CHAPTER ONE
BACKROUND TO THE STUDY
Who on this Universe can say that technology exist without Mathematics? Or can it be
possible that the world will go on successfully without the idea of Mathematics which
involves the study of pattern, operation computation and solution to every problem? Even
in the field of football the plays and more especially the Goalkeeper calculate to catch the
ball. Girls when playing Ampe count for the winner.
Before the introduction of formal education, our parents were used to counting since they
counted the number of children they gad up to the tenth born child called ‘Badu and in
trading. They knew the amount of items they bought and their prices of which they sell to
earn profit. It is an undeniable fact that, Mathematics is a discipline that cut across all
fields being it Nursing , Sewing, trading, Farming and many most not forgetting the
Geographers, Economists and the like. This makes it an important cause for study.
Moreover, in this computerized world, the idea of number is used throughout life; hence
there is the need for pupils in the primary level of education to learn Mathematics.
During the out – segment, I was posted to Assin Dawomako for the attachment. It is a
small town in Assin South District near a well known commercial town called Assin
Andoe in the central Region.
The population of the town is about six hundred. The inhabitance are mostly farmers, few
engaging in trading and very less literate and for that matter there is no highly educated
personnel’s such as Teachers. Nurses, Doctors, Ministers and the likes from the town
who will serve as a role model for the pupils to imitate rather their focus is on farming.
The parent s of the pupils know nothing about the need of education, they do not
encourage wards to attend school, some parent of those who attend school do not care
whether their wards study after school or not, do not buy required teaching and learning
materials such as pencils, exercise book, erasers and the rest for them, because all they
know is that after the elementary school the girls give birth and the boys end up in the
forest, therefore they do no value education. Some even come to school because of the
feeding program in the school. A teacher will give assignment to pupils and they will
return the questions to the teacher complaining there was no one to assist them. Others
send their wards to farm every Friday and on Wednesday they follow them to the market
1
at Assin Andoe, so you will only meet full class on Monday and Thursday but for the
rest, it very disappointing. While these unfortunate pupils are out, tuition must be in
progress and that in return their colleques will be ahead of them which make teaching and
learning of Mathematics very difficult since Mathematics runs through the time table
everyday.
STATEMENT OF THE PROBLEM
Most people view Mathematics from time immemorial as a difficult subject of which
was a victim. The researcher observed that pupils find it difficult in solving problems on
adding 2, 3 –digit numbers. The researcher could not just draw conclusion their to under
take a study and i observed that in their previous classes that is basic one and two where
the foundation of addition were to laid learning materials let alone activities. In their
current class my mentor is not used to teaching with learning materials therefore pupils
could not use teaching and learning materials in solving problem on adding two three –
digit numbers.
A pupil worked a problem as following.
466
+ 377
71313
I observed that the pupils has no or less knowledge on the concept of place value and
that starting from the right to the left 6 + 7 are in the ones column therefore he will write
3 down then carry 1 ten to the tens column to make 1 ten + 6 tens + 7 tens making 14 ten,
then 4tens down carrying 1 hundred to the hundred column to make 1 hundred + 4
hundreds + 3 hundreds making 8 hundred. The researcher wants to help pupils to solve
two three – digit numbers through activity method using abacus, Dienes block, place
value chart and the likes
PURPOSE OF THE STUDY
The researcher was once like these pupils and was one way or the other helped out and
thus her prayer is to help pupils to be able to manipulate teaching and learning materials
in solving addition of two three – digit numbers. It also the will of the researcher to
identify how pupils learn mathematics, the causes of pupils of Dawomako D/A primary
three difficulties in performing addition of two three – digit numbers and design
strategies to address it such as activity method.
However, it is the will of the researcher to come out with various teaching and learning
materials in order to help pupils to solve problem involving place value that is adding two
three – digit numbers using abacus, Dienes block and the like.
2
RESEARCH QUESTINS
Considering the problem at hand in order to carry out this research the following
questions were raised to serve as a guide to help in researching.
1. How do pupils learn mathematics?
2. What are the causes of Dawomako D/A primary three pupils inability to add two three
– digit numbers.
3. What materials can children use to solve problems on the addition of two three – digit
numbers very easily.
4. How should materials be used to help pupils to understand the concept of addition.
SIGNIFICANCE OF THE STUDY
This work is expected to come out to enhance effective teaching and learning of the
concept of addition of two three – digit numbers. The findings and suggestions will
provide a gate way of information to all interested stakeholders of education on policies
made in the teaching and learning of Mathematics and best they can obtain their aims.
However, it will also serve as a reference for other future researchers to improve upon
similar problem in the course of their study.
LIMITATIONS
The first limitation could be that fact that the rate of absenteeism is high at Dawomako
D/A primary and during the time to intervene most t pupil especially those who find it
very difficult to perform the addition of two three digit numbers will not be present.
Another possible limitation could be that pupils may feel reluctant to answer additional
questions for fear of making mistakes and be most at and this may affect the result of the
study
DELIMITATIONS
This study was done an only addition of two three digit numbers and it is delimited to
only pupils in basic three at Dawomako D/A primary school.
ORGANIZATIN OF THE STUDY
This study is organized in five chapters. The leading chapter deals with the background
of the study, statement of the problem the purpose of the study, the significance of the
study. Limitation, delimitation and organization of the study, second chapter review
related ideas and literature of the study. The third chapters also talk about the
methodological ways whiles chapter four consist of the presentation and analysis of the
main data. The last act not the least chapter being chapter five deals with the summary,
conclusion and the recommendations of the study.
3
CHAPTER TWO
RELATED LITERATURE REVIEW
This chapter deals with the ideas and review of related literature of the study. It is going
to throw more light on what some mathematicians and other related scientist have written
on how children learn Mathematics. The use of abacus.
Dienes block, exchange games and others to build the concept of addition.
Contributions made by some Mathematics on how children learn Mathematics and how
teachers are involve
According to Lie beck first published book [1989] on how children learn Mathematics,
she said they see counting as six different processes in order to count object. There are
matching object for property, sorting them in those that have this property and those that
do not. Ordering the relevant set in some way. Recalling the member names in
conventional order, fairing the ordered object with some members names in order and the
six processes are using the final number names in its cardinal series to describe that
whole set of object that you count. The activities of matching, sorting, ordering and
fairing have arisen and most importance steps in the process of counting furthermore
before children are able to count a set of object they must know some number names in
conventional order without necessary understanding what those names they know means.
Finally, they have see and associated it on the whole set of object.
Merthens argues in the same direction of Liebeck [1989] she says that when small
children arrives at school, they gave already come into contact with the notion of having
played with train tea set, loyo sets, so we can starts with the idea of a set, a group of
things which belong together. This idea can them be developed by sorting things into sets
and complements, that is thing that form the set and those that are not in the set;
In the infant classes that are from basic one, they learn pre – number activities of which
sorting is an absolute essential skill from that end. Sorting and ordering of information
from the foundation for all knowledge. These children who have difficulty increasing
disadvantage as they progress through the second system
Contributions made by psychologist like Piaget, Diens, Brunner and many more e are on
the fact that the mental development or level of a child must be taken into consideration
before concept is introduced, since children differ in the way they learn. The cognitive
Piaget categorized children learning of Mathematics in to four stages associated each
with characteristics exhibited. Among these stages which he named concrete operational
stage from 7 – 4 year up to Junior High School? He makes use of active experience of
learning.
According to Lumb and Paperidic [1978], the period is labeled as concrete operation
because children’s thinking is essentially tied to concept provided they based upon
contact with real things and actual situation.
This presuppose that we have teachers who are to methods, strategies, techniques and use
of real object and for that matter concrete object so that pupil will understand concepts
easily such as multibase block, abacus and many more
Teaching Mathematics without appropriate teaching and learning aids or material makes
teaching losses it value since at the end there will be no aim or objective to achieve.
Teaching and learning materials contribute largely to pupil’s understanding of
mathematics concept.
4
Teaching mathematics in primary school paling first published [1982] says that it is
necessary to record number in a more convenient form than the use of stone notched
knots etc. this led to the making of marks on stone and thus the introduction of symbols
for number. About a thousand and years ago a method of writing very easy.
The following paragraph is going to talk about what writers and other educationalist t
have written about the origin and use of abacus.
Fehr and Philips [1972] use counters, pegs markers and the abacus. The United Kingdom
Department of Education and since [1979] supports Fehr and Philips [1972] in the
direction. According to the department, the structural apparatus necessary for
mathematics testing are multibase Arithmetic Block including Diens and Tillichs Block,
stem structural materials, the Cuisenaire rod or set, the centicede and structs
Science Library Mathematics by Berganim [1984] the abacus in old Europe say that,
though most of Europe history and the abacus was the computer triumphant. The abacus
in the orient the Japanese calculate in the beads. The abacus is still the commonest
computer in Asia. Some abacus operation there can compute faster than clert with
modern adding an adoption of the abacus in Ohio. The 12 horizontal bars are for decimal
multiple.
The based colours of each abacus form the total at its right. The above abacus is one of
these rare mathematicians that are so simple yet so effective that they are passed of
unchanged from civilization to civilization. It may have 5,000 years ago in ancient
Babylonian that man first discovered that of his marked figure on a dust covered board
evolved into the counter abacus in which groves were cut ion a board and small disks
representing the numerals were move along the groove.
Caroline Poisard University of Auckland poisard maths. Auckland. Ac.nz. this paper is
part of a PHD research study about the teaching and learning of arithmetic’s in primary
school, in particular year student. They wrote about calculating instrument and the notion
of carried number. A French mathematician, Lucas [author of recreations mathematiques
in 1885], work in 1891 in a book about theory of numbers. The Chinese abacus was the
first autonomous and portable calculating instrument. Where taught to young children,
they will later calculate quickly and surely. He continued by saying for most experienced
users, calculating with the abacus can be faster than with a calculator. Primary
mathematics today William first published 1976 says that an abacus with four or five rods
open can also be use for scorting, ordering, using beads of different colours of shapes.
The illustration shows the random order and then the ordering on another abacus
according to which set has fewer and many more [see fig 1]
5
Fig. 1 diagram of the random ordering of abacus.
Mr. P. Apsemah and his colleague [19094] talk about the use of abacus and they said is
consist of several rows are worth ten beads from the row before. Abacuses do not
represent numbers structurally as bounding sticks and multibase blocks. With the same
view Martins [1994] said for teaching mathematics, he recommended abacus, Diens
block and the likes for teaching place value and algorithms of addition.
Universal world reference encyclopedia [1968] says something about abacus he says that
abacus is a calculating device of ancient origins still used in parts of the orient and
Middle East. The first abacus probably was spread as a slab or board which Babylonian
spread sand so he could trace letters. The world abacus is believed to be derived from the
Phoenician for writing. As the counting and computing its form was changed and
improved. Wax covered boards were introduced and later counter abacuses of bone flass
on a rural disk or rod were placed on a rural table drawn on the board. In a still latter
form the one used in some part of the world today the counter sliders in grooves oar on
wires strings. The table of the early the counter slide was composed of lines representing
abacus tens hundred or united of values such as shilling pence pound additions abacus of
this type probably was performed as represented. A late roman abacus upper row in the
British museum each upper button representing five units of the order in which the
common stank units of the buttons representing one of the same order. Ciero speaks of
the common name was calculi ‘pebbles’’ or abacus the piece were stone irony metal or
colored glass.
The earliest types of abacus in china seems to have been the bamboo rods that several
instead of counters. These were known as early as the 6th century B.C and they survived
in Korea unit the close of the 19th century. They found their way into Japan about the
years 600 and were known as Sangi or Sanchu unit recent times they were used to
represent algebraic co – efficiency being place on a rural board.
Other mathematicians and educationalist have said about Diens block and it uses as a
material use in teaching and learning of mathematics. The following paragraphs throw
more lights on what they have written.
6
Diens said the learning of mathematics should be based on the Childs experience. He
suggested that when learning mathematics concepts, several models should be used to
develop the concept. Such as the principle of multibase or multiple embodiments which is
the use of several models activities, experience and method to develop the concept. For
example to teach the concept of the fraction ½ the child can perform the following
activities
[1] Folding paper into two equal parts
[2] Separating sets into two several subset
[3] Cutting a strip into two equal parts
And to teach the concept of addition of 2, 3 digit numbers. Diens multbase block will be
suitable. It consist of number of small cubes, rods, flad squares and large cubes such that;
10 small cubes = 1 rod or long
10 rods/long = 1 flat and
10 flats
= 1 large cube
Diens Block
Cubes/units
rod = Ten
Flat
Hundred
7
Large cube/block
--- Thousand
William hisnary shaurd published by togmer states that the concept of place value can be
effectively taught with the Diens block. She said the process of building up from unit
cube to large and larger unit can be parallel by the process of breaking down a larger unit
to a smaller unit. If you take a large as a unit square to represent hundred. Then not are
gradually breaking hundred into ones and vice versa through activity and grouping
method.
Whiles much mathematician talk about how learning of mathematics is, the use of abacus
and Diens block there are others who also talk about how traders and other used numerals
and symbols to teach the concept of place value. It was from this that place value chart
was introduce. The paragraph which follows will talk about what others have talk about
the use of other materials and activities in teaching mathematics concept especially place
value.
About a thousand and years ago a method of writing very easy was introduced an
instrument which made it much easier to do written calculation. This method originated
from India and Arabic system. It is the base on ten. It most important different from other
system is that a symbol is introduced for zero with this symbol and the symbols 1,
2,3,4,5,6,7,8,9.It is possible to show any number by using the ideas of place values. For
example 5hundred 6tens and 3ones is shown as 563, 4hundred 6tens and 3ones is shown
as 465, 2 hundred and 5 ones is shown as 205
H
100
5
4
2
T
10
6
6
6
8
0-4
1
3
3
5
For this third figure 205, 0 is use simple because there are no tens at present and that if
we do not have a symbol for zero we might show 2 hundred and 5 tens as 05 which
means 60tens and 5 ones which would be confusing.
The book Mathematics for teacher Training in Ghana edited by J. I Matin [1994] page 64
also talk about the Hindu – Arabic Numerals. The book and the numerals we used today
originated in India and were later adopted by Arabic traders. The Hindus used only ten
different symbols to write all numbers. Although this form of these symbols has evolved
with passing time it is this system which has gradually been adopted by the whole world.
The symbol as we know them today are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.it continue that the
Hindus group units together to made tens and also tens together to make hundred etc. so a
number might be written;
5 hundred, 6 tens, 4 units
It also said the essential properties of a place value system are that, only a small number
of different symbols are need because the value attached to each symbol depends upon its
position in the number and A symbol for zero is necessary to show ‘empty’’ positions. He
also said sound knowledge of place value is important for all full understanding of the
algorithms for addition, subtraction, multiplication and division. Children need a great
deal of experience of the actions associated with changing. These experiences should be
with concerts materials children should be able to split a set into subset in t sizes of sets
of equal sizes. He continued by saying it is not enough for children to be able to group
only in tens, they should also be encouraged to group in group of any size and that many
teaching aid must be use to help such as the use of abacus, multibase block, bounding
sticks, exchange games and the rest.
Grossniclde and his colleague [1983] hold the view that children should be given the
opportunity to work with manipulated hands on a materials in Mathematics, abacus,
attribute block base ten block, geoboard, pattern blocks, unique cubs and pocket place
value chart. To him all these are materials that are designed to help children study
mathematics.
Martins [1994] said the use of bounding stick which consists of a number of sticks [for
units] which can be tied together in group [of ten]. These groups could be further groped
into forma hundreds. It is very cheap since children get access to them easily so they call
it counting sticks. If these are also included when teaching addition of digit numbers
children get it easily and it is active activity
Algorithms
The word algorithms originated from an Arabic Mathematics in the 9th century.
Alkohowarizme [also spelt Al – khwarizumi] who gave specific steps involved in
9
performing calculation s in the four roles of operations that is addition, subtraction,
multiplication, and division. Fehr and Philips 1972.
According to Morley [1978], the approach to calculation is a particular concern’’ the
strategy involved making it possible for sequence where children can be faced with the
problem of calculating with larger numbers. Working with a situation or model in which
they have confidence. He also said as a result the pupils can experiment refine as shorting
their methods to arrive at a procedure they can then practice and use
Addition Algorithms
From the view of Fehr and Philips [1972], Martins [1994], Grossnickles [1983] the
addition algorithms are types addition with regrouping or renaming and addition without
regrouping.
According to Grossninkle and his colleague [1983], the term regrouping and renaming
are used interchangeable. This process describe by either terms deals with a place in a
numeral that is our loaded which means there are more than nine [9] at a place which is
more than units
The word regrouping or place value devices are often associated with the physical
exchange of object. Whenever ten single objects are changed into one group of ten as a
bundle of ten is changed into ten one the materials have been regrouped. Symbolically,
the procedure or process of changing let say 45 into 4 ten and 5 ones is what we called
‘’renaming’’ numbers
From the view of Mrs. E. Afful and her colleagues [1994] the use of Exchange games
also help in teaching and leering of place value or digit numbers. She said the game can
be played in many different ways with many different materials but the principle is
always the same that is when you have enough object to form a group of the chosen size
then you exchange this and place it in the next column to the left. Materials such as base
ten blocks and bounding sticks the structure of the number can still be seen but with the
structure like the abacus or beads a group is exchange for single object or some – times of
different colour, which represent a larger group simple by virtue of its position
As Lebesque [1975 page 9] remind us, the invention of decimal numeration, maybe the
most important of the history of sciences, is still not fully used at school. In each rank the
decimal system [units, ten, hundreds.....] the digit from zero to nine can be written. As
soon as ten is reached there is the transfer of numbers between rank, that is to say 10
units = 1 ten, 10 tens = 1 hundred, 10hundred = 1 thousand and soon on. The carried –
number enables us to manage the change of place value by making the transfer of
numbers between ranks.
For instance, adding
538
+ 191
729
at tens rank, we do the addition 9 + 3 = 12, and 12 tens = 120 that is 2 tens and1
hundred. This for the addition of two numbers, if the addition is all at the unit rank, the
carried – number [if it exists] is one ten, At the tens rank the carried – number is one
hundred, and so on.
10
SUMMARY
The literature predict the effectively use of instructional material in the teaching and
learning of Mathematics. The techniques, approaches and various materials enhance the
understanding of pupil son mathematics concept very easily. As Martin [1994] said in his
book Mathematics for teacher Training in Ghana, he said pupils need to learn a set of
rules to deal with the four basic operations that is addition, subtraction, multiplication and
division. If pupils are able to go through these easily it increases their background
knowledge of mathematics and this develop interest in mathematics to a higher level.
CHAPTER THREE
This chapter deals with the approaches use for obtaining data for the research work. It
will elaborate on the description of the research design, problem sampling procedure used
and analysis. It will also light on pre intervention, intervention and post intervention.
RESEARCH DESIGN
This is an action research which is a kind of research activity in which the researcher
works collaboratively with other people to solve perceived problems and it aims at
improving a problem- related situation through change. This action research was carried
at Dawomako District Assembly primary school strictly pupils in basic three. The
researcher resorted to Action research and not any other form of research because it tries
to find immediate solution to the psycho- social problems of learners that hinders the full
achievement of learning objectives.
The researcher went through some short comings or weakness which was the time from
for the completion of the research was very small for the researcher to put this problem at
a complete arm length and also there were financial difficulties.
POPULATIN AND SAMPLE
The setting of this action research was conducted at Assin Dawomako D/A primary three,
with the population size of thirty – seven. The researcher used diagnostic test to sample
the population after considering the larger size of the population. After the test those who
came short of the topic adding two three – digit numbers were randomly sampled in a
form of lottery method as the experimental group. Ten out of the twenty pupils who fall
short were selected as the experimental group of which six were girls and four boys. The
researcher therefore observed them for her data collection. Another five pupils four girls
and a boy were chosen as the control group of which the experimental group would be
compared to after the intervention
RESEARCH INSTRUMENT
This stage deal with the instrument that was used by the researcher in finding information
from pupils and teachers in the school. The researcher used observation, test and
interview based on the research questions.
Observation is a type of research instrument that employs vision as the main means of
data collection. In other words the researcher collects data on the current status of the
11
subject by watching, listening and recording what she observed rather than asking
question above them. The researcher resorted, to this instrument because it provides first
hand information with out relying on the report of others. It was realized that considering
the class of which reading and writing seen to be a big problem for the pupils and for that
matter it will be very difficult to use questionnaire which consist of lest of question for
respondents of which the pupils cannot read. The researcher research her observation in
semi structure way. She observed the behaviour towards pupil participation towards
mathematics questions how they view addition concept and other sub – topic of which
addition of two three – digit numbers is inclusive.
Test, is a type of research instrument which diagnose the extent of a problem and again
determine the effectiveness of an intervention. The researcher used this as a diagnostic
instrument which is also know as pre – test be perceive the level of the pupils difficulty in
solving two three – digit numbers in addition form. in this case a pre- test was conducted
which involve the use of abacus place value chart, Dienes block and others. Those pupils
who are the experimental group could not do it as it was expected, therefore and
intervention was administered and after the intervention the same test was given to help
to know the extent of effectiveness of the method used.
When the experimental group performs addition problem of the sane kind with the
control group for comparison there was a behaviour change or improvement.
Interview which is also characterized by the fact that it employs verbal questioning as it
principal technique of data collection was also used by the researcher. In this case the
researcher used it on the pupils and two teachers, as comp0ared to the observation that
was used on only the pupils with that psycho – social problem. The researcher therefore
conducted one on one interview with the pupils and two teachers in the school. When
intervention was in progress and after the administration of intervention.
INTERVENTION PROCESSES
This stage involves finding practical judgment in concrete situation to come to terms
with, the reality on the ground of pupils in Dawomako D/A primary three. This
intervention process has been categorized in to pre – intervention, intervention and post –
intervention.
PRE – INTERVENTION
This is the procedure that the researcher adopts in trying to diagnose the perceived
problem before the actual interventions. The researcher instructed them on what they
were going to do and thus gave them place value chart, abacus and Dienes block. After
20kminutes the answers were collected and marked after which she realized that 65% of
the total population on adding two three – digit numbers. This prompted the researcher to
find the intervention to such a problem.
INTERVENTION
Two weeks was used by the researcher to exhaust the intervention of the project work.
Five days per each week in every one hour. Pupils were taking through the concept of
place value and their previous knowledge of addition fact without regrouping. The
researcher after observing the difficulties these pupils went through. It was made vivid to
the pupils that, the addition of the numbers starts from the right side to the left side using
12
the abacus. Again, it was also made known to them that the abacus is made in columns in
their case, and that must add in columns that is the rods on which the beads are thread on
of which we made used of cardboard of different colours and shape to represent a bead.
Therefore when adding first, add in columns from the right to left, if the addition exceeds
ones that is when is more than 9, you will write the digit in question for instance when
the answer is [10] and above you will only write the first digit on your right say [0] down,
then carry the second digit which is [1] to the second column from your right which is the
tens column in that order, tens are group to made hundred. With this concept and
knowledge at the back of the pupil’s minds, the usage of abacus was introduced to them.
The researcher gave this question
148
+ 363
Pupils knowing that on the abacus you start from the right hand side and move to tens
and to hundreds to the left. The researcher guides pupils to use the cards in their case in
adding on the abacus. To make things easier and for easily identification there were
different shapes of the cards; pupils were using rectangular shape for calculating of ones,
circles for tens and triangular shapes for hundreds. The research then guides them to add
eight rectangular cards and three rectangular cards making eleven rectangular cards [11]
which exceeds ones since it is two digit number, therefore ten of these eleven cards were
exchange for one circular card and carry it to the tens column where of belong making 1
circular card + 4 circular cards + 6 circular cards giving us 11 circular cards, 11 exceeds
tens, therefore 10 cards were also exchanged for 1 triangular card remaining only one
circular card for the tens column. This 1 triangular card was carried to the third column
giving 1triangular card + 1 triangular and + 3 triangular cards make 5 triangular cards on
the hundreds column. Therefore after the addition there were 5 triangular cards, 1 circular
card and 1 rectangular card. Since the figures are three we say is 5 hundred, 1 ten and 1
ones [511]. This is indicated diagrammatically with the abacus
The diagram is an abacus showing 5 hundred, 1 ten and 1 ones [511] with the ones
indicated by a rectangular card, circular card for tens and triangular cards for hundreds
for easy identification. Pupils worked questions using the abacus. The researcher
proceeded given different material to help pupils with this addition problem after some
13
days when they were through with the abacus. She taught pupils how to use the Dienes
block in adding digit numbers.
The Dienes block consist of a number of small cubes rod or long, flat and large cube such
that 10 small cubes = 1 rod, 10 rods = 1flat and 10 = 1large cube. The units are for ones,
rods are tens, flat are hundreds and the large cube is for calculating thousands. The
investigator first direct pupils using this material through exchange game, for pupils to be
familiar with how and when to use each component of this material. To play this game in
base ten since our addition of digit numbers is in base ten, pupils play with two dice, each
player throws the dice and takes a number of unit blocks equivatent to the number shown
on the dice, he or she places in the appropriate column on his or her table [see fig 2] when
he or she has ten or more units he exchange for long [rod ] and places this in the longs
column, when he has ten of the longs or rods he exchange for a flat. Since we are dealing
with adding 3 – digit number we will end at flat if not he would have exchange e flats for
large cubes. Therefore with the flat being the last block in our case, the winner of the
game is the one who first make flat,
Table of how a game is recorded. [Fig. II]
Groups
Flat column
Long column
Unit column
Pupils
A
Pupils
B
The researcher does this so that pupils will experience arranging a set into equal sized.
Smaller sets and then arranging a set of set and so on. They also learn to record this
arrangement in headed column and therefore realize that the value or meaning of each
digit in a number depends on which column a might be.
The researcher did not show the large cube because her concern was using those shown
to teach 3 – digit numbers and the large cube is use when dealing with 4- digit numbers.
14
The researcher aimed at involving pupils in various activities as remedy, therefore she
taught pupils again on how to use place value chart in adding three digit numbers
A PICTURE OF PLACE VALUE CHART
Fig. IV
H
100
2
+3
6
T
10
6
4
1
O
1
5
7
2
H
100
4
+4
9
T
10
5
4
0
O
1
6
9
5
This two chart do not use neither symbol nor cards, rather make use of numbers. The only
essential thing about these charts or material to the fact that you only place the numbers
at their corresponding columns as it was done with the exchange game table. Numbers
like those in the second chart [fig V] 456 + 449, 6 and 9 will be placed at ones column 5
and 4 be placed at the tens column [10] and 4 and 4 will be place at the hundred column
[100]
Adding using place value chart is the smart as using the abacus from the right hand side
to the next column on the left hand side. From the carts [fig IV and V] the answers were
612 and 905 respectively. The pupils in the experimental group tried their hand on this
With this knowledge acquired the researcher then direct pupils to solve problem on the
chalk board using the Dienes block
1. 276
+424
2. 436
+358
3. 466 4. 265
+ 377 + 347
5. 148
+ 363
The first question was solved by the researcher and pupils as an example. Knowing that
we add digit numbers from the right to the left from previous material used, we first add 6
small cubes and 4 small cubes making 10 small cubes, since these cubes were 10 it was
equal to 1 rod or long which was in the second column, therefore there was no unit left at
the ones column that is zero [0] whiles this one long was carried from units to rod column
making 1 rod + 7 rods + 2 rods = 10 rods, pupils know that 10 rods = 1 left, therefore
there was no rod at the rod column whiles 1 flat was carried to the third column which is
flat column from the right to left. 1 flats + 2 flats + 4 flats = 7 flat. The final answer using
Dienes block we got 7 hundred. The pupils in the experimental group tried their hand on
the rest of additional questions.
A PICTURE OF DIENES BLOCK
15
Fig. III
Rod [long]
Small cubes [unit]
10 small cubes = 1 rod
10 rods = 1 flat
Flat
POST – INTERVENTION
This is the third stage of the intervention process. After involving pupils through the
various activities, the investigators evaluate the out come of the action taken. A test was
given to both experiment group and control group for 20 minutes to submit their work,
the researcher after the submission of exercises done by pupils observed that the
experimental group performance in solving problems with three digit numbers has
improved tremendously, they were able to use abacus, Dienes block, exchange games and
place value chart to solve problems. As compared to the control group who were view of
not having problem the experimental group did very well.
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CHAPTER FOUR
RESULT, FINDINGS AND DISCUSSION
This is the last but one chapter of the research work. It deals with description and
interpretation of data collected.
PRE – INTERVENTION
Marks obtained by the experimental group and the control group
Experiment
Girls
Boys
al
Group
Cecilia Amoah
Gifty Sam
Gloria Koranteng
Hannah Opoku
Portia Afriyie
Matilda Asare
Alex Obeng
Filix Ampomah
Emmanuel Odoan
Kweku Debrah
Total
Control
group
Girls
Boys
mark
degrees
2
1
1
1
0
0
0
0
2
0
7
2/7x 360= 1030
1/7 x 360=510
1/7 x 360=510
1/7 x 360=510
0/7 x 360=00
0/7 x 360=00
0/7 x 360=00
0/7 x 360=00
2/7x 360= 1030
0/7 x 360=00
3600
mark
Degrees
Victoria Tieku
4/5
Edith Adjapong
4/5
Doris Entsie
5/5
Ayisha Asare
4/5
Sadik Agyare
4/5
21
17
4/21 x
360=690
4/21 x
360=690
5/21 x
360=840
4/21 x
360=690
4/21 x
360=690
3600
PIE CHART SHOWING THE PERFORMANCE OF PUPILS IN THE
EXPERIMENTAL GROUP.
Portia
Matilda
Alex
Felix
Debrah
Key
Cecilia
Gifty
Scale = 5 cm
Gloria
Hannah
Emmanuel
Five pupils
18
PE CHART SHOWING THE PERFORMANCE OF PUPILS IN THE CONTROL
GROUP
Key
Victoria
Edith
Doris
Aysha
Sadik
Scale = 5 cm
The researcher made use of the pie chart or divided circle and tables in discussing the
various findings during the pre – intervention. The experimental group during the pre –
test scored tow out of five as the highest score. This was scored by only two pupils out of
the ten pupils forming the experimental group. Three pupils scored one out of five whiles
the rest had zero out of five.
The researcher decided to take some pupil as her control group after which the
experimental group would be compared. In the control group only one pupil had all the
questions correct while the remaining four pupils had four out of five? The researcher
therefore used the control group as her target to achieved, after the intervention. In
looking at the divided circle for the experimental many of the sectors did not appear on
the chart because majority of the pupils scored zero out of the total marks. The researcher
therefore wishes that by the end to the intervention pupil din the experimental group’s
data can be represented as that of the control group.
19
POST INTERVENTION
After the researcher has taken pupils through place value chart, the use of abacus, Dienes
block and other activities the following score were obtained by both the experimental and
the control group
Experiment
al
Group
Girls
Boys
mark
degrees
Cecilia Amoah
Gifty Sam
4
5
Gloria Koranteng
5
Hannah Opoku
5
Portia Afriyie
Matilda Asare
4
5
4/42 x 360=340
5/42 x
360=430
5/42 x
360=430
5/42 x
360=430
4/42 x 360=340
5/42 x
360=430
4/42 x 360=340
3/42 x
360=260
5/42 x
360=430
2/42 x
360=170
3600
Alex Obeng
Filix Ampomah
4
3
Emmanuel Odoan
5
Kweku Debrah
2
Total
42
After the intervention the pupils who were having serious problem with the addition of 2,
3 – digit numbers could perform so tremendously. Most of the pupil who were scoring
one and zero could now solve similar question by scoring four out of five. Whiles others
were scoring even five. The researcher therefore represented the pie chart.
20
PIE CHART SHOWING THE PERFORMANCE OF PUPILS AT THE
EXPERIMENTAL GROUP AFTER POS - INTERVENTION
Scale = 6 cm
Cecilia Amoah
Gifty Sam
Gloria Koranteng
Hannah Opoku
Portia Afriyie
Matilda Asare
Alex Obeng
Felix Amponsah
Emmanuel Odoom
Kweku Debrah
21
After the diagrammatical representation of the data on the pie chart, it was realize that all
the pupils’ marks were able to be represented on the pie chart because no one had zero. It
presupposes that all the pupils had sector on the whole circle as compared to the pre – test
pie chart by experimental group.
Portia Afriyie, Matilda Asare, Alex Obeng, Felix Amponsah and Kweku Debrah whose
data were not represented on the pie chart oft the pre – test, but after the intervention
these same pupils data was able to be represented on divided circle with out getting zero
degree.
A TABLE SHOWING THE PERFORMANCE OF THE CONTROL AFTER THE
POST INTERVENTION
Experiment
Girls
Boys
mark
degrees
al
Group
Doris Entsie
5
5/23 x
360=780
Victoria Tieku
4
4/23 x
360=630
Edith Adjapong
4
4/23 x
360=630
Aisha Asare
5
5/23 x
360=780
Sadik Agyare
5
5/23 x
360=780
TOTAL
23
3600
PIE CHART SHOWING THE PERFORMANCE OF THE CONTROL GROUP AT
THE POST INTERVENTION
Key
Doris Entsie
Victoria Tieku
Edith Adjapong
Ayisha Asare
Sadik Agyare
Scale = 4cm
22
From the diagram, it indicate that after the intervention the performance of the control
group has also increased in the sense that three pupils had all the questions correctly
whiles only two pupils had four out of five as compare to the chart before intervention
though they did well only one pupil had all the questions correct, so there is an
improvement.
In comparing the performance of both the experimental and control group, it was noticed
that five pupils were able to get all the questions correct. The least mark of the
experimental group was two act of five after the intervention. Though the control group
the least mark was four out of five, I can say the experimental group Perform marvelous
because initially the least mark was zero and they are ten pupils who had problem whiles
this control group were the best pupils. The objective of the researcher was achieved after
comparing the two groups, since five pupils from the experimental group had five out of
five which is a behaviour change.
CONCLUSION
In conclusion, the above findings indicate that teachers should make effective use of the
available instructional materials for the stated educational objectives of Ghana Education
Service to be attained.
23