CHAPTER THREE

METHODOLOGY

This chapter is the icon of the entire action research. It describes the research design, population and sample selection, research instruments, Data collection procedures and data analysis plan.

Research Design

Research is the search for an answer to an unresolved and perplexing question(s) using the scientific approach. The research design used by the researcher is the Action Research. Action Research is defined by William (2004, pg. 47)” as a study concerned with immediate solution to local problems”. He said the purpose of action research is to solve classroom problems or local school problem through the application of the scientific method. Action research is a kind of research activity in which the researcher works collaboratively with other people to solve perceived problems. It is an approach which aims at improving a problem-related situation through change. In other words, action research does not only focus on generating new knowledge, it also enables both the participants, that is, the teacher-researcher and the pupils, to develop appropriate intervention strategies aimed at finding solutions to the problems identified in the teaching-learning situation.

The rationale for the design was to help teachers to understand what actually goes on in teaching-learning situation and also to come out with some practical activities that will help pupils improve on their performance on fractions. Findings from action research provide teachers with the opportunity of acquiring a better understanding of all aspects of their own practice, be it in relation to subject, content, the curriculum or the methods appropriate to the level of the pupils in that class.

However, action research has the following weaknesses: It is limited and specific approach so findings cannot be applied to all situations. This is because of it narrowness to a particular and specific situation. One can also spend time without getting any better information needed for an immediate change. Also Action research is not applicable in all areas of study.

Population and Sample Selection

According to Polit and Hungler (1996) defined population as the entire aggregation of cases that meet a designated set of criteria. This means that the target group about which the researcher is interested in gaining information and drawing conclusion is what is known as the population. Whiles sample consist of a carefully selected subset of the units that comprise the population. This enables the researcher to study a relatively small number of units in place of the target population, and to obtain data that are representative of the whole target population.

The research population include all the pupils of Namoo Junior High School “A” form One (J.H.S 1) in Bongo District. The target population for the research is fifty (50) pupils of J.H.S One. the fifty of them thirty (30) are girls and twenty (20) are boys. Since an intervention solution was designed to help all the pupils in the class to overcome their inability to solve word problems involving addition and subtractions of integers, the sample size constituted all the fifty (50) pupils in the class. This will help the researcher to gather data on all the pupils in order to avoid over generalization.

Research Instruments

The instruments used for the collection of data were observation and test.

Observation

Observation is the action of closely observing or monitoring something or someone. The reason for the use of the observation is that it promises a wider coverage, and no false information is collected it is being administered by the researcher himself. Also the information pupils are unwilling to offer is being taken. The procedure used for administering this instrument was that during lesson periods, the researcher uses participatory observation to collect data he does this by going round individual by individual. The researcher critically noted down the behavior of pupils towards mathematics in the classroom and outside the classroom. The researcher observed pupil’s participation in Mathematics class and other subjects for about three weeks.

Again in order to find out whether pupils can work word problems on addition and subtractions of integers or not, the researcher wrote questions under the concept of integers on the chalk board and grouped the class of 50 pupils into seven (7) groups and asked them to answer the questions. While they were working on the questions the researcher went round and observed the groups and recorded the results as shown in chapter four table 1. At the end of the work the researcher saw that the pupils did not work the questions well. He also observed how the pupils behave during lessons and break times in order to get information on how they relate with each other as well as their teachers vis-à-vis their academic work.

Test

It is an instrument or a systematic procedure for using a numerical scale or a classification scheme. The test used was easy test because, it affords the pupil the opportunity to be individualistic, it also consists of relatively few items that call for extended answers. The activity under test performance was categorized into two of which they are pre-test and post-test to enable students understand the concept of word problem involving additions of integers. The pre-test activities were the activities and test preformed before the intervention and the post-test activities were the activities performed after the intervention. Since the pupils can read and write, tests were used to diagnose the extent of the problem. The tests were conducted in two different categories. That is, a grouped work and a class test which were administered at different time. The questions were set aimed at knowing the weakness and strength of pupils. The researcher prepared five test items each for the grouped work and the class test and they were scored 25 marks each. The researcher organised the test in the pupil’s classroom and the pupils were made to sit individually and the test was then administered to them and after forty-five minutes the papers were collected.

Data Collection Procedures

The data collection procedure is grouped into three (3) which includes: pre-intervention, intervention and post intervention. During these interventions process, students were given practical questions to solve and through that the needed data was gathered from the respondent.

Pre-Intervention

The pre-intervention is a procedure that the researcher adopts in trying to define the perceive problem. During the pre-intervention stage, the activities used in diagnosing the problem were testeds. The objective of the activities adopted by the researcher was to know whether pupils can work word problems involving addition of integers or not and to determine their level of understanding the concept of addition and subtraction of integers as well. So as the researcher tries to find out the cause of the pupil’s inability to solve word problem involving addition and subtractions of integers, the researcher conducted the pre-test which were five test items and were marked over (25) marks of which he realised that the performance of the pupils wereas not encouraging and that led him to find ways of improving pupil’s performance.

Intervention

Intervention can be explained as a series of concrete measures or approaches put in place to solve specific problems. It involves a step by step procedure which is constantly monitored over varying period of time. The researcher used four weeks in carrying out the intervention activities. The first week the researcher organised the materials needed for the lesson he also introduced the topic to them. On the second week, the researcher led pupils by helping them to interpret mathematical operations in table 1 below. Also on the third week he helped pupils to add and subtract integers using the number line as shown below. And on the fourth week he helped pupils solved the actual word problem in integers.

First week

The Monday of the first week was used by the researcher to gather the basic materials needed for the lessons and briefed the pupils on the essence of the activities that will be done. They were told of the materials needed to be used, and that, they needed to always be regular and punctual in class. Out of the days, Tuesday was used by the researcher to introduce the topic to the pupils and to tune their minds to the task ahead. During the introduction, the researcher made the pupils to understand that integers are positive and negative whole numbers. He did this by using the number line and other practical instances such as temperature below and above zero degrees Celsius (0? c).

For example, the researcher used the number line below and explained to the understanding of the pupils that: all numbers on the right hand side `of the number line are positive numbers whereas numbers on the left hand side of the number line are negative numbers and zero is the origin as shown below.

Figure 1: A Line Graph Illustrating Negative and Positive Integers

Second Week Activities

Activity 1: During the first day of the second week, the researcher performed activities which involved leading pupils to be able to interpret English sentences or words in to their mathematical operations as shown in the table below.

Teacher/ learner activity

Table 1: Showing Mathematical Words and the Mathematical Operations Used

Word/phrase Mathematical operation

Sum, total, increased by, addition, greater than, rises

Difference, decreased by, debt subtraction, deduct, less than ,falls (+)

(?)

On the second meeting of week two, pupils were taught how to add integers using the number line.

Activity 2: Adding Integers Using the Number Line

We can use the number line as a model to help us visualize adding and subtracting of signed integers. When you think of addition and subtraction as directions on the number line, there are several rules and properties that define how to perform these basic operations. For instance, Students were made to understand through illustration on the chalk board that they can:

Teacher/ learner activity

Add a positive integer by moving to the right on the number line.

Add a negative integer by moving to the left on the number line.

Add integers having the same sign by keeping the same sign and adding the absolute value of each number.

Add integers with different signs, by keeping the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.

Third Week Activities

In the third week, the activities below were performed to help pupils understand the addition of integers better.

Activity 1: How to add two positive integers say 3 + 4 =?

You can add three to four by starting at positive three on the number line and moving four units to the right, you end up at positive seven. Also, these integers have the same sign, so you can just keep the sign and add their absolute values, to get the same answer: positive seven. That is, 3 + 4 = 7 as shown in the number line below.66484516319500

3124200273685003+4 = 7

8572510985500

– 3 – 2 – 1 0 1 2 3 4 5 6 7 8

Activity 2: How to add two negative integers say -3 + (-4) =?

If you start at negative three on the number line and move four units to the left, you end up at negative seven. Also, these integers have the same sign, so you can just keep the negative sign and add their absolute values, to get the same answer, negative seven. Hence -3+ (-4) = -7 as shown on the number line below.

828675200660008572536131500

– 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3

Activity 3: How to add a negative integer to a positive integer say -2 + 5 =?

This can be done by starting at negative two on the real number line and moving five units to the right, you end up at positive three. Also, these integers have different signs, so keep the sign from the integer having the greatest absolute value and subtract the smallest absolute value from the largest. That is, subtract two from five and keep the positive sign, to get positive three as shown in the number line below;

– 2 + 5 = 3

10382259906000-25717528130500

– 3 – 2 – 1 0 1 2 3 4 5 6 7 8

Activity 4: How to add a positive integer to a negative integer say 3 + (-4) =?

Start at positive three on the real number line and move four units to the left, you end up at negative one. Also, these integers have different signs, so keep the sign from the integer having the greatest absolute value and subtract the smallest absolute value from the largest or subtract three from four and keep the negative sign, gives negative one as shown on the number line below.

1381125322580003 + (- 4) = – 1

8572510985500

– 3 – 2 – 1 0 1 2 3 4 5 6 7 8

After performing those operations above, the researcher wrote the question below on the chalk board.

Mr Joe has seven Ghana cedis (GH? 7:00) in his bank account and owns the bank three (3) Ghana cedis (GH?3: 00). How much will he has after paying the bank?

Solution

Below shows how the question was solved.

The researcher guided the pupils to work it on their note books as he was illustrating on the chalk board. He made the pupils to understand that the statement can be written as 7 + (-3).

Below are the steps used in answering the question.

The researcher guided the pupils to draw a number line and number it as shown below:

8572510985500

– 3 – 2 – 1 0 1 2 3 4 5 6 7 8

2. He assisted the pupils to start at zero (0) and moved seven units to the right as shown below.

52304726543000481774514605000

-3 -2 -1 0 1 2 3 4 5 6 7 8

933328407312003. From 7 on the number line, the students were guided to move three units to the left as shown below.

5017770698500 -3 -3 -2 -1 0 1 2 3 4 5 6 7 8

378142517081500497014518986500 Please merge the diagrams to avoid shifts and disconnections.

After the students have done that, they then realized that they have ended up at four (4) on the number line. Hence he will have four (4) cedis left after paying the bank.

Fourth Week Activities

The first meeting of the fourth week was used to perform the activities below:

Activity One

Atanga has three (3) pens and the school awarded him another two (2) pens for he was first in the school mock examination. How many pens will he have in all?

Steps:

Five Pens were given to pupils as counters.

852805104521000The researcher asked the pupils to group the pens given to them in to two groups; one is grouped into three (3) pens and the other into two (2) pens. Below are diagrams illustrating the above information;

339471012382500

Three (3) Pens Two (2) Pens

3. He then asked them to put the two groups together and count them as shown in the diagrams below.

402907511366500201930085090000889000

350964529845000162877517081500

Three (3) Pens Two (2) Pens Five (5) pens

The pupil then realized that the statement represents 3 + 2 = 5.

Activity Two

In an experiment, the temperature on a thermometer drops from -20 degrees to -24 degrees.

What is the change in temperature?

Afterwards the reading decreases by 8 degrees. What is the new reading?

Solution

Final temp = -24 ?C

Initial temp = -20 ?C

Change in temperature = final temp – initial temp

(-24) – (-20) = -4 ?C

(b) New reading -24 – 8 = -32 ?C

The Last Day of the Intervention (fourth week)

On Tuesday, the last meeting of the fourth week the researcher performed the following activity with the pupils.

Activity

There is a number, and that number and 4 sums up to 20. Find the number.

The solution was illustrated on the chalk board as follows:

There is a number. Let the number to be = x

The number and 4: That is x and 4.

Sum up to 20. That is x + 4 = 20

?x + 4 = 20

X = 20 – 4

X = 16. Therefore, the number is 16

In conclusion, the lessons designed were activities based lessons, where pupils had the opportunity to interact with the teaching and learning materials. It was ensured that chalkboard illustrations as well as concrete and semi-concrete materials accompanied the practical activities. As a result, pupils gained some happiness for the exercises and had wished it will continue every day. As a result, the researcher encourages the students to always learn and practice Mathematics whether at school or home. This perhaps will develop pupils’ interest for mathematics and for that matter mathematical word problems involving addition of integers. The fact cannot be denied that, having developed interest in this direction, the pupils would be interested in solving problems on addition and subtraction of integers even at home.

Post – Intervention

The post –intervention evaluate the outcome of the action taken. This is to ascertain mathematical word problems whether pupils have understood it or not and may be able to solve those involving addition of integers or not. Having done all those activities above, a post-test was conducted which was easy test items to evaluate the intervention design to address the problem. The tests were in two folds a group work and an individual test which was made up of five (5) test items each. Pupils were asked to answer all questions for both the group work and the class test. They were administered at different time.

Data Analysis Plan

The data collected before the intervention, during the intervention and after the intervention of the study will be illustrated in a simple percentage tables, charts and graphs. These would give guidelines on how the results and findings were made from the administration of the tests on the research work. Moreover, these illustrations would help the reader understand what is involved in the data collected and its analysis.

Let’s see the tables and charts as said. Normally the tables are captured in chapter three and not four. Chapter four explains the findings. Each objective and its corresponding findings are made to determine whether the objective is achieved.