, America: Aladin Paperbacks.
Einstein, A. (1882) Sex difference in learned helplessness, The contingencies of evaluative
feedback in the classroom, Boston: Pearson Education.
Fennema, E.(1987), Gender difference in mathematics performance,
A metal analysis: Psychological bulletin, Waltham: Academic Press.
Gerdes, P. (1988), Educational Studies in mathematics,
an international journal in mathematics, Lisbon, Portugal: Aletheia Editores.
Lewis, R.H. (1964), Basic issues and gender differences in mathematics,
UK; Baysgarth Publication.
Marshal, T.S (1982), Educational psychology for the teacher in Africa, South Africa:
Edward Arnold Publishers Ltd.
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Piaget, J. (1987), Development stages of learning, New York: Thomas Publishing Company.
Pierce, B. (1880), Social forces, shape, Maths attitudes and performance signs Birmingham:
Brimston Press.
Portman, J. (1997), Mathematics Teachers Association: Brochure, Germany: Heineman
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Pranti et al (1983), understanding mathematics course enrolment and mathematics
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American educational research journal.
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LESSON PLAN
WEEK ENDING: 10-04-2015 REFERENCES: Maths Syllabus for primary
CLASS: BASIC FIVE schools, Teachers’ guide.
SUBJECT: MATHEMATICS
Day/ Date
Duration
Topic/
Subtopic
Objectives / R.P.K Teacher Learner Activities Teaching
and
Learning
Materials
Core Points Evaluation
Exercise
Day
Monday
Date
6/04/15
Topic
Operation on
fractions
Subtopic
Addition of
equivalent
Objectives
By the end of the lesson,
the pupil will be able to:
1. identify equivalent
fractions
2. Add two or more
INTRODUCTION
Let pupils identify fractions as part of
a whole.
DEVELOPMENT
Activity 1: Using the paper strips,
lead pupils to identify equivalent
Designed
fractional
board , strips
of paper
12=2
4
=
Add the following
equivalent
fraction;
a) 26
+ 12
37
Duration
60mins
fractions equivalent fractions
R.P.K
Pupils are familiar with
fraction as part of a
whole
fractions.
Activity 2: Guide pupils to add two
or more equivalent fractions using the
fractional board.
Activity 3: Guide pupils to solve
world problems on equivalent
fractions
Conclusion
Summarise the salient points of the
lesson and give pupils exercise
12+ 2
4=2+2
4= 4
4
48+ 8
16=8+8
16=16
16
18+ 1
8=1+1
8=1
2
b) 14
+ 28
c)4
12 +
824
REMARKS
Lesson was
Successfully
taught
38
39
APPENDIX A
Sample of the Questionnaires for parents/ Guardians
INSTRUCTION: Please read carefully and tick in the box with appropriate answers to the
questions.
Do girls need mathematics in their daily lives?
Yes No
Have you taken it upon yourself to find out your wards’ performance in mathematics?
Yes No
Do you provide any supplementary mathematics textbooks for your wards to practise at
home?
Yes No
Does your child go to bed early?
Yes No
Do you encourage your wards to study at home after school?
Yes No
40
APPENDIX B
Sample of the interview guide for the pupils
Do you study mathematics at home?
Do you have any mathematics textbooks at home?
Do you like mathematics and feel happy when lesson are in progress?
Does your mathematics teacher call you often to answer questions during lessons?
41
APPENDIX C
Sample of pre – test for pupils
Add the following equivalent fractions:
1.12+ 2
4=¿
2.4
12+ 1
3=¿
3.4
16+ 5
20=¿
4.26+ 3
9=¿
5.12+ 2
4+ 4
8=¿
42
APPENDIX D
Sample of Post – test for pupils
Add the following equivalent fractions
1.12+ 2
4=¿
2.4
12+ 1
3=¿
3.4
16+ 5
20=¿
4.26+ 3
9=¿
5.12+ 2
4+ 4
8=¿
43