CHAPTER ONE
INTRODUCTION
Background of the Study
According to Deringol (2018) our everyday lives, mathematics has always played
a part in it. According to, mathematics is needed by children to acquire the knowledge and
skills for everyday life Calculation, measurement, counting, analysis etc. mostly influence
our day to day lives for instance games, buying and selling etc. Mathematics is found in
almost all sectors of the economy being it business, politics, finance, education,
agriculture, trading etc. therefore one ought to seek knowledge and understanding in
mathematics.
According to Unlu et al. (2017), mathematics is an important subject to be studied
by students, because mathematics can encourage various abilities of students. This is the
actual reason why mathematics part of the core subjects in our educational curriculum
both at the Basic and Senior High schools and one must have a minimum of pass to be
admitted to a higher institution. It also plays leading and important roles in all aspects of
human endeavor.
The fundamentals of mathematics is made up of the concepts of additions and
subtractions. Therefore no algorithm of mathematics can be put up without the
fundamental concept of addition. It is one of the most important concepts of mathematics
and one’s inability to do simple addition, fails to continue one’s academic pursuit. This
also goes a long way to greatly affect their career lives too.
The in-in-out programme of the Colleges of Education offers Teacher-trainees the
opportunity to do their practices in their attached schools. This helps them to meet, interact
and help solve certain pressing issues and problems facing pupils' education in the
1
communities. In the writer's school of attachment, Greenland School at Asokore –
Koforidua Eastern region of Ghana, it was observed that, some pupils in class three were
unable to do simple addition of two and three digits numbers. When the class teacher and
the previous class teacher were consulted, they both said much effort had been put into
solving the problem, but they have all proved futile. When the problem was identified, the
writer took it upon herself to delve into the roots of the pupils' inability to solve problems
in addition of two and three digits numbers. In view of this, the writer is aimed at bringing
to light the causes of pupils' problem.
Statement of the Problem
Pupils' inability to do simple addition involving two and three digits numbers at
basic one level in Greenland school is pathetic and worrisome. Addition is something the
pupils' should learn before they advance to basic two.
Purpose of the Study
The researcher wants to find out the causes of pupils' poor performance in
mathematics. The study is also to design an appropriate teaching and learning activities
that will aim at developing numeracy in the learners.
The study will also provide a framework that would help teachers to improve upon
their delivery of instruction, because it would assist them to modify ideas to suit the need
of their pupils. It is also to create the awareness such that the policy makers would come
out with appropriate policies that would help to develop pupils' numeracy skills at the
basic level.
2
Finally, the research will provide a framework that will serve as a source of
information to students or anybody who would like to further research into a similar topic
of the same topic.
Research Questions
This research seeks to find answers to the following questions;
i.
Will the use of teaching and learning materials influence teaching and learning of
addition of two and three digits numbers?
ii.
What role does a detailed lesson plan play in teaching and learning of addition?
iii.
Will the intervention processes help to curb and sustain pupils' interest so as for
them to overcome their handicap in the addition of two and three digits numbers?
Significance of the Study
This research will not be useful to the pupils' understudy, but also to other pupils
who may have similar problems. Teachers will also benefit from the research. Moreover,
parents as well as the community and the stakeholders in education – such as the
government, Ghana Education Service (GES) and the Ministry of Education, science and
Sports (MOESS) – will also benefit from the study. It is also to help the pupils in the
mentioned school improve their addition of two and three digits numbers and addition in
general.
3
It will also help teachers in the school to develop new ideas to improve upon their
lesson delivery in mathematics to meeting the needs of the pupils they are teaching. They
will also be abreast with the appropriate usage of teaching and learning activities. It will
also create the needed awareness in parents and guardians the best ways to assist their
wards to improve their academic performances. The community's economic and social
activities would also be greatly improved since the school will produce quality and skillful
graduates. The study also seeks to aid the policy makers identify loopholes and rough
edges which need to be smoothened and straightened as far as the teaching of mathematics
is concerned.
Limitations
Most of the pupils were not regular to classes during the intervention period. Other
who came, were always almost late with some not having enough books and other writing
materials.
There was no readily available statistics and logistics to help the researcher trace
for more information on the pupils understudied. Some of the regular teachers were not
willing to support the researcher with the needed information. As the community is
predominantly a business one, some parents were also not willing to let their wards attend
extra classes after the close of normal classes.
Delimitations
This research has been narrowed to only basic one pupils of Greenland School at
Asokore – Koforidua Eastern region of Ghana.
4
Organization of the Study
The first chapter of this study covers the introductory section. It spells out the
background of the study, statement of the problem, purpose of the study, research
questions, and significance of the study, delimitation and limitation and organization of
the study and the summary.
Chapter two deals with review related literature. These are textbooks, journals,
magazines, etc., represents theoretical perspectives and empirical data that have been
conducted by renowned researcher in the areas understudy.
Chapter three, methodology, describes the procedure followed in going about this
research. The main components includes the research design, population of the study,
sample and sampling, instrumentation, data collection, intervention design and data
analysis.
In chapter four, is the analysis and discussion of findings. It also represents the
results on the study conducted.
Chapter five, which is the conclusive part of the research consists of summary,
suggestions, conclusion and recommendations.
Summary
First of all, the researcher gives the background of the study as follows. According
to Deringol (2018) our everyday lives, mathematics has always played a part in it.
Mathematics is found in all sectors of our economy being it business, politics, finance,
education, agriculture, trading etc. one ought to study it with all seriously.
5
According to Unlu et al. (2017), mathematics is an important subject to be studied
by students, because mathematics can encourage various abilities of students so it has been
made core subject in both junior and senior high schools so one has to pass to advance in
education. The fundamentals of mathematics is made up of the concepts of additions and
subtractions. This is to say that if one is unable to do simple addition, one fails to continue
academic pursuit as well as affect ones career life. The in-in-out programme of the
Colleges of Education offers Teacher-trainees the opportunity to do their practices in their
attached schools. This helps them to meet, interact and help solve certain pressing issues
and problems facing pupils' education in the communities for which Greenland school
was my school of attachment.
Secondly, the researcher made a statement of the problem as follows; Pupils'
inability to do simple addition involving two and three digits numbers at basic one level
in Greenland school is pathetic and worrisome. Addition is something the pupils' should
learn before they advance to basic two.
Furthermore, for the purpose of this study, the researcher wants to find out the
causes of pupils' poor performance in mathematics, design an appropriate teaching and
learning activities, provide a framework that would help teachers to improve upon their
delivery of instruction as well as this research will provide a framework that will serve as
a source of information.
Moreover, this research seeks to find answers to the following questions as it states
Will the use of teaching and learning materials influence teaching and learning of addition
of two and three digits numbers? .What role does a detailed lesson plan play in teaching
and learning of addition? . Will the intervention processes help to curb and sustain pupils'
6
interest so as for them to overcome their handicap in the addition of two and three digits
numbers?
Again, this research will not be useful to the pupils' understudy and to all pupils,
teachers, stakeholders of education such as such as the government, Ghana Education
Service (GES) and the Ministry of Education, science and Sports (MOESS). This research
will go a long way in helping pupils improve their addition of two and three digits numbers
and addition in general, help teachers in the school to develop new ideas to improve upon
their lesson delivery in mathematics to meeting the needs of the pupils they are teaching.
The community's economic and social activities would also be greatly improved since the
school will produce quality and skillful graduates. The study also seeks to aid the policy
makers identify loopholes and rough edges which need to be smoothened and straightened
as far as the teaching of mathematics is concerned.
Also, with the limitation of the study, most of the pupils were not regular to
classes during the intervention period, others were late and other did not have enough
books, statistics and logistics to help the researcher trace for more information on the
pupils understudied were unavailable, there exist some sort of unwillingness on the side
of teachers to provide needed information to support the researcher, some parents in the
community were also not willing to let their wards attend extra classes after the close of
normal classes
In addition, the delimitation of this research has been narrowed to only basic one
pupils of Greenland School at Asokore – Koforidua Eastern region of Ghana.
Finally, in the organization of the study, the researcher gives the structure of the
research as follows. The first chapter of this study covers the introductory section. It spells
out the background of the study, statement of the problem, purpose of the study, research
7
questions, and significance of the study, delimitation and limitation and organization of
the study and the summary. Chapter two deals with review related literature. These are
textbooks, journals, magazines, etc., represents theoretical perspectives and empirical data
that have been conducted by renowned researcher in the areas understudy. Chapter three,
methodology, describes the procedure followed in going about this research. The main
components includes the research design, population of the study, sample and sampling,
instrumentation, data collection, intervention design and data analysis. Chapter four, is
the analysis and discussion of findings. It also represents the results on the study
conducted. Chapter five, which is the conclusive part of the research consists of summary,
suggestions, conclusion and recommendations.
In conclusion, the chapter one of this research is made up of background of the
study, statement of the problem, purpose of the study, research questions, and significance
of the study, delimitation and limitation and organization of the study and the summary.
8
CHAPTER TWO
REVIEW OF RELATED LITERATURE
This chapter talks about related written materials and opinions of experts in the
field understudy. It also talks about mathematical concepts addition, with its associates.
Moreover, the written related materials will include textbooks, journals, magazines and
the writer's own opinion.
Concept of Mathematics
The subject mathematics does not have a single definition which has been given
and accepted world wide. Several people have drawn definitions in the manner that they
perceived it. It is against this background that Addae (2006) came out that mathematics is
"quietly fragment without the operation of addition and its reciprocal subtraction". From
the New Cambridge Advanced Learner's Dictionary, mathematics "is the study of
numbers, shapes and space using reason and usually with a special system of symbols and
rules for organizing them". It also pointed out that mathematics includes algebra,
arithmetic, and geometry.
However, this explanation can be affirmed with the appreciation of mathematical
knowledge in the construction of tools and shelter in the early years. This goes on to
ascertain that fact that, without knowledge in mathematics, man, will be completely lost
on earth and other planets that is believed to support life.
Today, it is believed that mathematical knowledge in this modern world is
advancing at a faster rate than ever before. Theories that were once isolated have been
incorporated into those that were comprehensive and complicated. This calls for the
empowerment of curious minds to be abreast with the changing trends in the application
9
of mathematics in all fields of endeavour. Mathematics is deemed as the main switch
behind science and technology. Mathematics also plays a vital role in the life of every
individual. The impact mathematics has in the development of the world today cannot be
left out, yet a large number of people are afraid to pursue programmes that are
mathematically related. All these are attributed to the fact that many people are
arithmophobia.
The study of relationship among quantities of elements, magnitudes and their
properties of logical operation are declared as in set, pose a great challenge and
discourages many pupils.
Turmudi (2008), mathematics has been taught to students informatively, students
only get information from the teacher. Thus, their memory is only temporary.
The principle of learning is at the heart of creating a classroom environment where
pupils can better learn to do mathematics and to explain their mathematical thinking
(Sinwell, 2007)
Concept of Numbers
Numbers are topics within the domain of arithmetic. Numbers are important in learning
mathematics in elementary schools (Fauzi & Suryadi, 2020; Pitta-Pantazi, 2014; Jordan
et al., 2010). According to Verschaffel et al. (2007), numbers are important to learn
because it relates to the students’ real life, serves as a basis for understanding other
materials, and becomes one of the first materials taught in formal schools. In addition,
students' dispositions for mathematics often depend on this material. Counting numbers is
the basis for all subsequent integer calculations such as calculating decimals, fractions,
comparisons, and percentages. Calculating at a later stage does not only depend on the
students' knowledge of number structure and basic numeracy skills, but also on insights
10
into basic numeracy strategies, mathematical attitudes, and general interests in broader
mathematics (Treffers & Buys, 2001).
Concept of Addition
The concept addition, according to the Oxford Learner’s Advance Dictionary
(2001), “is the process of adding two or more numbers of distinct values together to find
their totals”.
Simply put, addition refers to the act of putting two or more things together to
increase the size, number, amount and so on.
Apronti (2001) said “addition and subtraction are the basis of mathematics”. He
supported Asante (2001) who said that, “the main idea which are mostly used in our daily
activities bring to light that almost all the concepts in mathematics are developed out of
addition”. For instance, the concept of measurement and algebra are made up of addition.
He advised that substantial attention must be given to the methods and teaching techniques
as well as teaching aids to enrich its understanding. Adequate teaching and learning
materials should be designed by the teachers.
From Land (1975), the letter and symbols which denote numbers are the short form
of mathematics and for that matter, greater attention should be given to it in order to make
pupils understanding permanent so as to foster learning in the classroom. More so, it has
11
been noted that most pupils normally find it very uneasy to cope with addition involving
the place value concept.
The Role of Instructional Materials in Teaching Mathematics
Instructional materials are the physical objects used in the classroom
during teaching and learning. In recent years, attention was focused on the use and role of
instructional materials in Mathematics to improve students’ academic performance. This
implies that the teaching of Mathematics without the use of instructional materials may
certainly result in poor academic performance. Adebanjo (2007) Students get motivated
when they are actively involved in the teaching learning process and this will minimize
teaching of Mathematics in abstraction.
(lji, 2002 and Obodo, 2007) have therefore, been continuously exploring ways of
ensuring that Mathematics is properly taught and learned in the school. The implication
here is that effective teaching of Mathematics should emphasize active learning.
Adebanjo (2007) affirmed that the use of instructional materials in teaching and
learning of Mathematics makes students to learn more and retain better what they have
been taught and that it also promotes and sustains students’ interest. It also allows the
learners to discover themselves and their abilities. Students learn more when they see what
they are being taught.
(Gagné et al. 2005)
12
(Gagné et al. 2005) instructional materials have the capacity to develop into students the
highest order of intellectual skills as they illustrate clearly, step by step how to follow the
rules/principles and elaborate on the concepts, all of which have positive impact on 16
solving new problems by analyzing the situation and formulating a plan. According to
Gagne et al, instructional material can be used to develop higher learning abilities to the
learners through self-teaching or guided learning. This implies that the instructional
materials mainly comprise “eliciting performance” and “providing feedback on
performance correctness,” in addition to “providing learning guidance” for guided
discovery learning
Instructional Material Theories
Instructional material theories assume that there is a direct link between the materials that
the teachers use, and the students’ learning outcomes. These outcomes include higher
abilities to learn, quality strategies to learn and perform classroom activities and positive
attitude towards learning. Further, these theories assume that instructional materials have
the capacity to develop into students the highest order of intellectual skills as they illustrate
clearly, step by step how to follow the rules/principles and elaborate on the concepts, all
of which have positive impact on 16 solving new problems by analyzing the situation and
formulating a plan (Gagné et al. 2005). According to Gagne et al, instructional material
can be used to develop higher learning abilities to the learners through self-teaching or
guided learning. This implies that the instructional materials mainly comprise “eliciting
performance” and “providing feedback on performance correctness,” in addition to
“providing learning guidance” for guided discovery learning. Many of Gagné’s 9 ideas
have broad implications for secondary teachers in community secondary schools in
Rombo district. Many of these ideas have capacity building undertones with themes of
13
students’ acquisition of critical thinking and problem-solving skills. However, the theory
does not relate to whether or not students can think critically in what aspects or how they
can solve a particular problem by themselves. However, I have the opinion that the
purpose of instructional materials or technology in education is to stretch students’
imagination and to encourage them to solve problems in their lives.
Availability of instructional material
Etsey, Y. (2005) confirm that the availability and use of teaching and learning materials
(TLMs) affect the effectiveness of a teacher's lessons. The use of TLM will influence
pupils' comprehension of lessons. This can be realized through the development of the
pupils’ manipulative and analytical skills and high level of interest in the learning process.
Finally, Fianu (2005) explains that, a poor school environment for teaching, hostile
attitude from the teachers towards the child will impede the progress of the child in school.
In conclusion, it has now come to light that teaching learning materials plays an
importance role in teaching and learning. Also, care should be taken in their selection and
use, for the teaching and learning materials, to achieve it aim, conductive learning
environment must equally be created.
Methods of Teaching Mathematics
14
According to the New Cambridge Advanced Learner’s Dictionary, teaching ‘is the
act of given someone knowledge or to instruct or train someone’. It continues to explain
that teaching ‘improves someone’s future behaviour’.
logical knowledge is not acquired from reading and listening to peoples’ talk but
to construct from actions on objects. This in one way or the other calls for a more practical
and interactive approaches to the teaching of concepts in mathematics to enable learners
use it to communicate, describe its common features and to define it. It is also good to use
distinct examples and materials when necessary, to impact mathematical concepts to
learner’s at all levels.
This means that mathematics teachers should be abreast with the terminologies,
symbols, signs so as to enhance efficient tuition of the subject at all levels and in all
spheres of life.
With regards to the opinion of Copley (2000), the method of teaching is one of the
important factors that will affect mathematics achievement. Therefore, it is essential for
teachers to ascertain this and teach pupils at all stages accordingly. Actually, learners
relevant previous knowledge in the basic schools, houses, markets and various fields of
endeavour in sorting, grouping, analyzing, classifying, generalizing among others are
fundamentals and should serve as spring board for the understanding of new concepts in
addition at the primary school level. Admittedly, it is clear that pupil’s relevant previous
knowledge should be traced before any meaningful teaching and learning can take place.
In addition, Davidson (2001) expressed that schools could be built, adequate
textbooks can be provided but if pupils are not given proper tuition and skills, then, we
should be counting numbers backwards on the progress chart. Tutors are to make good
15
use of teaching and learning materials to arouse curiosity. When pupil’s curiosity is
aroused, that pupil will be able to work on any given activity until he/she is satisfied with
the outcome or results.
DISCOVERY METHOD
(Fonna, 2018b: Alfieri et al, 2011), one of the learning models that provide
opportunities for students to develop and find their own understanding, the information
presented is easily absorbed, processed and stored well by the student memory system as
well as provide opportunities for students to play the more active role in the classroom is
a model discovery learning. Children who succeed on a given task using the discovery
method will be highly motivated and will want this method to be used in later
mathematical learning. They will want to experience again the joy they often attained from
a successful discovery.
Hosnan (2014) states that discovery learning is a method for developing active
learning methods by finding oneself, investigating on their own, then the results obtained
will be faithful and durable in memory. Through learning discovery, students can also
learn analytical thinking and try to solve their own problems. Some teachers think that the
discovery method is time consuming, thus not allowing them to cover enough of the
syllabi. Such teachers should remember that mastery of the content is a major goal of
instruction and that if a syllabus is covered hurriedly using more traditional methods, most
of the pupils do not achieve mastery of the content.
By contrast, pupils who are taught by the discovery method even though may cover
less initially, they will learn faster as a later stage. This is because, they will understand
the basic fundamentals and will catch up with and eventually out stride pupils who were
rushed through.
16
QUESTION METHOD
. This may be one reason why pupils are more responsive and more actively
involved in classroom when they are made to examine the content of the lesson more
closely by the use of questions. Students’ answers to questions also enable the teachers to
judge their level of understanding and to assess their progress. They added that I a
mathematics class, therefore, it assist teachers in their mathematics lessons. They
however, cautioned that in asking questions, it is desirable that teachers use simple
language which children understand. If incorrect answers are given to teachers’ questions,
it should understand that, it may arise from pupils’ inability to comprehend the language
in which the questions are framed. At other times, failure to give correct answers may be
due to the length of the questions of the difficulty of its mathematical content.
Desirable as it is to use simple questions, such questions should not be trivial.
Trivial questions may not stimulate thinking in the desired manner. For example, asking
an average primary three pupil for the answer to 3 + 4 is trivial.
The Role of the Teacher in Mathematics Teaching
Dondieu (2002) states that, the more use of teaching and learning materials does
not guarantee effective teaching and learning. Rather it is the careful selection and skillful
handing by the teacher that ensures the usefulness in facilitating learning. The preparation
and effective use of the materials however presents problem to teachers especially
beginning teachers.
Most teachers fail to prepare lesson plan or notes because they see it to be a waste
of time. every lesson plan should have instructional objectives that describes what pupils
are to do at the end of the instructional period. These objectives should specify the content
17
of the context in which they are to do it. It should contain only one verb which tells what
pupils will do.. For example, the objectives ‘pupils will be able to tell the time’ has the
content ‘time’ which can be interpreted to mean reading the time to the hour or half-hour
or to the minute. There is the need for further clarification as to what is meant by ‘time’
in this statement of objective. He gave six examples of well stated instructional objectives;
1. Pupils’ will be able to find the mode of a given set of numbers,
2. Pupils’ will be able to add two whole numbers whose sum is less than 10,
3. Pupils’ will be able to identify cuboids, cube and sphere by name,
4. Pupils’ will be able to arrange three of four numbers in order of sizes ,
5. Pupils’ will be able to find the factors of a whole number less than 50 and
6. Pupils’ will be able to say the missing number in an addition sentence like
[ ] + 8 = 15.
The practices exercises in the mathematics textbooks, are designed to help pupils
understand the lesson and to recall the new knowledge when it is required of them with
the help of a teacher. Some teachers for fear of too much work load – marking of exercises
for the day and tiredness – fail to give pupils adequate practices for a days work. Some
teachers find it tedious in going through pupils mistakes with them. They just mark the
exercises and go their way.
It is the role of the teacher to identify and bring to their notice if there is any
mistake in the solution of a problem. It is not sufficient for the teacher to just mark the
answer wrong. The teacher needs to underline or circle the stages where the errors
occurred, particularly the first error. The teacher should bring these errors to pupil’s
attention. A summary of the type of mistakes made by the pupils will suggest the kind of
18
remedial teaching that has to be done. It is also the teacher’s duty to bring some individual
own peculiar mistakes out to them to be identified, corrected and explained adequately.
teachers’ should avoid cultivating the habit of working out all the problems in the
assignment or test on the chalkboard and then ask pupils to copy the solution. This is very
wrong though this practice is useful in assisting pupils to record the correct solution for
future reference. It is also helpful in making them learn the correct method and skill. It
becomes much more beneficial if pupils are given new problems similar to the ones they
missed out or gotten wrong and asked to solve them.
. Instructional materials arouse and sustain pupils’ interest during teaching, thus
making their foundation very solid and permanent.
CHAPTER THREE
METHODOLOGY
This methodology chapter describes the procedure followed in carrying out the
study. The main components of this chapter are the research design, population, sample
and sampling procedure, instrumentation, data collection and data analysis.
Research Design
Research design describes the basic design used in the study and its application
to the study. It refers to the researcher’s overall plan for obtaining answers to the research
questions. The research design used for the study was the action research which is a type
of design used to solve classroom problem scientifically. It is normally conducted in a
19
local setting. The researcher, therefore in an attempt to find immediate solution to the
problem; resorted to the use of action research design. This action research was used to
investigate critically into pupils poor performance in mathematics and specifically in
addition of two and three digit numbers.
The strengths of this design are as follows; it helps the researcher to study
individual behaviours. It also provides an orderly framework for solving problems
identified by the researcher. It also provides a platform for the researcher to monitor the
changing rates in behaviour patterns of the people understudy.
A great set back in the use of action research is that the procedure used in solving
a problem at one locality may not work successfully within another locality; hence results
obtained cannot be generalized.
Population
The pupils in basic three at Endwa R/C, the teachers, parents and guardians in
the Endwa community were the targeted group.
Sample and Sampling
In many cases, a complete coverage of the population in a study is not possible;
therefore, the researcher had to select some of the targeted population for the study. In
doing so, the researcher used random sampling procedure – to make sure that there was
fairness, as they were too many – to select twelve (12) pupils out of thirty-three (33) as
the sample for the study.
20
Instrumentation
The tools used in collecting data were observation, test and questionnaire.
Observation is the procedure whereby the researcher collects data on the current
status of the subjects by watching, listening and recording what is being done by the
targeted group. This tool provides first hand information without relying on reports from
others.
In the writer’s observation, it was noticed that the class teacher used no
instructional materials in teaching, he solely depended on oral presentation and for that
matter, and the pupils did not pay much attention during the lesson. Also the teacher’s
question distribution was not evenly done. His questions were directed to the few pupils
who are vocal or considered intelligent, thus making the majority of the pupils become
observant.
Some of the methods he used in teaching certain aspect of the topic were just
inappropriate. This made the lesson dull thereby creating a fertile ground for pupils to
sleep or doze as teaching was in progress. The researcher used three weeks to observe the
regular class teacher teach the pupils.
Data Collection
The researcher haven gathered all the relevant materials needed in the study. The
researcher decided used tests (pre-test and post-test questions) to assess the pupils. In
observing the pupils and the teacher in the two upper primary classes, the researcher used
three weeks. Also printed questions were given out to the sampled group and the group
was given enough privacy to answer the questions. Two weeks later, the questions were
21
submitted. Some parents (illiterates) were also interviewed in their local dialect and their
responses recorded.
Questionnaire
Questionnaire is made up of the questions related to the aims of the study. The
research questions were to verified and answered by the respondents in writing form. It
has an advantage of being less expensive; it has a wide range coverage and greater
assurance of anonymity.
The researcher during the study, printed questions and administered to teachers
to answer. Both closed-ended and opened-ended types were used. The questionnaire was
divided into two sections; the first section was designed to seek for the background
information of the respondents in respect of sex, age, educational background and
occupation. The second section sought information from respondents on how they
perceived teaching and learning mathematics in the primary school.
Pre-test
The researcher conducted a pre-test to determine pupils’ entry behaviour in terms
of their ability to solve problems in addition involving two and three digit numbers. The
questions for the test were selected for the pupil’s textbooks. The questions were based on
the topic already treated and were made of five items. Two of the questions were addition
involving two digit numbers while three of them were addition involving three digit
numbers. Twenty minutes was the time duration and after and after which their exercise
books were collected, marked and scored.
22
Pre-test Questions
1). 3 4
2). 5 6
3). 432
4). 663
5). 945
+25
+ 89
+ 359
+ 942
+ 237
Below are some examples of how some of the class three pupils answered the
pre-test questions
1). 3 4
2). 5 6
3). 432
4). 663
5). 945
+25
+ 89
+ 359
+ 942
+ 237
59
1315
7811
15105
11712
Intervention
Two days was selected from all the weeks to be used for the intervention. They
were Mondays and Thursday only.
Week One
On Monday, the researcher gathered the basic materials needed for the lesson
and briefed the pupils on what was at sake. They were told of the things they would use
and the need to always be regular and punctual.
Thursday was used by the researcher to introduce the topic to the pupils and to
retune their minds to the task ahead. They were reminded of their duties as pupils.
23
Week Two
During the first day of the second week, the researcher took the opportunity to
assess pupil’s performance on two digit numbers involving addition. After it had been
marked the researcher was able to detect and also helped her to design the appropriate
activities for the pupils.
On the second meeting, the researcher used place value concept to teach pupils
involving the addition of two digit numbers. The abacus was used as a teaching aid to help
pupils to understand the concept better.
Week Three
The two days of the third week was used to take pupils through the use of the
abacus in solving simple questions involving two digit numbers. Others who had little
difficulties were made to use coloured counters and where systematically taken through
the concept of carry-over.
When pupils were given some examples to try their hands on, the results was
encouraging, as most of them, were able to work them successfully.
19
36
45
+22
+27
+25
41
63
70
Week Four
24
Pupils were introduced to solving addition involving three digit numbers; this
was after they had successfully solved problems involving addition of two digit numbers.
The researcher used the place value chart to solve 436 + 234.
The researcher gave pupils numbers that were three digits to mark on a line. They
were then asked to separate the digits and place each digit under its place on the line.
Those who had some difficulties were assisted by the researcher, especially adding the
two numbers on the separate line in their rightful places.
Hundreds
Tens
Ones
4
3
6
2
7
3
6
7
9
= 679
Pupils were directed as to how the additions of three digits are solved in a stepby-step procedure.
Week Five
25
Week five was devoted to working more examples on three digits numbers using
the place value charts.
Week Six
During the sixth week, various types of activities were used together with some
teaching learning materials (TLM) so as to make the lesson more concrete to the learners.
Example, using the abacus to solve addition of 376 and 262. . For 376, six beads were put
on the ones column, seven beads were put on the tens column and three beads were put
on the hundredth column. The same was done for the 262 where two beads were put on
the ones column, six beads were put on the tens column and two beads were put on the
hundredth column.
The addition then started from the right end, 6 ones added to 2 ones gave 8 ones.
On the tens column were had 7 tens added to 6 tens which gave us 13 under the tens
column. With the hundredth column, 3 was added to 2 to give us 5 under the hundredth
column. The results were on the ones column, we had 8, 13 on the tens column and 5 on
the hundredth column. From the tens column, 1 (which is actually a hundred) was taken
from the 13 and carried on to the hundredth column thus making the hundredth column 6.
It was therefore concluded that 376 added to 262 gives 638, mathematically 376 + 262 =
3
7
2
5
13
8
nes
6
Tens
2
dreds
638.
262
6
376
Ones
Tens
dreds
26
Post-test
Another test was conducted after the intervention. This was to see whether the
interventions put in place had had any positive effect on pupil’s performances. Questions
were selected from pupil’s mathematics book 3. They were given twenty minutes just as
during the pre-test, to solve the five-item problems. The researcher collected, marked and
scored accordingly.
Post-test Questions
(1) 3 4 5
+3 2 1
(2) 6 7 9
+3 0 1
(3) 7 3 0
+4 1 9
27
(4)
22
+ 33
(5)
42
+39
This time almost all the pupils were able to at least 4 questions correctly.
Samples of how most pupils answered the questions are shown below.
(1) 3 4 5
+3 2 1
666
(2) 6 7 9
+3 0 1
980
(3) 7 3 0
+4 1 9
1149
(4)
22
+ 33
55
(5)
42
+39
81
Data Analysis
With reference to the scripts marked for both pre-test and post-test, the scores
that were obtained were collected and analyzed using basically quantitative approach. The
outcome of the test results are analyzed in the nest chapter, four.
CHAPTER FOUR
DATA PRESENTATION AND ANALYSIS
This chapter presents the results on the study. It deals with the analysis of data
collected in an attempt to uncover the reasons behind basic three pupils of Endwa R/c
Primary three pupils’ inability to solve addition problems involving two and three digits
numbers.
The findings of the study constitute the results of the researcher’s analysis of her
data. The findings will also be discussed later in the chapter.
28
The chapter consists of two sections, the first section will analyze the
background data of the respondents and the second section will cover the breakdown of
the responses of the respondents to the items in the questionnaire. Analysis of data will be
summarized in appropriate tables.
Presentation and Analysis of Data
Table 1
Sex Distribution of Respondents
Sex
No. of Respondents
Percentage (%)
Males
12
60
Female
s
8
40
20
100
Total
The table above provides the distribution of male and female respondents who
took part in the study. From the statistics above, 60% of the respondents were males while
40% were females.
Table 2
Age Distribution of Respondents
Age
No. of Respondents
Percentage (%)
21 - 30
10
50
31 - 40
6
30
41 - 50
4
20
20
100
Total
29
The table above indicates that 10 out of 20 (50%) respondents fell between 21 –
30 years, 6 (30%) of the respondents fell between 31 – 40 years with the rest 4 (20%)
falling between 41 – 50 years.
Table 3
Occupation of the Respondents
Occupation
No. of Respondents
Percentage (%)
10
30
Nurses
2
10
Students
3
15
Farmers
9
45
20
100
Teachers
Total
Table 3 above illustrates the occupation of the respondents. 3 (15%) of the
respondents were students, 2 (10%) of the respondents were nurses, 9 (45%) of the
respondents were farmers with 10 (50%) of the respondents being teachers and forming
the greater number of the respondents.
Table 4
Educational Background of the Respondents
Level of Education
No. of Respondents
Percentage (%)
Degree
0
0
Diploma
2
10
Teachers/Nurses Certificate
10
50
G.C.E. O/A Level
3
30
15
M.S.L.C
5
25
From table 4 above, none of the respondents had a degree certificate. 2 (10%) of
the respondents had a diploma certificate, 3 (15%) had either an ‘A’ level or ‘O’ level
certificate. 5 (25%) had the Middle School Leaving Certificate (MSLC) and the majority
of the respondents 10 (50%) had either the Teachers Certificate ‘A’ or SRN (State
Registered Nurses) Certificate.
Table 5
Respondents view on why pupils do not perform well in mathematics
Reasons
No. of Respondents
Percentage (%)
Unqualified Teachers
8
40
Teachers attitude towards maths
3
15
Poor teaching methods
5
25
Failure to use TLMs
4
20
20
100
Total
31
Information from the table above indicate that 8 (40%) of the respondents shared
the view that pupils perform poorly in mathematics because of unqualified teachers
handling the subject in the school. 5 (25%) of the respondents attributed pupils failure in
mathematics to poor teaching methods used by teachers in lesson delivery. 4 (20%) of the
respondents said that failure of teachers to use teaching learning materials accounts for
pupil’s poor performance in the subject and 3 (15%) were of the opinion that it was due
to teachers attitude towards the subject contribute to pupil’s poor performance.
Table 6
Respondents view on the methods for teaching mathematics
Methods
No. of Respondents
Percentage (%)
Activity Method
4
20
Discussion Method
8
40
Questioning Method
2
10
Demonstration Method
6
30
20
100
Total
From table 6 above, 4 respondents representing 20% supported the activity
method, 8 (40%) supported the use of discussion method, 2 (10%) supported the
32
questioning method and 6 (30%) of the respondents supporting the use of the
demonstration method.
Table 7
Respondents view on why teachers fail to use teaching learning materials
(TLMs)
Reasons
No. of Respondents
Percentage (%)
TLMs waste too much time
6
30
TLMs are too difficult to use
10
50
TLMs are not available
3
15
TLMs are too expensive
1
5
Total
20
100
From the table above, it is clear that 6 (30%) of the respondents are of the view
that using TLMs waste too much time, 10 (50%) think it is too difficult to use TLMs in
teaching. 3 (15%) says, that TLMs are not readily available in the school and 1 (5%) is of
the view that TLMs are too expensive to buy.
Table 8
Level
Respondents view on pupil’s performance in mathematics.
No. of Respondents
Percentage (%)
Very good
0
0
Good
4
20
Weak
Very weak
10
33
6
50
30
None of the respondents graded pupils’ performances in mathematics as very
good. Only 4 (20%) of the respondents graded pupils’ performance as being good. 10
(50%) of the respondents graded pupils’ performance as being weak with 6 (30%) grading
pupils’ performance as being very weak.
The researcher used the pre-test scores to determine the performance of the
pupils. It was through these scores that the researcher came in with her interventional
activities.
Table 9
Respondents view on whether pupils have access to mathematics
textbooks.
No. of Respondents
Response
Percentage (%)
Yes
6
30
No
14
70
Total
20
100
From the above table, only 6 (30%) of the respondents said that pupils had access
to mathematics textbooks while 14 (70%) said that pupils do not have access to
mathematics textbooks.
34
Table 10
Respondents view on whether parents support children to study
mathematics at home.
Percentage (%)
No. of Respondents
Response
Yes
4
20
No
16
80
Total
20
100
Statistics from the table above show that only 4 respondents representing 20%
said parents supported pupils to study mathematics at home and 16 (80%) of the
respondents shared the view that parents do not support pupil to study mathematics at
home.
Table 11
Distribution of pre-test score
Scores
0
1
2
3
4
5
6
7
8
9
10
4
3
5
7
8
4
1
1
0
0
0
12.1
9.1
15.1
21.2
24.2
12.1
3.03
3.03
0
0
0
No. of Pupils
Percentage
The table above gives the result of the pre-test conducted at the beginning of the
study. It could be seen that only 6 pupils scored between 5 and 7 with no one scoring 8, 9,
or 10. A greater number of the pupils scored below 5 marks, an indication that their
performance in mathematics was poor.
Table 12
Distribution of post-test score
Scores
0
1
2
3
4
35
5
6
7
8
9
10
No. of Pupils
0
0
0
2
2
3
7
3
5
6
5
Percentage
0
0
0
6.1
6.1
9.1
21.2
9.1
15.1
18.2
15.1
The table above provides the results of the post-test conducted after the
intervention. None of the pupils scored between 0 and 2. 2 pupils each scored 3 and 4
respectively. 3 pupils each scored 5 and 7. In general 29n pupils scored 5 and above. The
results from the post-test show clearly that there has been a great improvement in pupils’
performance in mathematics after the intervention.
Further Discussion of Results
Based on the analysis made, a number of factors have been identified as causes
for pupils poor performance in mathematics. Factors like unqualified subject teachers,
teachers’ attitude towards the subject, poor teaching methods and teachers’ failure to use
teaching learning materials to teach were disclosed. However, it came to light that,
unqualified subject teachers and the use of poor teaching methods accounted most for
pupils’ poor performance in mathematics.
Another important thing which surfaced was that teachers do not use the activity
method in their lesson delivery. The activity method promotes the effective use of teaching
learning materials and would have sustained pupils’ interest in the subject.
It was clear that teachers even though knew the usefulness of teaching and
learning materials; they were not using them to teach but instead gave flimsy excuses for
their failure to use them in their lesson delivery. To add up, the teachers were well aware
of pupils’ poor performances in mathematics and they deemed it to be normal by attributing
it to pupils being lazy and not ready to learn.
36
CHAPTER FIVE
SUMMARY, CONCLUSION, RECOMMENDATIONS AND SUGGESTIONS
Summary
This research study was conducted with the aim of improving teaching and learning
of mathematics (addition involving two and three digit numbers) more meaningful to the
pupils.
The study was conducted on basic three pupils of Endwa Catholic Primary as the
targeted population. Questionnaires and tests were the main instruments used in collecting
data for the study. Pre-test was followed by intervention where a lot of activities were
performed by both the researcher and the pupils. After the intervention, a post-test was
conducted to assess the success of the intervention strategies put in place by the researcher.
37
It was observed that pupils did not have interest in mathematics in general at the
initial stage of the study. To the researcher, pupils of today are different from pupils of
yesteryears. This is because whiles the former live in a scientific and technological age,
the later lived in pre-scientific age.
To add to the above, the study revealed the causes of poor performance in
mathematics among Endwa Catholic Primary 3 pupils as poor teaching methods employed
by teachers, teachers’ attitude towards mathematics, unqualified subject teachers handling
the subject and failure of teachers to use teaching and learning materials during their lesson
delivery, etc.
The study further brought to light that teachers did not teach the basic fundamental
skills and topics in kindergarten and in the lower primary where pupils needed in order to
be able to perform well in mathematics.
Finally, it was also identified that to help improve solving mathematical problems,
mathematics lessons should be planned in such a way that, teaching and learning materials
would be used effectively in class for better understanding of mathematical concepts and
mathematics textbooks should be made available to pupils all the time.
Recommendations
The researcher, haven gone through the study successfully came out with the
following recommendations for future consideration.
That effort should be made right from the kindergarten to take pupils through some
aspects of numeracy in order to prepare them adequately for the subject. This will help
them develop interest in the subject.
38
That the Ghana Education Service (GES) should liaise with the Ministry of
Education, Science and Sports to provide teaching learning materials for the teaching of
mathematics in the basic schools.
Parents and guidance should be encouraged to support their children to study
mathematics at home. They should motivate their wards to study by relieving them of some
household chores so that they can get some time for their personal studies.
That teaching learning materials should be structured to suit this scientific and
technological age and the use of the child-centered approach to teaching should be
encouraged and practiced by all teachers especially those in the lower and upper primary
to make teaching and learning interesting and sustainable.
Conclusion
The researcher found out that, pupils in basic 3 of Endwa Catholic Primary school
inability to solve problems involving two and three digit numbers stems from the fact that,
they received low motivation from both parents and teachers.
The findings is of relevance to all those who are concerned and have interest in the
education of the child at the primary level. It is of great importance to teachers and parents
or guidance as it will help them to identify pupils problems early – especially in
mathematics – and join hands to help find solutions early to avoid the unexpected.
Suggestions
The researcher suggests that regular in-service training and workshops and courses
be organized for mathematics teachers at the basic schools.
39
There should be more periods on the time table for mathematics lessons in the
primary schools.
References
Adedoton, O. Kalejaiye (Dr.) (1985), Teaching Primary School Mathematics U.K,
Longman Group Ltd
Askew Mike (1998), Teaching Primary Mathematics. Britain, Mulriplex Techniques Ltd
Biggs Edith (1985), Teaching Mathematics 5 to9. Britain, Library Cataloguing in
Publication data
Brown Margret (1985), Children Learning Mathematics, Library Cataloguing in
Publication data
Brownwell, W. A. (1928), The Development of Children Number Ideas in Primary Grades,
Chicago, The University of Chicago
40
Bruner. J. S. (1966), Towards a Theory of Instruction, Cambridge, Massachusetts, Belkap
Press
Golding, A.S. (1971), Inter Nation Study of Achievement in Mathematics, New York,
Wiley
Hubbard Ruth (1991), Interesting Ways to teach Mathematics, U.K Technical and
Educational Service Ltd
Land Frank (1975), The Language of Mathematics, Britain, Murray John Publishers Ltd
Mottershead Lorraine (1985), Sources of Mathematics Discovery, Britain, Basil Blackwel,
Oxford
Skemp Richard (1985), Structural Activities for Primary Mathematics, Britain, T J
(padstow) Ltd. Padstow, Cornwell
APPENDIX
The main objective for this questionnaire is to identify ways in which basic school could
improve pupil’s performance in solving an identified problem in mathematics.
Sex:……………………….
Age:…………………………………….
Educational Background:………………………………………………………………
Occupation:………………………………
Class Handling:………………………...
Tick your choice
1. Do you have interest in teaching mathematics?
Yes
No
2. How do you see the level of pupil’s performance in mathematics? High Low
3. Which of the following is the cause of pupil’s poor performance in mathematics?
41
a. Poor teaching method
b. Failure to use TLMs
c. Teachers inadequate knowledge about subject
d. Unqualified teachers
4. How often do you see teachers using TLMs in teaching mathematic?
a. Very regular
b Regular
Occasional
5. What is your view about the use of TLMs I teaching mathematics?
a. Too difficult to use
b. They are not readily available
c. Waste too much time
d. They are too expensive.
6. Which of the following methods do you think teachers often use in teaching
mathematics?
a. Activity-oriented
b. Discovery method
c. Oral presentation
d. Demonstration
7. Is there any mechanism to improve pupil’s performance in mathematics?
Yes
No
8. What is your view about the level of pupil’s in mathematics?
a. Very good
b. Good
c. Weak
42
d. Very weak
9. Do pupils have access to mathematics textbooks?
Yes
No
10. Do parents support pupils to study mathematics at home?
Yes
No
43