CHAPTER ONE
INTRODUCTION
This chapter deals with the introduction, background to the study, statement of the
problem, purpose of the study, significance of the study, research questions, delimitation,
limitations and the organization of the study.
Background to the Study
Mathematics as a subject in Ghanaian education syllabus serves many purposes.
It forms the basis of all other subjects and professions. Some are Mechanical Engineering,
Civils, Electrical Engineering, Statistics, Economics, Pharmaceutical, Medicine and other
related jobs or professions. Mathematics is part of the core subjects in the syllabus of
Ghana Education Service.
However, most parents see their children’s education as an investment and as such
the outcome of their children after school may determine their position or status in future.
Djotan (2005), a developmental psychologist suggests that, “learning must begin
from the application of child’s actual experiences”. He continues that, “Learning a new
mathematical concept such as addition must involve working with several models of such
concept such as abacus, multi base blocks and so on.
Piaget (1961), a developmental psychologist in his theory of “stages of
development explains that, “……….. at this stage, children between the ages six and
twelve begins the development of logical system of thought, they cannot use more than
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one operation to solve complex task given them. They begin to put things into groups or
classes and are able to perform more mental activities or actions.”
This view from Piaget clearly shows that, when concrete models are used, they
create mental picture in the minds of the children and promote their understanding in the
concept and make them effective participants in the lesson. As a result, it makes teachers
use concrete materials in their teaching instead of teaching in abstract. It therefore
provides confirmation in relation to the two theories of the psychologists that, when
concrete models such as abacus, multi base block and semi concrete materials are used in
mathematics lessons, children will understand the lesson better and take active part in the
lesson.
It is highly unfortunate that when the researcher started her out-segment
programme of Diploma in Basic Education course at Tafi Agome E.P. primary school.
The primary four pupils could hardly add three-digit numbers correctly. Tafi Agome is
found in the Afadjato South District 20km from Ve-Golokwati district capital. Some of
the nearby communities include Tafi Abuife, Tafi Mador etc.
The population of Tafi Agome as at September 2014 stands about eight hundred
(800) people. The people of Tafi Agome are mostly farmers. They cultivate crops such
as cassava, plantain and maize. Apart from farming, others also engage in trading.
This has resulted in making parents so busy that, they do not pay attention to their
children education.
Some parents also involved their children to assist them in their occupations and
sometimes ask them to stop schooling hence people find it difficult to attend school
regularly and also affect them to understand what they have learnt. This leads primary
2
four (4) pupils at Tafi Agome E.P. primary school to find it difficult to add three-digit
numbers correctly. These situations have prompted the researcher to embark on this study
to help reduce the seriousness of the problem.
Statement of the Problem
The problem understudy was improving the understanding of addition of threedigit numbers among class four pupils of Tafi Agome E.P primary school. This problem
was identified through class exercises, class activities, home works and evaluation.
These problems were attributed to the fact that, their teachers used “teacher
centered approach” to teach and hardly not involved the pupils in their lessons. Again,
the teacher neglected the use of teaching and learning materials (TLMs) such as abacus,
multi base blocks and place value chart in teaching of addition.
A good activity based method and appropriate use of TLMs such as multi base
blocks, abacus and place value chart may help to address the problem.
Below is a statistics of results of pupils who took mathematics promotion
examination for five consecutive years.
YEAR
TOTAL
NO. OF
PUPILS
NO. OF
PUPILS
WHO
PASSED
PERCENTAGE
PASSED (%)
NO. OF
PUPILS
WHO
FAILED
PERCENTAGE
FAILED (%)
2002/03
2003/04
55
49
20
16
36.6
32.65
35
33
63.64
67.34
2004/05
52
16
30.76
36
69.23
2005/06
54
15
27.78
39
72.22
2006/07
56
14
25.00
42
75.00
SOURCE: Tafi Agome E.P primary school. Tafi Agome.
3
The statistics above showed that the failure rate of mathematics was high every
year among basic four pupils of Tafi Agome E.P primary school, Tafi Agome.
It was in this connection that the researcher thought it is wise to find out the
relative effect of using multi base block, abacus to improve upon the academic
performance of basic four pupils in mathematics.
Purpose of the Study
The researcher’s main concern was to work with other teachers and pupils to
create good learning conditions in the classroom to enable pupils to acquire the basic
mathematics operations (addition, subtraction, division and multiplication). Four
objectives guided the study. They were to determine:
1. The causes of Basic Four (4) pupils’ inability to add three-digit numbers correctly.
2. An intervention strategies to help pupils improve upon their performance such as
child centered approach.
3. The effectiveness of their intervention.
4. The strategic intervention to help improve pupils’ problem in addition.
Significance of the Study
The study will benefit pupils of Tafi Agome E.P. primary school. This is because,
it will equip them to understand the concept of adding numbers using abacus, multi base
blocks and place value chart and applied the knowledge gained
4
Teachers would also benefit from the study because the study will emphasize on
varying teaching methods. When adopted would ensure effective teaching and learning
process.
Parents would also benefit from this study because it will help them access the
performance of their kids. It will also motivate parents to buy the necessary materials like
exercise books, pen, pencil etc. to their kids that will enhance their performance in study.
Research questions
The following questions were addressed by the study;
1. What are the factors that accounted for pupils’ inability to add three-digit
numbers?
2. How best would the use of multi base blocks, abacus and place value chart
improve pupils’ ability to add three-digit numbers correctly?
3. What teaching strategy would be appropriate to improve pupils’ ability to add
numbers among basic four (4) pupils?
Delimitations
The study was conducted at Tafi Agome E.P primary school in the Afadjato south
district of Volta Region, Ghana. Though the study would benefit other pupils, the study
was restricted to only Basic Four (4) pupils of Tafi Agome. This was to make data
collection easier and also to promote effective participation of pupils in the lesson.
5
Limitations
Though the study was limited to Basic Four pupils the study was impeded by
several factors. Most of the pupils interviewed could not express themselves orally and
fluently about the problem understudy.
Also, some of the pupils were not present on the days the intervention was carried
out and this badly affected the study. The researcher had wanted to extend the study to
some classes like Basic 2 and Basic 3 but due to time constraints, she could not but had
to depend only on Basic Four (4) pupils of the school.
Organisation of the Study
This research was organized in five chapters. The first chapter deals with the
background to the study, the statement of the problem, purpose of the study, significance
of the study, the research questions, delimitation, limitations and organisation of the
study.
Chapter two provides a detailed study into the topic and other related issues as expressed
by other writers. The third chapter was the methodology, which concentrated on the
research design, population, sample and sampling techniques used, instruments,
intervention processes and data analysis plan have all been considered.
The fourth chapter was about the researcher’s analysis of the data obtained from the study.
The fifth chapter which is the last of the chapters dealt with the summary, conclusions
and recommendations made by the researcher for future research.
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CHAPTER TWO
REVIEW OF RELATED LITERATURE
This chapter deals with related ideas expressed by other writers on the area of
study. It also finds answers to the research question raised in the first chapter such as the
reasons for pupils’ inability to add three-digit numbers correctly among Basic Four pupils.
It also touches on the use of abacus and multi base blocks as teaching and learning
materials in addition to three-digit numbers and their importance as stated by other
writers.
The following areas will be focused:
1. What is mathematics?
2. The definition of addition.
3. Causes of pupils inability to add three-digit numbers correctly.
4. What are multi-base blocks?
5. Abacus as a teaching material.
6. The importance of an abacus.
7. The pace value chart as a teaching and learning material.
8. Summary of Literature Review.
What is Mathematics?
Wikipedia (2008), the free web encyclopedia defined mathematics as, “The body
of knowledge centered on such concept as quantity, structure, space and change and also
the academic discipline that studies them.”
7
Pierce (2008) identified mathematics as, “The science that draws the necessary
conclusions”. With this some schools of thought maintained that it seeks out pattern
whether found in numbers, space, science, computers, imaginary abstraction or
elsewhere.
The Definition of Addition
Wounda (2003) defined addition as, “The arithmetic operation of finding the sum
of two or more numbers. The symbol of addition is (+) and it is read as “plus”. The
numbers to be added are called “addends”.
Wikipedia (2008) a free web encyclopedia also stated that, “Addition is a
mathematical operation that represents combining of objects together into a larger group.
It is signified by the plus sign (+).
Streeter et al (1998), see addition as combining two or more objects or group of
the same kind.”
The fifth edition of the Advanced Learners Dictionary (1995), defines addition as,
“The action or skill of adding two or more numbers to find a total.”
Again, the world book encyclopedia (1992), defines addition as, “A way of putting
together two or more numbers of the same kind to find out the total or how many are there
all together”.
Moreover, Longman Dictionary of Contemporary English (1995) defines the
concept of addition as “A process of adding numbers or amounts to find out a total.”
8
The Oxford Students Dictionary (200) also defines addition as, “A person or thing
being added or joined together”.
Considering the explanations given to addition above by these writers, one can
obviously think of addition, as an arithmetic operation for finding the total of two or more
objects. In a more advanced level in mathematics, variables (technical mathematical
quantity which can represent several different amount). Equal variables when used to
represent numbers can be added together to form a sum, but unequal variable when added
together cannot form a sum. For example a + a = 2a and b + a.
Because (a) and (b) are not variables of the same kind, they could not be added
together to find a total but (a + a) gives out the sum of (2a) because they are alike and can
be put together to find a total.
In the concept of addition, there are two signs involved. These are plus (+) and
equal to (=). “Plus” means to add the quantities involved together and the “equal to” sign
means that, total number on one side of the equal sign is the same as total number on the
other side of the sign.
Causes of Pupils Inability to Add Three-Digit Numbers Correctly
Dr. Flegg (2003), expresses the view that, “The use of ‘cumbersome’ teaching
technique can be considered as a major contributing to the poor performance in addition
algorithms.
This is because the technique might end up setting confusion among the pupils.
Unsuitable vocabulary and teacher’s ability to present lessons logically to learners causes
pupils or learners to have problem with the concept understudy. Therefore the pupils’ in
9
Basic 4 inability to add three-digit numbers correctly could be attributed to such kind of
teaching technique since they are not matured enough and any teaching technique of that
sort will not help them.
Again, lack of teaching and learning materials or inadequate teaching and learning
materials can greatly contribute to this problem understudy. However, if lessons in such
class should be activity based, this come as a result of the use of the manipulative
materials. Inadequate use of teaching and learning materials ceases to make the lesson
activity based can also cause this problem of addition of three-digit numbers.
Kalijaye (2002) is also of the view that, teaching and learning materials should be
used to facilitate easy understanding when teaching new mathematical concepts. Because
they help to illustrate mathematical relationships, which facilitate the understanding of
basic concept by creating mental actions in the minds of pupils which makes it easier to
recollect the ideas taught.
For example, using bottle tops, pebbles and match sticks in teaching addition of
numbers, it becomes easy for the pupils to understand the concept because in the absence
of the teacher, the child can work it out by himself or herself with those materials.
However, it makes it factual that, the absence of teaching and learning materials can be a
contributing factor to the problem understudy.
Therefore, teachers in trying to avoid this problem of the difficulty in adding of
numbers should use appropriate models such as abacus and multi-base block in teaching
the pupils.
Reys et al (1998) point out that, developing algorithms that work with multi-digit
numbers has to start from pupils understanding of place value chart. A thorough
10
understanding of place value chart therefore becomes necessary in the learning of the
algorithms of addition, subtraction, multiplication and division in a more meaningful way.
In relating this to the problem understudy, it becomes necessary that the pupils had no
idea of place value chart which makes it possible for the pupils in Basic 4 to develop the
concept of addition.
Reys et al (1998) used manipulative materials such as multi-base block, place
value chart and abacus. He pointed that the materials were very essential in developing
the understanding of algorithm theories making the lesson an activity based.
What Are Multi-Base Blocks?
Mathematics for Teachers Training Colleges in Ghana (1994) noted that, “Multibase blocks sometimes called the Dienes Blocks or Tillich Blocks consist of small cubes,
rods, flat squares and large cubes”. These materials are used in teaching mathematics
algorithms such as addition, subtraction, multiplication and division.
Abacus as a Teaching Material
Martins et al (2006) stated that, an abacus involves several beads threaded on a
line or spike. Each line takes a maximum of nine beads representing various units. The
abacus does not represent numbers structurally as other materials do.
Kalijaye (2002), described an abacus as a device for teaching counting the idea of
place value chart and the basic operation of addition of whole numbers. An abacus
involves straight lines or rods or spikes fasten to a common base. Cubes or beads with a
11
whole in the middle are put on the spikes represent different numbers. A spike or line
takes a maximum of nine beads.
Moreover, the World Book Encyclopedia describes an abacus as a device for
performing arithmetic problems. It can be used to add, subtract, multiply, divide and to
calculate the square roots of numbers and the cubes. The lines or spikes on the abacus
which usually appear as thread are labelled from the right as ones, tens, hundreds,
thousands and so on to the left.
The ones column represents numbers, one to nine (1-9), the tens spikes represent
numbers one hundred and ninety-nine (100-199) and so on.
Lastly, Wounda (2003) stated that, an abacus is a mechanical aid for counting
though it is not a calculator. The abacus is constructed with hard woods and appears in
various sizes. The frame of an abacus consist of series of vertical rods (spikes) on which
a number of beads are allowed to slide freely.
The Importance of an Abacus
Wounda (2003) stated that, in China and Asia, the abacus is used to settle accounts
by shopkeepers.
Rey et al (1998), also stated that, the abacus is used for teaching addition,
subtraction, multiplication and algorithm form. The World Book Encyclopedia also
expressed that, the abacus is used for finding the square and cube roots of numbers. Again,
it is used for teaching the concept of place value chart.
12
Lastly, in the school of the blind, it is used as a teaching and for mathematics. The
diagram below shows the spike abacus represents the number two thousand, four hundred
and forty-six.
SPIKE
BEAD
BASE
AN ABACUS
THE PLACE VALUE CHART AS A TEACHING AND LEARNING
MATERIAL
Donkor et al (2005) and Wounda (2003) present the place value chart as shown
below;
Thousand
Hundreds
Tens
Ones
4000
2000
30
6
3000
100
20
1
They explained that the place value chart present numbers with respect to their
values as shown above. The table has four thousand, two hundred and thirty-six as the
first number and the second number is three thousand, one hundred and twenty-one.
The primary school mathematics syllabus embarks on the use of the place value
chart in teaching the algorithms of addition. The chart therefore becomes very essential
13
in teaching the concept of place value chart among children at the early stages for it clearly
shows the value of numbers on the table.
Summary of the literature review
In this chapter, the researcher discusses some various definitions of addition as
given by other writers of such as Wound a (2003), Streeter et al (1998), Oxford, Advanced
Learners Dictionary (1995) were also mentioned.
Furthermore, multi-base block as a teaching and learning material has been added
to the review.
Also, the causes of pupils’ inability to add three-digit numbers correctly with
reference to Flegg (2003), Kalijaye (2002) and Reys et al (1998) were discussed.
Not all, abacus as a teaching and learning material and its importance with
recognition to other writers such as Wounda (2003), Rey et al and so on have been written
down.
Lastly, the use of place value chart as a teaching and learning material has also
been discussed in this chapter.
14
CHAPTER THREE
METHODOLOGY
Introduction
In this chapter, the methods and procedures used by the researcher in carrying out
the study have been dealt with. Also, the chapter describes the research design for which
the researcher used in her study. The population, sample selection, research instrument,
data collection procedure and data analysis.
Research Design
This research work was designed under the action research design. The action
research design aims at finding out a solution to a particular situation. The researcher
perceives a problem and finds ways of improving the situation or problem perceived. The
problem could be a classroom situation like reading, handwriting, subtraction, addition,
etc.
Action research requires a situation to a particular classroom or school related
problem. And since this research work is based on improving a concept of addition in
mathematics which is solely a problem in a typical classroom or learning environment, it
is considered as such.
Population
Population is the number of people living in any defined area at a particular time.
It also refers to the universal set of an element under consideration.
15
In research, population refers to the establishment of boundary which specify who
shall be included in or extended from the population. The targeted population consisted
of twenty-six (26) pupils of class four children of Tafi Agome E.P. primary school.
Sample Selection
The researcher observed the class and took particular notice of the pupils who
hardly not got most of their oral responses to question right and were inactive, unwilling
to answer questions in class even when they have been called to do so.
When references were made to their mathematics exercise books; it was
discovered that, they had attained low marks in their exercises. When a test was conducted
on addition they could not answer them correctly.
The sample was made up of 10 boys and 10 girls. This was to enhance easy data
collection and also to enable the researcher to find out how pupils with such difficulties
could be helped with regard to appropriate teaching and learning materials such as abacus,
multi base blocks and place value chart to be used.
Research Instruments
The instruments used include interviews, test and observation.
Observation
This was one of the tools used to collect information according to Collins
Electronic Dictionary for Advance Learners is an action or process of carefully watching
someone or something naturally in order to learn more about it. According to the Wiki
16
answers, an internet definition, observation means the use of your five (5) senses and the
ability to ask questions and answer them. Wikipedia free internet encyclopedia define
observation as “the actions or process of observing something or someone carefully to
gain information.”
The researcher took time to observe pupils involvement in the classroom
discussion and how they presented their ideas in class. The instrument mad it possible for
the researcher to gather information about pupils abilities. It was observed that most
pupils did not take part in home work being given to them because most of the students
help their parents in selling.
Interview
According to the Cambridge International Dictionary of English “An interview is
a way or means of asking a person a series of question in formal situation usually, in order
to obtain information about them”.
Wikipedia, Free Encyclopedia defined interview as “a meeting of people face to
face especially for consultation” a formal meeting in person, especially one arranged for
the assessment of the qualification of an applicant.
In such situation, there are two parties involved, the interviewer and the
interviewee with the former (interviewer) and the later, the one who expected to provide
answers to questions (interviewee). The researcher used this instrument to acquire
information from the students. Interview was used to identify pupils’ problems and how
best it could be improved. The interview were also used to discover the real factors that
were responsible for the pupils inability to add three-digit numbers correctly and design
an appropriate intervention to meet them. During the interview, most students complained
17
about the fact that parents failed to provide the necessary things like exercise books, pens,
etc. These resulted in their reducing interest in school. Concerning interview with parents
it was confirmed that most of them are farmers and traders as well as single parent. In this
instance, they earn low income, which cannot provide for their basic necessities and their
wards in school.
Test
A test is an examination or trial questions to evaluate students or a class. It is a
means used to determine the quality, content, etc. of something. In our school setting, test
is organized as the name depicts to check students level of performance. The researcher
decided to use the test so as to ascertain the true predicaments of her pupils. The
researcher, in using this instrument to gather data on pupils’ inability to add three digit
numbers correctly. The researcher called on pupils randomly to solve addition of threedigit numbers on the chalkboard. The researcher sometimes gives exercise based on
addition of three-digit numbers for them to solve it. During the test, the researcher found
out that most pupils were scoring low marks because most of the students were not taking
the exercise seriously when it was given to them.
Pre-Interventions
For the researcher to get to the root of the problem, she decided to give a set of
questions to the pupils to answer. She then recorded the marks they scored taking into
account individual errors and ways of answering questions. This was for the researcher
to be provided with reliable and authentic information as to what should be done to solve
the perceived problem.
18
Intervention
The researcher used three weeks throughout the intervention period. In the first
week, the researcher demonstrate how to guide pupils to play an exchange game in base
nine (9) using the multi base block.
The size chosen for the game was nine (9). The game was such that anyone who
get the chosen size (that is nine (9) cubes) wins the game.
Two dice were used in the game. The game was played individually and was
played in turns. For example, if a pupil throws a dice and four (4) shows up, it will be
represented by four (4) shows up, it will be represented by four (4) cubes.
In the second week, the game was played in base ten (10). So the one who gets
the ten (10) will exchange it for a rod. It was played individually. The player who gets
the chosen size (10) will be given a rod which represents ten cubes.
In the third week, it was played in hundreds. The chosen size was hundred. The
player who gets the chosen size will be given a flat (10 rods or 100 cubes). This is
illustrated in the diagram in a week.
19
CIBES
FLAT
ROD
Multi Base Block
Multi base black sometimes called Dienes block or Tillich block consist of a
number of small cubes, rods, flat squares and large cubes (flat) as shown above.
10 cubes = 1 rod
10 rods = 1 flat
The researcher obtained a wood from a carpenters shop. He cut the wood into
cubed, rods and flat. In using the multi base blocks, pupils were guided to count small
cubes. If the figure exceeded nine cubes then pupils replaced it with a rod. For example,
ten (10) cubes will be replaced with one rod (1 rod). If the figure exceeded ninety-nine
(99), they will exchange the nine rods and nine cubes with a flat.
20
Example 344 + 436 = ?. The pupils took three (3) flats, four (4) rods and four (4) cubes
to represent 344 and four (4) flats, three (3) rods and six (6) cubes to represent 436. They
were asked to put them together to obtain seven (7) flats, seven (7) rods and ten (10)
cubes. The ten cubes were changed for a rod to obtained seven (7) flats and eight (8) rods.
There were no cubes.
This was represented by 780. The activity has been illustrated using the number tray.
344
+ 436
Example:
780
Flats
Rods
Cubes
+
+
+
3
4
4
3
7
7
7
7
7
8
4
6
10
1
0
21
The Dienes Multi Base Blocks
In the description the researcher worked together with the pupils as they collected
cubes and joined them together with other cubes to find the sum after teaching them.
The concept of how to use the multi base blocks by way of exchange games. The
researcher used game to help the pupils find figures. During the three weeks, the pupils
used cubes in the first week but in the second week, they were exchanging cubes more
than ten (10) for rods and rods for flat in the third week.
Post-Intervention and Data Collection Analysis
After the researcher had carried out the intervention, she gave another set of
questions to the pupils to answer. This was to evaluate how effective the intervention had
been or how best her teaching and learning and the method used had worked for her and
the pupils.
She had also wanted to know how best the pupils have developed a rational
understanding of addition of three-digit numbers. The results of the post intervention
exercise proved the success of the interventions.
Data Analysis Plans
The researcher used tables and percentages. The mean used by the researcher to
enable her finds out how the average performance of the pupils were in both the pre-
22
intervention and post-intervention stages. It was also to make a comparative analysis on
how best the performance of the pupils had improved.
The percentages were also used to find out the factors that accounted for the pupils
difficulties as well as to enable her assess the level of improvement after the intervention
was used.
23
CHAPTER FOUR
RESULTS, AND DISCUSSIONS
This chapter gives a detailed data collected on the pupils of Tafi Agome E.P.
primary four (4). The researcher represented the data in table form.
Table 1
The causes of the difficulty of addition of three-digit numbers to pupils.
Reasons
Number of respondent
Percentages
Lack of interest
10
33.333
Refusal to use TLMs
10
33.333
The use of L2 frequently
10
33.333
Total
30
100
The table above clearly shows that, out of thirty (30) pupils interviewed ten (10)
pupils representing 33.333 percent expressed their dislike for the subject which has gone
a long way to affect their output or performance in the subject. The researcher then got to
know that it is a major contributing factor that has accounted for their inability to add
three-digit numbers correctly. She therefore brought up an intervention in the form of
Diene’s multi based block.
The Diene’s multi base block is to be learn with so that it helps the pupils to derive
interest in the subject and learn it on their own when their teacher is not available. This
proved successful at the end of the post test.
Refusal to use teaching-learning materials by their teacher in mathematics lesson
also has contributed to this problem understudy. According to ten of the thirty pupils
24
sampled representing 33.333%. Based on this reason, the researcher realized that the
Diene’s multi base block or material will be of help and also make the lesson activity
based which will involve the pupils to work them out themselves even in the absence of
the subject teacher. This practice enhanced the understanding of the pupils to gain the
concept of addition meaningfully.
Ten (10) of the pupils sampled also related to the problem to the use of English
Language fluently by the teacher who was teaching mathematics lesson. Because the
teacher was not from the Ewe tribe but was just brought up from the Ashanti Region and
was an Akan. She has the difficulty in speaking the local dialet of the pupils (Ewe) in
explaining concept in mathematics to pupils. Due to this, they could not hardly respond
to the various questions being posed by the teacher on the problem.
Table 2: Is the subject Mathematics difficult?
Response
Male
Female
Total
Percentage (%)
Yes
8
12
20
66.6667
No
7
3
10
33.333
Total
15
15
30
100
It can be seen from the table 2 that, seven (7) males and three (3) females representing
33.333% denied the fact that mathematics is not a difficult subject.
On the other hand, eight (8) males and twelve (12) females representing 66.6667%
accepted that mathematics is a difficult subject. They proceeded by telling the researcher
25
that they had been told that mathematics is a difficult subject and even if you study it or
not you will still find difficulties in solving mathematical sentences.
Because of what they had been told, they had also developed the same negative
attitude towards the subject and therefore had no interest in studying it. This has therefore
contributed to their low achievement in mathematics.
Table 3: Do your parents or guardians assist you in studying mathematics at home?
Response
Male
Female
Total
Percentage (%)
Yes
8
7
15
50
No
7
8
15
50
Total
15
15
30
100
Table 3 above depicts that fifteen (15) pupils representing 50% do not get
assistance when studying mathematics at home. This stems from the fact that, some
parents are illiterate and therefore had little knowledge about the subject. These parents
(50%) had cultivated negative attitude towards education and for that matter, told their
wards that whether school or not, they will still come back to the farming sector. This had
made the learning or studying of the topic not understanding and hence scoring low marks
in mathematics.
26
Table 4: Do you study mathematics at home?
Response
Male
Female
Total
Percentage (%)
Yes
3
7
10
33.333
No
12
8
20
66.667
Total
15
15
30
100
From the table 4 above, it can be seen that three (3) males and seven (7) females
representing 33.333% accepted the fact that, they become tired whenever they come back
from farm since their parents are predominantly subsistence farmers. Most of the pupils
also revealed to the researcher that they rely solely on tourchlight. That single tourchlight
is used in the kitchen hall and if the time comes for them to study, the tourchlight may be
engaged somewhere i.e. in the kitchen. These poor lighting system go a long way to affect
them adversely and hence low performance in the topic understudy.
27
Table 5:
The table below shows the marks scored by thirty (30) pupils in the pre-test. In the test,
pupils were given letters of the alphabet in place of their names.
Pre-test score
Names of pupils Scored out of ten (10)
Number of pupils
Percentage (%)
A
2
4
13.333
B
4
3
10
C
1
3
10
D
5
4
13.333
E
3
4
13.333
F
6
4
13.333
G
4
4
13.333
H
3
4
13.333
Total
28
30
100
From the above table, we can deduce that, pupils were scoring low marks only
four (4) out of the thirty (30) scored six (6). This clearly showed the seriousness of the
pupils inability to add three digit numbers at which their solutions where presented.
After the intervention exercise post intervention test was conducted and the
following scores were recorded on the post-test as shown in the table below.
28
Table 6:
Post-Intervention scores
Names of pupils
Scores out of ten (10)
Number of pupils
Percentage (%)
A
8
4
13.333
B
7
3
10
C
8
3
10
D
7
4
13.333
E
9
4
13.333
F
9
4
13.333
G
8
4
13.333
H
9
4
13.333
Total
65
30
100
Average mean score =
scores out of 10
number of pupils
65
30
= 2.166
From the post-intervention test table above the average mean score was 2.1666. This
makes it explicit that there has been a tremendous improvement in the performance of the
pupils in adding three-digit numbers. Pupils have leant to carry out writing raw sums.
This in general brings to minds that the instrument used by the researcher have proved
useful in data collection from pupils.
29
The use of observation as an instrument in the project work report enabled the
researcher at some level to identify pupils who had problem in adding three-digit
numbers.
Interview also helped the researcher to have a clear knowledge on what had really
constituted the existence of the problem. Again, the interviews conducted gave the
researcher a clear cut overview of the problem and the appropriate intervention to be used.
After the use of the first two instruments that is observation and interview, the
researcher used test to identify the seriousness of the problem. The use of the interventions
were useful in the sense that, they helped the pupils to understand the whole concept of
Diene’s multi-base material and has improved pupils ability to add three-digit numbers
correctly.
The use of teaching and learning materials and the teacher-learner activities
designed for the pupils at the intervention stage, helped the pupils to understand the
concept of Diene’s multi-base materials, equipping the pupils with the ability to add threedigit numbers correctly. It also promotes the pupils interest in the subject as well. In this
case, it was identified that all the aspects of the problem understudy were addressed.
Table 7:
The table below highlights on the average score of the pre-test and post-test addressing
the level of improvement after the intervention was used.
Pre-test
Post-test
Average mean score of pre-test
Average mean score of post-test
0.9333o
2.1666o
30
As the overview of table 7, a tremendous improvement in the ability of pupils to add
three-digit numbers had been achieved since the average score in the pre-test which was
0.9333o being increased to 2.166o after the post-test.
Research Questions
(a) How would the Diene’s multi-base block be used to improve upon the performance
of the pupils in Tafi Agome E.P primary four in addition of three-digit numbers?
The Diene’s multi-base block can be used by:
i.
Guiding pupils to understand what the Diene’s multi-base block material is
about or represent.
10 cubes = 1 rod
10 rods = 1 flat
ii.
Guiding pupils to use Diene’s multi-base block when teaching addition of
three-digit numbers.
(b) What effects will the Diene’s multi-base block material have on the learning ability
of the pupils in Tafi Agome E.P. primary Four?
i.
The Diene’s multi-base block material will help the pupils to understand the
addition of three-digit numbers correctly when it is been taught.
ii.
It will also help the pupils to like mathematics especially addition.
(c) What is addition of three-digit numbers?
Addition of three-digit number is summing up of the three digit numbers to get a total.
Summary
A careful look at the first table shows the causes of difficulty in adding three-digit
numbers. A lot of teaching and learning materials were used in the intervention stage
31
to eliminate the problem. The post-test stage showed the performance over the pretest after the intervention.
Again one say certainly that, the problem of solving addition of three-digit
numbers has been reduced if not totally eradicated.
32
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
This chapter gives the summary of the whole project work. It also contains the
researcher’s conclusion of the project work and some recommendations.
Summary
The study was designed in order to help pupils overcome the problem of solving
addition of three-digit numbers at Tafi Agome E.P. primary four (4). An interview and
test were conducted to find out pupils knowledge of addition of three-digit numbers.
A pre-test and post-test were conducted. Diene’s multi-base block materials were
used to overcome pupils’ difficulty in solving three-digit numbers.
There was massive improvement in pupils’ performance after the use of the Diene’s
multi-base block materials. There was a tremendous improvement in the ability of
respondents to add three-digit numbers had been achieved since the average mean score
in the pre-test which was 0.9333 being increased to 2.167 after the post-test.
On the whole, pupils performance had increased tremendously after the
intervention. It can be concluded that, use of Dienes’ multi base materials is one of the
best teaching and learning materials to use in improving pupils performance in solving
addition of three-digit numbers.
Again, the researcher advised teachers to use child-centered approach when
teaching addition of three-digit numbers and this will help pupils to understand it well.
33
Parents were also advised to buy the necessary items such as books, pens, pencils
etc. for their wards to enable them to come to school everyday and also monitor them at
home to learn.
Conclusion
In conclusion, pupils’ inability to find solution in solving addition of three-digit
numbers had improved. The use of the Diene’s ways to help pupils performance in solving
questions related to addition of three-digit numbers.
However, it could be deduced that pupils’ performance was greatly enhance after
the use of the Diene’s multi-base materials.
It is an emphatic truth that when Teaching and Learning Materials (TLMs) such
as Diene’s multi-base block materials are used in the teaching of addition of three-digit
numbers, there is easy understanding of the concept and also makes lessons interesting.
Again, the appropriate instructional methods for teaching were not used by most
teachers. Some methods were more teacher-centered than child-centered method. This is
because when the child-centered approach was used in teaching of addition of three-digit
numbers, the pupils were fully participating in the lesson and also getting the
understanding of the concept.
34
Recommendation
As a result from the findings, it was important to make the following
recommendations.
Firstly, there should be the introduction of school based in-service education for
the teachers in the school to be abreast with new skills of teaching especially preparation
of instructional materials.
Head teachers should provide funds for the purchase of teaching and learning
materials.
Teachers should allow pupils to carry out activities on their own to arouse and
sustain their interest. The researcher is appealing to parents to invest in their wards
education by buying them materials such as exercise books, pens, pencils etc.
This could be discussed during Parent-Teacher Association meetings (P.T.A.).
35
REFERENCES
Asafo-Adjei R., (2002). Teaching Basic Mathematics. Kwame Nkrumah University of
Science and Technology press; Kumasi, Ghana.
Basic Education Certificate Examination (B.E.C.E.) (2006). Chief Examiner’s report on
mathematics for Junior High School, Accra, Ghana.
Brunkhorst, B.J, (1996) World Book Encyclopedia, London.
Brunner, J., (1996). Towards a theory of instruction. Harvard University press, New York.
Desforges A. and Cochburn A.D., (1987). Understanding the mathematics teacher: a
study practice in the first school. University of East Anglia (U and A). Flammer
press, British.
Donkor, C.J. (2005). Primary mathematics, pupils book four (4). Unimax Macmillan
Accra, Ghana.
Gelman H. and Gallistel, F., (1978). Numerical system and childrens concept of numbers.
Harvard University Press. Cambridge.
Martin, J.L, (1994). Mathematics for Teacher Training in Ghana. Accra
Ministry of Education (M.O.E) report in Daily Graphic 27th January 2007.
Past H., (1976). Style and Strategies of Learning. British journal of Education
psychology, 2(64), 78-88.
Piaget J and Diene’s G. (1959). The growth of mathematical concept in children through
experience. University of Chicago press. Neuchâtel. Switzerland.
Reys E.R., (1998). Helping children learn mathematics. McGraw Hill. London.
36
Streeter A.J., (1998). Mathematics skills with geometry.
Wheatley N. and Wheatley D., (1979). Developing spatial ability mathematics in school.
University of Chicago press. Neuchâtel. Switzerland.
Wikipedia, (2003). http//:www.wikipedia.com
Wounda P., (2003). Teaching Basic mathematics. Longman Group. Limited.
37
APPENDICES
Appendix A
Interview guide for basic four pupils.
1. Do you study mathematics at home?
a. Yes [
]
b. No
[
]
2. Do your parents assist you to learn mathematics at home?
a. Yes [
]
b. No
[
]
3. Do you help your parents in the farm after school?
a. Yes [
]
b. No
[
38
]
Appendix B
Questionnaire for teachers
1. Do you have any copy of mathematics syllabus in your school?
a. Yes
[
]
b. No
[
]
2. Do you regularly attend mathematics workshops?
a. Yes
[
]
b. No
[
]
3. Do you use appropriate methods during mathematics (addition lesson)?
a. Yes
[
]
b. No
[
]
[
]
4. Do you have teacher’s guide?
a. Yes
[
]
b. No
5. Do you involve pupils in delivery of mathematics lesson?
a. Yes
[
]
b. No
[
]
6. Do you think it is important to use teaching and learning materials in delivery
mathematics lessons?
a. Yes
[
]
b. No
39
[
]
Appendix C
Questions for pre-test
1.
2.
3.
274
+112
373
+241
641
+ 163
448
4. +383
5.
6.
7.
207
+ 339
708
+ 149
245
+ 430
245
8. + 430
9.
10.
890
+ 104
523
+ 383
40
Appendix D
Questions for post-test
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
402
+ 296
493
+ 185
349
+ 380
600
+ 104
354
+ 187
834
+ 105
284
+275
269
+180
247
+ 432
264
+ 438
41