Sunday, May 24, 2009


3rd – 21ST July 2008

In this project, I introduced the effective ways in order to improve the multiplication skill of students in the process of learning mathematics. I wish to thank to 3 Cekal pupils from Sek. Keb. Permatang Damar Laut, Batu Maung, Pulau Pinang for their contribution in the completion of this research study.

An action research was performed with the main aim of investigating ways of improving primary school pupils conceptual understanding of multiplication. Thirty five pupils in second class participated in this action research project. This action research involved pupils in answering pre-test and post-test on multiplication. Pupils also reflected on their progress and the success of their studying strategies. The revise teaching of multiplication was integrated with the various techniques to perform children’s activities which have the potential to develop conceptual understanding of the subject. The data collected indicated that some pupils improved their understanding but some pupils needs more time to re-learn the subject. This research only presents some practical solutions proposed within the time available.

Table of Contents
Background of Research
Literature Review on Action Research
Problem Statement
Table on Action Research
Research Methodology Design of Research Respondent
Research Limitation
Data Analysis

Background of Research

Sekolah Kebangsaan Permatang Damar Laut comprises of pupils from various backgrounds. The pupils are placed based on their achievement in Mid-term examination. Top pupils will enter excellent classroom which 3 Iltizam while the others will be placed in 3 Cekal and 3 Gigih classrooms. Pupils in 3 Cekal are the second class. So, I decided to do a research towards 3 Cekal pupils’ which a bit weak in mathematics facts, especially multiplication and search for solutions to increase their ability and understanding in multiplication facts. This was according to the interview that had been done with Mathematics teachers Miss R.Alagusundari in this school. The primary purpose of this action research study was to see whether the choice of strategies can foster pupil confidence and independence in learning mathematics.

Literature Review on Action Research

1. Definition of Action Research
Action Research represents a growing field of educational research whose chief identifying characteristic is the recognition of the pragmatic requirements of educational practitioners for organized reflective inquiry into classroom instruction. Action Research is a process designed to empower all participants in the educational process (pupils, instructors and other parties) with the means to improve the practices conducted within the educational experience (Hopkins, 1993)[1]. All participants were knowing, active members of the research process.

Action Research has been described as an informal, qualitative, formative, subjective, interpretive, reflective, and experiential model inquiry in which all individuals involved in the study are knew and contributing participants (Hopkins, 1993). Action research has the primary intent of providing a framework for qualitative investigations by teachers and researchers in complex working classroom situations.

2. The Design of Action Research
The essentials of action research design are considered by Elliott (in Hopkins, 1993) as the following characteristics cycle:

- Initially an exploratory stance is adopted, where an understanding of a problem is developed and plans are made for some form of intervention strategy. (The Reconnaissance & General Plan)

- Then the intervention is carried out. (The Action in action Research)

- During and around the time of the intervention, pertinent observations are collected in various forms, (monitoring the implementation by observation)

- The new interventional strategies are carried out, and the cyclic process repeats, continuing until a sufficient understanding of (or implement able solution for) the problem is achieved (reflection and revision).

3. Principle of Action Research
What gives action research its unique flavor is the set of principles that guide the research. Winter (1989) provides a comprehensive overview of six key principles[2].

Reflexive Critique
In sociology, reflexivity is an act of self-reference where examination or action 'bends back on', refers to, and affects the entity instigating the action or examination[3].

Dialectical Critique
Critique of Dialectical Reason attempted to show how what we call class is a special instance of a human grouping, or rather several levels of human groupings.[4].

Collaborative Resource
The implications of including it in classroom teaching for instructors who may consider including a collaborative pedagogy in their classroom[5].

A variety of risks makes it difficult to develop and implement new processes.

Plural Structure
Data is a curious word which is actually a plural noun. This realization requires attention and careful consideration[6].

Problem Statement

Year 3 Cekal pupils in Sekolah Kebangsaan Permatang Damar Laut are experiencing a problem to mastery the multiplication concept and skill were taught and learnt effectively as intended. There were several pupils still unable to recall rapidly the multiplication facts. There is a strong need to improve pupils’ mathematical understanding. The goal of this action research was to improve the multiplication skill for year 3 pupils and enhance their learning.

Research Methodology
Design of Research

A. Observation

1. Problems faced by pupils in Mathematics
a) The pupils cannot master the multiplication concept and skill were taught and learnt effectively as intended.
b) There were several pupils still unable to recall rapidly the multiplication facts.

2. No teaching and learning materials that were used to assist and attract pupils in having positive attitude in learning Mathematics.

B. Planning the strategy

The approaches that can be consideration are:
1. Reinforce the idea that multiplication is repeated addition.
a) Using material
i. Egg Carton Math
ii. Square Rods
b) Using number properties
i. Cuisenaire Rods
ii. Grid Number

2. Make a multiplication table for each pupil.

C. Implementation of the strategies

A pre-test on multiplication was used to find out the understanding level of the pupils in this research study. The pre-test has a total of 16 questions (Appendix 1). The test is reliable as it gives a measure of the attainment of pupils in acquiring the concepts and skills in multiplication. Based on the areas of weakness through the use of pre-test, there were customized remedial lessons instead of one-size-fit-all instruction. A post-test (Appendix 2) is the similar like same test questions with pre-test. It was given by the end of the remedial classes to evaluate the effectiveness of the implemented activities and strategies during remedial lessons. Those activities and strategies are planned to help me teaching multiplication facts in remedial classes. Let’s look up the activities and strategies to get this plan accomplished.

1. Reinforce the idea that multiplication is repeated addition.
a) Using material

(i) Egg carton math.

Have each group of pupils bring in an egg carton or a plastic container with some type of little objects. These could be buttons, paper clips, matches and whatever. When we say and write a problem, such as 3 x 4, the children need to display this problem using different sections of the egg carton to hold each group.
By the way, in the remedial classes, I always told my pupils to think of the X in a multiplication problem as meaning "groups of." So 3 x 4 is "3 groups of 4."

Using the egg carton, then they would only use 3 compartments, and they would put 4 items in each of those 3 compartments, counting as they go. And also after the problem is set up, they can count by those 4's: 4, 8, 12.

Then we could say, "4 x 3." Now they need 4 groups of 3, so they'll use 4 compartments and put 3 items in each, but they will still have 12. Count by those 3's: 3, 6, 9, 12.

Picture pupils used “Egg Carton Math”.

(ii) Turn multiplication problems into Square rods.
The cheapest way is just to use in square rods. So again, with 3 x 4 (3 groups of 4), to show 3 groups of 4, pupils would color 3 rows with 4 square rods in each row (4 + 4 + 4). To show 4 x 3 (4 groups of 3), pupils would color 4 rows with 3 square rods in each row. They can then compare these two rectangles and see that in both cases, 12 squares rods, but one looks like the other, turned 90 degrees. It does proceed with other example.
Picture pupils used “Squares”.

b) Using Number Properties
Provide the pupils with related multiplication problems. Discuss the meaning of each problem, for example, 10 X 3 = , so 9 X 3 = , as “ten sets of three” and “nine sets of three”. Look for the pupils to use either knowledge of the fact or part-whole methods to solve each problem and to derive one fact from the other. For example, 10 X 3 = 30, so 9 X 3 = 27, three less.
Suitable problems are:

2. The next thing I did was to make a multiplication table for each pupil using centimeter graph paper. It had the numbers 1 - 10 running down the left side and running across the top, with a multiplication sign in the top left corner. Then there was a thicker line to separate out the answers. (Or we could write those numbers 1 - 10 in a different color from the answers. But it still helps to have a thicker line.) Either I or the pupils would fill in the answers, but it is essential that they are accurate.

I wanted my pupils to each have a set of "Cuisenaire rods" that we made our own 2D version. Then the pupils colored portions of the grid paper with crayons, using the 10 colors needed to match the rods and then cut them out with scissors. So, for instance, red rods are the length of two units (the white rods). The rods colors are:

If I ask them to show 3 x 4, they will think: Okay, 3 groups of 4, so I need 3 of my purples. They will lay these down on the multiplication grid, starting at the top left corner of the answer area. Then they will peek under the bottom right corner of their rectangle. They should find a 12 there. Now if you ask them, 4 x 3, they will think, Okay, 4 groups of 3, so I'll need 4 light-greens. They will lay these down in the same way and peek under the bottom right corner. Again they should find a 12.

I'm going to try to insert a few graphics here: first the grid (this one shows all the answers to 10x10):

And now the two problems showing 3 x 4 and 4 x 3 (with the grid numbers covered by the rods shown):


This action research project involved one Mathematics teacher and one class of pupils (35 pupils) at Sekolah Kebangsaan Permatang Damar Laut, Pulau Pinang. The teacher was the regular Mathematics year 3 teachers who taught in that class. The pupils were mostly the weakest amongst year 3 pupils especially in Mathematics.

Research Limitation

As with all research, there are that need to be considered when trying to meet the objectives of this research study. The following is a discussion of some of these issues.

1. Time limitations
The pupil were taught and implementing those strategies for only 2 periods of lesson. Teaching mathematics concepts consume many hours in an elementary classroom. More time should be allotted to more activities of learning in remedial lessons.

2. Resources available
It is very important to have enough teaching materials. Some pupils did not bring their own egg carton and little objects. It made the hands-on activities ran very slowly.


I choose this topic because multiplication concepts are one of our curriculum mandated goals. I took several strategies to help me teach this concept. It is hands-on approaches that got me excited about teaching multiplication. I also was excited about the chance to watch my pupils take responsibility for their own learning, and this allows the pupil to take charge, and puts the teacher in more of a facilitator role once the basic skills are taught.

Firstly, I gave the pupils a teacher-made multiplication pre-test. Out of 35 pupils, 16 failed it. They completed 2 – 6 questions correctly. The nine pupils who scored above 10 out of 16 questions had good understanding about multiplication facts. I taught two lessons as remedial to that class at week 2 and 3. Almost half of the class did not master the multiplication concept and skill at the beginning of the lesson in week 2. I gave the pupils a post-test when the lesson concluded. 19 students passed the post-test with grid numbers. The sixteen pupils that did not pass understood the process of multiplication, but their inability to master basic facts keep them from getting the right answers.

Those strategies planned are great way to help pupils to learn multiplication facts. I definitely plan to use these strategies in future years during my works. I believe it will help my pupils understand the multiplication facts better because they will have activities that help them master the concepts. These strategies use such a step by step process that makes it easier for the pupils to understand. The different colors of Cuisenaire rods also help the pupils to visualize their multiplication. I also learned that it is not an easy process to teach in the beginning. Each step must be done slowly and understood before moving on to the next level of the tree. Overall, I really like these strategies and plan to improve on it.


Teacher working collaboratively using a variety of teaching strategies have help pupils make significant progress to master multiplication facts. Most pupils liked the activities that using concrete materials as teaching aids. They liked to learn because they were able to see and do hands-on activity in their classroom. Using this hands-on method allow the teacher to see exactly where a pupil is “getting stuck” and help that pupil get back on the right track. Most pupils reported that those activities were fun. Conversely, several pupils did not like doing those activities, and claimed that the mathematics activities were boring. These pupils were generally in the lower ability groups. I noted that some pupils who lacked intrinsic motivation did not progress as rapidly as other pupils. One of the factors that interfere with learning is classroom behavior and time on task. This study demonstrated how effective planning can make a difference in achievement and pupil attitude.


Mok Soon Sang (2004): A Primary Education Course in MATHEMATICS for Post Graduate Diploma (KPLI), Kumpulan Budiman Sdn. Bhd., Subang Jaya.

Altrichter, H. Posch, P & Somekh, B. (1993): Teacher investigate their work: An introduction to the methods of action research. London:Routladge.

Bell, A. W, J. Costello & D. Kuchemann (1984): A Review Of Research in Mathematical Education: Part of Research On Learning and Teaching. NFER, Nelson,England.

George Polya (1988): How to Solve It. Princeton,NJ: Princeton University Press.

Mok Soon Sang (1996): Pengajian Matematik Untuk Diploma Perguruan. Kuala Lumpur, Kumpulan Budiman Sdn. Bhd.



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