CHAPTER ONE
INTRODUCTION
Background of the Study
Mathematics as a subject in the school curriculum is compulsory, both at the
Basic and Senior High schools. It also plays leading and important roles in all aspects of
human endeavour.
The use of mathematics is found in many areas of real life situations. The field of
management, business and marketing are no exception. In the history of education,
mathematics has held its leading position among all other school subjects because, it has
been considered as an indispensable tool in this technological fast growing world.
The foundation blocks of mathematics is made up of the concepts of additions
and subtractions. Therefore no building of mathematics can be put up without the solid
basic foundation concept, which is, addition. It is one of the most important concepts of
mathematics and ones inability to do simple addition, fails to climb the academic ladder
of education to its topmost height.
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. In the writer's school of attachment, Endwa R/C Primary, 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
1
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 three level is pathetic and worrisome. Addition is something the pupils' should
have learnt when they were in basic two.
Purpose of the Study
The researcher wanted 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.
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.
2
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 ply 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 form 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.
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
3
and rough edges which need to be smoothened and straightened as far as the teaching of
mathematics is concerned.
Delimitations
This research has been narrowed to only basic three pupils of Endwa R/C
Primary School.
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 farming one, some parents were also not willing to let their wards
attend extra classes after the close of normal classes.
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.
4
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.
5
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.
The Meaning 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
6
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.
Wren and Wren (1985) attributed a larger portion of difficulties and fear to the
fact that it presents a radically new and different approach to the study of quantitative
relationships characterized by new symbolisms, concepts, language and much higher
degree of the generalization and abstraction than they have ever met.
Despite the meaningful learning of Brownwell (1978) and insightful
psychological and learning theories of Piaget (1958), Brunner (1966) and Golding
(1971), the learning of mathematics is still far from satisfactory.
Gibb (1980) also observed that while psychology has provided us with general
theories of learning, there is no established general theory to learning mathematics to
provide a basis for mathematics education.
7
The Meaning 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 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.
Benjamin (1992) states that, “the use of instructional materials makes unique
contribution to improve teaching and learning at all levels”. This can be realized through
8
the development of the pupils’ manipulative and analytical skills and high level of
interest in the learning process.
School (1983) also says that, “mathematics knowledge in knowledge derived
from thinking about experience with objects through our interaction with them.
According to Gallglur and Raid (1981),”teaching and learning should be centered
on instructional materials and adequate practices to enable learners identify how things
are related and improve on their mental in solving mathematical problems both at school
and in their daily live activities”.
Kalejaiye (1988) stated that, “the selection of a variety of teaching aids often
follows the choice of methods of teaching mathematics in primary schools”. This is
because primary school children are at the concrete operational stage – the stage when
they learn working with physical objects. The teaching aids will enable them understand
better the basic principles of mathematics, such as number relationships, the idea of
place value among many others. According to Kalejaiye, mathematics teaching aids are
produced commercially but because of financial limitation, most schools cannot afford
to buy all of them. Therefore, teachers may have to produce most of these instructional
materials themselves. There are however, some standard manufactured aids which a
school may have to buy. These include tape measures, weighing balance and
geometrical instruments. Mathematics teaching aids that can be made by the teacher are
number pattern cards, one-to-hundred square chart, abacus, geo-board and many others.
Kalejaiye on his part concentrated on the number pattern cards which each unit is
represented by a small square. This can be used to represent numbers. Figure 1 below
shows the pattern cards for the representation of the numbers ones, tens and hundreds.
The number card can be uses to represent any number.
9
One
Ten
Hundred
Figure 1
Dots can be entered on small squares to produce ‘dot pattern’ card.
Figure 2
The number pattern cards can be used to teach the idea of ordering numbers,
place value and the basic operation of addition, subtraction, multiplication and number
bends.
Skemp (1989) on his part also talked about one-to-hundred square chart. A large
square unit with whole numbers 1, 2, 3, …, 100 written on each small square so that the
number sit neatly at the centre of each small square as shown in figure 3 below.
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Figure 3
A 1-100 square can be drawn on the large size cardboard for class teaching or on
smaller cards or sheets of paper for group and individual work by pupils. The chart is
used for teaching counting by leaving out some numbers on the chart and asking pupils
to supply them. It can also be used to teach addition and subtraction of numbers.
Example, the result of 59 + 6 = 65 and 60 – 4 = 56 can easily be obtained from the chart
by forward and backward movements respectively.
11
The patterns of multiples of numbers can also be shown on the chart. For
example;
3
12
15
21
18
24
27
33
36
42
39
45
51
48
54
57
63
60
66
72
69
75
81
30
78
84
87
93
96
90
99
Figure 4
Pupils can be asked to show patterns of multiples of other numbers by putting
seeds or bottle tops on the chart to cover the required numbers.
Cockcraft (1982) also talked about one of the commercially produced
instructional materials. Cockcraft talked about a device for teaching counting, the idea of
place value and the basic operation of addition and subtraction of whole numbers. An
abacus is made up of straight wires on a frame or curved stuck to a common base. The
abacus with curved wires has a wooden board separating the two parts of wires. Each of
the wires carries ten beads which are pushed down along them to represent whole
12
numbers. This abacus has the advantage that only the beads which are required for
showing numbers are seen by the observer. The rest are hidden by the separating board.
Another type of the abacus as described by Cockcraft is the spike abacus. This is
made by sticking wires to a common wooden base. A spike of the abacus is made to
hold only nine beads or cubes. If it is desired to show the number ten on a spike, this is
done by threading only one cube on the wire to the number which is threaded to a cube
or bead on the wire immediately to the right. This also can be use to teach the idea of
place value.
Methods of Teaching Mathematics
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’.
According to Phil Bookman in a closing address at ATM conference on the
theme “believe in seeing” accepts that teaching is not mere passing of information to
learner’s but it is a process of accelerating learning. This indeed attest to the fact that a
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.
Pimm (1987) came out with the rich view that mathematics “is a language in the
metaphoric sense, since written mathematics is read aloud, it emerges as spoken English
13
with a developed register that can be transformed into natural language”. 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 Ansubel (1968), it is appropriate to note that, the
most important single factor influencing learning is what the learners already know.
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
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.
Kalejaiye (1985) stated that selecting a method or combination of methods with
appropriate teaching aids, the teacher can help pupils to learn mathematics easily and
successfully. He continues to explain that methods such as discovery, questionnaire,
grouping, individual approaches are very useful methods of teaching mathematics, but in
his case, he concentrated on discovery method of teaching. He said, “Discovery method
14
is the most useful method of teaching mathematics”. According to him, ‘success breeds
successes’.
Explaining that, 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.
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.
Ruth Habbard (1991) and the great psychologist Jerome Brunner advocated for
the question method of teaching mathematics. They observed that, it is easier for people
to fall asleep while reading or listening rather than speaking or writing. 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
15
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.
Edith Biggs (1985) also stated that, “the choice of a teaching method depends on
so many factors such as the level of the class, the ability of the pupils, the nature of the
mathematics topic and the facilities available in the school”. She continued by saying
that ‘many teachers prefer to teach the class as a whole all the time’. The approach often
may not yield the desired educated results, since weak pupils do not profit much being
taught in a large class of mixed abilities. Edith suggested that teachers should divide the
class into groups of five or six of about the same ability and teach them in groups. The
class may be taught together for part of the lesson before pupils settle into their groups
for further work and practice exercise. This procedure will enable the teacher to attend to
the weak groups and also give the more able groups more challenging work.
The Role of the Teacher in Mathematics Teaching
Most teachers fail to prepare lesson plan or notes because they see it to be a
waste of time. It is on this note that Mike Askew (1995) stated that, “it is the teacher’s
duty to prepare a detailed lesson plan”. He emphasized that 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 of the context in which
they are to do it. It should contain only one verb which tells what pupils will do.
16
According to Askew, some teachers fail to define clearly pupils’ behaviour after the
lesson so that, it does not lead to misinterpretation. In addition, teachers should make the
content of an instructional objective specific and must convey a uniform meaning to
teachers in the same subject discipline. 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.
Skemp (1989) also stated that, “Practices given to pupils enhance their
understanding in mathematics”. He said, teachers must give more practical exercises to
pupils. He continued that teachers should teach pupils with much practice on the concept
that has been acquired, they will then understand, retain and be able to recall. 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. Margaret
17
Brown made these observations and said that some teachers find it tedious in going
through pupils mistakes with them. They just mark the exercises and go their way.
Margaret Brown (1985) said “pupils make mistakes in working out problems
which are given them either as class working out problems or home work”. 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 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.
Margaret Brown added that teachers’ should not cultivate 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.
Lorraine Mottershead (1977) said, “Teachers important role is to help pupils
understand lesson taught by collecting instructional materials relevant to the topic to be
taught”. Instructional materials arouse and sustain pupils’ interest during teaching, thus
making their foundation very solid and permanent.
18
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 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.
19
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.
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.
20
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 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
21
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.
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
22
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.
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
23
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
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.
24
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
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
25
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 = 638.
2
6
3
7
2
5
13
8
262
6
Hundreds
Tens
Ones
Hundreds
Tens
Ones
376
(5 + 1)
3
8
6
3
8
26
Tens
Ones
376 + 262 = 638
Hundreds
Ones
Tens
Hundreds
Rename
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
(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.
27
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.
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
Sex Distribution of Respondents
No. of Respondents
Percentage (%)
Males
12
60
Female
s
8
40
20
100
Total
28
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
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
Occupation of the Respondents
No. of Respondents
Percentage (%)
10
30
Nurses
2
10
Students
3
15
Farmers
9
45
20
100
Teachers
Total
29
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
15
M.S.L.C
5
25
20
100
Total
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.
30
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
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.
31
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
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
32
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.
Respondents view on pupil’s performance in mathematics.
Table 8
Level
No. of Respondents
Percentage (%)
Very good
0
0
Good
4
20
Weak
10
50
6
30
20
100
Very weak
Total
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.
33
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.
Table 10
Respondents view on whether parents support children to study
mathematics at home.
Response
No. of Respondents
Percentage (%)
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.
34
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
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,
35
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.
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.
37
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.
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
38
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.
There should be more periods on the time table for mathematics lessons in the
primary schools.
39
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
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
40
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:………………………………………………………………
Class Handling:………………………...
Occupation:………………………………
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?
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.
41
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
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
42