Conceptualizing a Framework for Mathematics Communication in
Malaysian Primary Schools
CHEAH Ui HockSoutheast Asia Ministers of Education Organization
Regional Centre for Education in Science and Mathematics
Penang, Malaysia

In looking into the culture of the mathematics classroom, communication
emerges as an important component to examine and consider.
Communication serves as an important an essential tool for the teacher tolook and probe the pupils thinking. This paper examines some of thepresent practices in schools and suggests a plausible framework forcommunications in the Malaysian primary classroom. Communication is
examined in the context where it is collectively considered together withrich mathematical tasks, environment and lesson evaluation as importantcriteria in the creation of a classroom that focuses on mathematicalthinking. Components for communication for the Malaysian context arealso suggested.
Introduction
The Malaysian National Philosophy of Education (NPE) which was first drafted in 1988
has been the principal guide in the development of the school curriculum across various
disciplines. The NPE states that
Education in Malaysia is an on-going effort towards further developing thepotential of individuals in a holistic and integrated manner, so as toproduce individuals who are intellectually, spiritually, emotionally andphysically balanced and harmonious based on a firm belief in anddevotion to God. Such an effort is designed to produce Malaysian citizens
who are knowledgeable and competent, who possess high moral standards
and who are responsible and capable of achieving a high level of personal
well-being as well as being able to contribute to the betterment of thefamily, society and the nation at large. (Curriculum Development Centre,
2006; p.vi)
While placing importance on the development of a wholesome individual through holistic
education, the national curriculum also highlights the expectation of good citizenship andthe creation of individuals who are able to contribute to society. It is thus seen that withevery curriculum revision, the Ministry of Education (MOE) has also endeavored to keep
up with the changes and trends of education world-wide. This is reflected in the
Mathematics discipline too as was seen in the 2001 revision of the curriculum. Problemsolving, communications, reasoning, connections and application of technology were
explicitly included in the curriculum (Pusat Perkembangan Kurikulum, 2001). These- CHEAH Ui Hock 1 -inclusions, which continue to be included in the latest revision of the curriculum(Curriculum Development Centre, 2006) seem to follow closely the standards asenvisioned by various institutions concerned with the teaching of mathematics (National
Council of Teachers of Mathematics, 2000; Curriculum Planning and Development
Division, 2001; Departemen Pendidikan Nasional, 2003). The inclusion of communications
can be seen as an initiative by the MOE to make mathematics more meaningful andrelevant to children in their pursuit of acquiring mathematical ideas.
Communications in the Malaysian Mathematics Curriculum
Communications in the mathematics curriculum is therefore taken in the context that
school mathematics should collectively highlight the processes of communication
problem solving, reasoning, and making mathematical connections. In clarifying ways ofenhancing mathematical communications the curriculum highlighted three main areas ofcommunication: values and aims of communication, oral communication and written
communication.
Values and aims of communication. Several considerations were suggested which
includes identifying relevant contexts, pupils’ interest and teaching materials, ensuring
active, stimulating meta-cognitive skills, inculcating positive attitudes and creating a
conducive learning environment (Curriculum Development Centre, 2006).
Oral communication. Some of the suggested communication techniques include
story-telling, asking and answering questions, structured and unstructured interviews,
discussions and presentation of assignments.
Written communication. The curriculum suggests communication activities suchas doing exercises, keeping scrap books, keeping folios, undertaking projects and doing
written tests.
State-of-the-Art and Sate-of-the-Practice: The Missing Gaps
While the curriculum does specify various activities that the teacher can use in classroom
communication it does not provide examples nor a model which the teacher can use as a
guide in planning a mathematics lesson. Thus even when the teacher does carry out
communication using the suggested techniques, it may not achieve the desired purpose i.e.
to enhance meaningful acquisition of mathematical ideas. Communication need notalways imply that meaningful mathematical discourse that leads to conceptual
development of mathematical ideas has taken place. As Richards (1991) pointed out,
communication in school mathematics is often trapped in discourse that is focused onteacher-pupil talk that is used to solve habitual unreflective questions. Very often thechildren just attempts to pick answers that the teacher expects without inquiry.
The state-of-the-practice. In a study conducted on 16 secondary mathematics
teachers who were considered effective by the school principals, assistant principals andthe head of departments, it was found that 93.2% of the observation time was spent oninteracting with pupils (Mohd. Majid Konting, 1997). The teaching episodes werecollected though 1,450 observations which covered 604 minutes of teaching time. It was
found that the mathematics teachers spent 93.3% of the time making contacts in theinteraction while the pupils only 1.6% of the time making contacts with the teachers.

- CHEAH Ui Hock 2 -Further the teacher-pupils interactions were more commonly of a low cognitive level.
The findings show that communications in the mathematics classroom were more of aone-way process dictated by the teacher.
In a more recent study on communications in a mathematics classroom, Ruzlan(2007) compared two Malaysian primary lessons on fractions; one in an urban setting
while the other was in a rural school. From the study it was found that there were fourphases that were common in the lessons. The consolidation phase deals mainly with theintroduction to the lesson. During the core-content phase that follows the teacher would
introduce the content. In the study it was found that the content of both lessons were
essentially the same: finding the value, interpreting the symbolism and developing theprocedural proficiency. In the rehearsing phase the pupils would practice solving
problems which were similar to those given in the core-content phase either in the formof board work or seatwork. For board work the students would be called to work on
problems on the board in front of the class. During seatwork the children would remain in
their seats while working on problems similar to the one given during the core-content
phase. The lesson closure phase refers to the activities that bring the lesson to a close.
Figure 1 shows a diagrammatic representation of the progress of the lessons.
In his findings, Ruzlan (2007) further found that all the questions posed by theteachers were the closed-ended in nature, where the children were anticipated to arrive atcertain answers expected by the teachers only. No open-ended questions were found.
Typical of some of the close-ended questions were closed procedural questions (“Alright,
what is one times five?”), close-routine questions (“Do you understand?”), closed
complete-the-statement questions (“Fractions have a numerator and denomina…?”
students complete the statement with “…tor”), closed verification questions (“Is theanswer right?”) and closed terminology questions (“What do we call this fraction?”).
Figure 1 show the progress of the lessons. It can be seen that in both lessons, most of theteaching focus shifted between core-content and rehearsing ultimately emphasizing
procedural competence as the aim of the mathematics lessons. Quite clearly the lessons
were a deep contrast to mathematics learning as intended in the curriculum.
UBT3's Teaching Progress
Consolidation Core-content Rehearsing

R C T 5 's T e a c h in g P ro g re s s
C o n s o lid a tio n C o re -c o n te n t R e h e a rs in g

C lo s u re

Closurei. (3 m in s )i. (12 mins)ii. (3 m in s )ii. (8 mins)

Boardwork

S e a tw o rkiii. (6 m in s )iv . (9 m in s )iii. (9 mins)

S e a tw o rkv . (8 m in s )iv. (7 mins)

Seatworkv i. (4 m in s )v.(11 mins)

S e a tw o rkv ii. (2 4 m in s )vi. (2 mins)

Urban School Settingv iii. (1 m in )Rural School Setting

Figure 1. Teachers use of teaching phases in lessons on fractions (from Ruzlan, 2007).

- CHEAH Ui Hock 3 -Some constraints to consider. In attempting to construct a plausible model forcommunications in the Malaysian primary classroom, it is important to consider someconstraints that tend to impede the conduct of a lesson that focuses a more progressive
approach to mathematical thinking. Lim (2006) highlighted three of these constraints: (1)teachers’ beliefs that it is more efficient to give clear explanations as opposed to allowing
students to work on tasks and construct their own mathematical ideas, (2) theexamination-centered culture that only reinforces teachers’ beliefs about teacher-centeredclassrooms and procedural competency, and (3) the common belief that hard-work and“practice-makes-perfect” as the key ingredient for success in learning mathematics.
In 2003, the MOE made a bold policy change involving the use of English as themedium of instruction in science and mathematics lessons. However, recently there has
been some disquiet towards this policy from several quarters appealing to the MOE torevert the medium of instruction of mathematics back to the mother tongue, claiming that
pupils find it difficult to communicate and understand mathematics when it is instructedusing the English language. Undeniably, any change in the medium of instruction willpose an added constraint to classroom communications as classroom discourse isembedded in the language of instruction. The use of a second language in teachingmathematics has therefore posed a further challenge for teachers as he communicateswith his pupils.
The state-of the-art. Solving mathematical problems is not all about deductive
methods only. In his thesis, Lakatos (1976) argues that heuristics and processes such as
conjecturing, critiquing and providing counterexamples are important processes inmathematical problem solving. While the work of Lakatos (1976) does provides aphilosophical basis for developing a framework for communication in the mathematics
classroom, it would however be difficult to imagine that pupils in the primary school
would be able conjecture and critique to the level as espoused by Lakatos. Mindful that
the Malaysian perception of school is much alike that of the East Asian perspective thatplaces emphasis on product rather that processes, and on effort in achieving success indoing mathematics (Leung, 2000; Lim, Fatimah & Tan, 2003), focusing on mathematicalprocesses would need to consider changing the mindset of the teachers. Teachers would
need to be convinced that focusing on mathematics processes will actually be a better
alternative in producing mathematical success. However if schools were to be the training
ground for future mathematicians, and for the creation of a thinking society that isdeemed necessary in the present age of information technology, then it is inevitable that
acquiring mathematical processes should be one of the important aims of schoolmathematics.
A more plausible model for communication can perhaps be found in Mason,
Burton and Stacey (1982) which looked into the different phases of problem solving andsuggested some heuristics to assist the learner in the problem solving process. Some cuesthat were suggested to assist the learner in problem solving were to clarify what the pupil
already knows and what he needs to know, conjecturing, justifying and convincing, andspecializing and generalizing. The role of the teacher is thus to probe and ask relevant
questions in order to assist the pupil move towards solving the problem. Much of thesuggestions can be seen taking place in the lesson study videos on Japanese classrooms(e.g. Hosomizu, 2006). In the videos the lesson starts with a rich mathematical task

- CHEAH Ui Hock 4 -where the pupils work together to arrive at mathematical ideas and formulas. First theteacher probes the students understanding of the problem; what the students already know,
and what the students want to know in the problem. The teacher then encourages thepupils to suggest solutions and make conjectures. He probes the pupils’ thinking andthoughts, using questions to cleverly invoke the pupils’ thinking until they arrive at thesolution which was acceptable by the teacher.
A plausible framework for communications in the mathematics should placecommunications in the context of the classroom together with other important criteria forplanning a good lesson: rich tasks which enable the pupils to engage in mathematicalthinking, constant evaluation of the lesson by the teacher both during and after the lesson
and the creating of a suitable environment so the mathematical discourse can take place(National Council of Teachers of Mathematics, 1991; Bahagian Pendidikan Guru, 1998).
Figure 2 shows the four important aspects of a lesson focusing mathematical thinking andthe key features of classroom communication. Classroom communication is mutually
influenced by the tasks, the environment and the analysis/evaluation of the lesson and theteacher thus needs to consider classroom communications together with these important
entities of the lesson.
Components of Mathematical Communication in the Primary Classroom
Communication in the classroom brings along with it the values of the community. In thecase of the primary classroom, the teacher who is obviously older, more mature andknowledgeable than the children from the ages of seven to twelve holds the key in valuetransmission in the mathematics classroom. Not only do the pupils learn mathematicalfacts and ideas but they also acquire the informal knowledge about mathematics: what itmeans to study and do mathematics and the values the nature of the subject carries
through the informal activities of the lesson such as through communication (Bishop,
1988). Keeping in mind the constraints and impediments in attempting to carry out amore process-focused mathematics lesson as was discussed earlier, I would like tosuggest the following features that would be appropriate components of communicationin the primary mathematics curriculum in Malaysia:
1. Classroom communication is very much influenced by the multilingual andmulticultural nature of the classroom. Communication on a formal level in
Malaysia is carried out using English which is often the second language for boththe teachers and pupils. Granted that there is a growing urban middle-class thatspeaks English at home, it is however generally an uncommon occurrence in
Malaysia.
2. Communication can be enhanced through various means of representation, suchas through symbols, diagrams, drawings, charts and graphs which are commonlyused in mathematics. This feature becomes an even more important consideration
when mathematical communication is carried out in a second language.

- CHEAH Ui Hock 5 -Rich Mathematical
Tasks

Communication

Lesson Focusing
Mathematical Thinking

Environment

Analysis/ Evaluation

•
•
•
•
•
•
•
•
•

Do the pupils understand the given task?
Are the assumptions pupils make the same as implied in
the task?
Allow students to clarify the assumptions. Teacher toclarify pupils’ understanding of the assumptions.
Allow pupils to work on task towards a solution and makeconjectures.
Use of various means of representations for elaborationand clarification.
Allow pupils to explain solutions and conjectures
Listen, understand and look for gaps in pupils’
explanation.
Probe and test pupils’ conjectures by providing examples
and counter-examples. Encourage pupils to provide
examples and counterexamples.
Encourage pupils to test the heuristic/algorithms used.

Tools:
Story- telling
Problem-solving
Discussions
Assignments
Projects
Scrap-books
FoliosInvestigations
Exercises
Tests

Figure 2. A framework for communications in the Malaysian primary mathematics
classroom.

3. Communication is dialectic and to encourage its use in the classroom, teachers
need to develop a belief that even when they are in authority; there is a need toempower the pupils and coax them into dialogue. This would mean that teachers
should patiently probe pupils’ thinking through questioning and allowing andencouraging pupils to elaborate on their ideas instead of just telling.

- CHEAH Ui Hock 6 -4. Communication in the mathematics classroom ought to promote the value thatmathematics is rationale. What is acceptable as right in the classroom is not
through authority but rather through reasoning and logical arguments?
5. Communication is used as a means of promoting the idea that mathematicalknowledge is developed through collaboration and not by authority.

Conclusion
Communication is an essential part of the mathematical classroom. Students may use
verbal language to communicate their thoughts, extend thinking, and understandmathematical concepts. They may also use written language to explain, reason, andprocess their thinking of mathematical ideas. Communication thus becomes a tool which
can assist pupils to form questions or ideas about concepts. Classroom communication istherefore one of the key components in a classroom that focuses on promoting
mathematical thinking. As the teacher is unable to see directly what the pupil thinks,
communication then becomes a window to view the pupil thought processes. Throughcommunication the teacher is then able to coax and guide the pupil to develop further hismathematical thinking. Therefore communication is a necessary and importantcomponent to be analyzed in the Lesson Study as improved mathematical thinking is verymuch dependent on good classroom communication.

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- CHEAH Ui Hock 8 -