Paper to be presented at the 3rd APEC-Tsukuba International Conference: Innovation of classroom teaching
and learning through lesson study- focusing on mathematical communication, December 9-14, 2007 at
Tokyo and Kanazawa, Japan.

Mathematical Communication in Malaysian Bilingual Classrooms

LIM, Chap Sam & CHEW, Cheng Meng
School of Educational Studies
Universiti Sains Malaysia
Penang, Malaysia
cslim@usm.myAbstract
This paper begins by arguing the importance of mathematical communication inmathematics teaching and learning. This is then supported by the emphasis ofmathematical communication as stated in Malaysian mathematics curricula. However, theimplementation of mathematical communication in Malaysian bilingual classroom
remains challenging and much to be desired. Possible factors include the proceduralapproach of mathematics teaching and the poor mastery of English language as themedium of instruction for both teachers and students. A proposal of a study to promotemathematical communication will be shared at the end of the paper.

Roles of mathematical communication
Mathematical communication plays a significant role in mathematics education.
As argued by Lindquist and Elliot (1996), “We all need to communicate mathematicallyto fulfil the societal goals of a mathematically literate workforce, lifelong learning,
opportunities for all, and an informed electorate” (p.1). Besides, communication is also
central to students’ learning of mathematics and to the solving of mathematical problems.
During mathematics learning, students need to relate their everyday language tomathematical language and symbols. When solving mathematical problems, students
need to make important connections between concrete information and abstract situation.
Through effective communication students will be able to organize, consolidate andexplain their mathematical thinking coherently and clearly to peers, teachers and others.
They can also analyze and evaluate the mathematical thinking and strategies of others.
In addition, Baroody (1993) proposes two more reasons for focusing on
mathematical communication. First, mathematics is essentially a language by itself.
Mathematics is not only a thinking tool that helps us to discover patterns, solving
problems and drawing conclusions, but also a tool for communicating our thought, avariety of ideas clearly, precisely and succinctly. In fact, mathematics is considered “theuniversal language” (Jacobs, 1982) with its unique symbols and structures. People all- LIM, Chap Sam & CHEW, Cheng Meng 1 -over the world can use it to communicate mathematical information despite differences intheir native languages.
Second, mathematics teaching and learning are social activities that involve at least two
parties, teachers and pupils. In the process of teaching and learning, it is crucial thatthought and ideas are communicated to others through language. Basically thisinterchange of ideas and experiences constitute the process of teaching and learning.
Indeed, communicating with peers is essential for the development of communication
skills so as to learn to think like a mathematician and to solve genuine problems
successfully (Baroody, 1993). Thus, Baroody (1993) proposed that by encouraging
children to talk about their ideas is an excellent way for them to discover gaps,
inconsistencies, or lack of clarity in their thinking. This implies the importance ofensuring pupils be proficient in a language so as to be able to communicate and to learn
well using that language.

Mathematical communication as stated in Malaysian mathematics curriculum
A review of the recent Malaysian primary and secondary school mathematics curriculum
indicate that mathematical communication is one of the essential objectives ofmathematics education. It was stated explicitly as one of the objectives in themathematics curriculum for secondary school mathematics: “able to communicate
mathematically” (Ministry of Education Malaysia p. 3, 2003). It was further elaborated asfollow:
Communication is one way to share ideas and clarify the understanding ofMathematics. Through talking and questioning, mathematical ideas can bereflected upon, discussed and modified. The process of reasoning analyticallyand systematically can help reinforce and strengthen pupils’ knowledge andunderstanding of mathematics to a deeper level. Through effective
communications pupils will become efficient in problem solving and be able toexplain concepts and mathematical skills to their peers and teachers.”(Ministry of Education Malaysia, 2003, p. xvi)
Besides arguing the important role of communication as a way to share ideas and tounderstand mathematics, it also links communication to mathematical thinking andmathematics reasoning such that,
The development of mathematical reasoning is closely linked to the intellectualdevelopment and the communication ability of students. Therefore,
mathematics reasoning skills must be emphasised in all mathematics activities
so that students learn to understand better the world around them. It isimperative, therefore, that these reasoning skills be incorporated inmathematics education so that students learn to recognize, build and evaluate
mathematics conjectures and statements. (Ministry of Education Malaysia,
2003p.1)
Furthermore, the use of precise and accurate mathematical language is also very muchemphasized for efficient communication in mathematics,- LIM, Chap Sam & CHEW, Cheng Meng 2 -When students are giving their opinions and solving problems orally and inwriting, they are guided to use correct language and the accurate mathematics
register. Students are also trained to select information presented either inmathematical language and non-mathematical language; interpret information;
representing this information in the form of tables, graphs, diagrams, equations
or inequalities; and subsequently present this information, without changing
the original meaning, in other forms that are clearly and easily understood.
(Ministry of Education Malaysia, 2003, p.2)

Nevertheless, to what extent is mathematical communication implemented in Malaysianclassrooms?

Mathematical communication in Malaysian classroom
Several local studies examined classroom discourse in some primary (e.g. JamaliahKamal, 2001; Ruzlan Md Ali, 2007) as well as secondary (e.g.Chiew and Lim, 2003)
mathematics classrooms. Their findings coherently point to a Malaysian mathematics
classroom teaching is characterised by “the teacher will present the day’s lesson in theform of questions-answers, or present a brief explanation of the topic through examples,
either taken from textbooks or workbooks, followed by drill exercises.” (Jamaliah, 2001,p.164). Ruzlan (2007) observed the communication styles of two Malaysian primaryteachers when teaching fraction.
“The outcome of his observations indicated (i) all teaching was whole classteaching with teacher doing most of the talking. Pupils were generallyinactive, responding only to the significant number of questions. These
questions were not only of the closed type but could also be conceptualized
as reminder of the procedural to be used when working out the solutions toworked examples, and (ii) The central focus on teaching was on theprocedures and algorithms that pupils should acquire to solve the worked
examples. “ (p.350)
The above data were mostly collected before the latest curriculum reform in mathematics
education. The medium of instruction was then in the national language, which is mothertongue language for the majority of Malaysian students.
However, in January 2003, the Malaysian government took a brave move to switch themedium of instruction for Mathematics and Science to English. This new policy(Teaching of Mathematics and Science in English, or better known as PPSMI) wasimplemented in progressive phases, begin with Primary One, Form One and Lower Six in
2003, and then gradually to encompass all the other levels of the entire school system.
The entire changeover is expected to be completed by 2008 for all primary and secondary
schools in Malaysia.
In brief, there were four rationales (Choong, 2004) that prompted the implementation ofthe PPSMI policy, namely:- LIM, Chap Sam & CHEW, Cheng Meng 3 -a) the significant role of English language as an international language forknowledge acquisition and communication;b) to arrest the decline of the English language proficiency levels among students,
both at the school and the tertiary level;c) to equip future generation with a language that enable them to access new
development and advances in science and technology to meet the challenges ofglobalization; andd) to overcome the increasing challenging task of translating the latest technologicaldevelopments into Malay language.
In conjunction to the change in medium, the PPSMI also aims to reform the mathematics
teaching and learning strategies that promote mathematical thinking and mathematicalcommunication. These aims and emphases were explicitly stated in the latest revision ofmathematics syllabus and curriculum specifications (Ministry of Education Malaysia,2003). Billions of Ringgit Malaysia was allocated to achieve these aims. One major
strategy was providing intensive in-service training programme for teachers through“English for the teaching of Mathematics and Science” (ETeMS) by the English
Language Teacher Centre (ELTC). This was to develop the teachers’ English language
proficiency in order to access the wealth of information on the Mathematics subject area
currently available in English texts. It was also to help the mathematics teachers todevelop the practical competence to deliver their Mathematics subject matter in English.
In addition, information communication technology (ICT) resources such as special
computer courseware, reference and hardware were provided to equip teachers with thelatest technology. Mathematics teachers were given 5-10% critical allowance as special
incentive for teaching mathematics in English.
However, after nearly five years of implementation of this new policy that costconsiderable amount of resources in time, money and effort, have our mathematics
teachers ready to cope with the change? What is the scenario of mathematics discourse inthe Malaysian classroom now?
Gurnam Kaur Sidhu (2005) made ten classroom teaching observations of ten different
mathematics teachers. These teachers were teaching at the primary school level (2 urbanand 2 rural) and secondary level (4 urban and 2 rural). Her findings highlighted two
pertinent issues concerning the language and communication in the mathematics
classrooms. These two issues are (i) linguistic competency of the teachers and (ii)
instructional practice.
Her results showed that rural students possessed very limited English language
proficiency as compared to their urban counterpart. Consequently this changed in themedium of instruction might have resulted in some students having a negative attitude
towards mathematics. One of the teachers that she interviewed added that“…some of them have this psychological block. They entered secondary one
with limited language proficiency and when mathematics classes wereconducted in English, they immediately switched off and this has resulted intheir poor performance in mathematics and their inability to cope. Therefore- LIM, Chap Sam & CHEW, Cheng Meng 4 -it is not surprising that some teachers have opted to explain and clarify
concepts in Bahasa Malaysia”. (p. 55)
Subsequently, she observed code-switching was an increasing common phenomenon in
the mathematics classroom. Compounded with limited English language proficiency,
some teachers tended to use colloquial language during their classroom interactions. For
example:T: okay, can you add 12 and 3, and how much now?
12 story books I get, I have, then yesterday is my birthday, my mummy got
more 3 for me, so now how much I got now? 12 add 3 equal how much? (p.57)
In addition, outcome of her observations indicate that on average the ratio of teacher talkto student talk in the ten observed mathematics lessons was 3:1.
The above phenomena are alarming. Due to language deficiency, teachers and students
might not be able to communicate effectively, more so to communicate mathematicallyusing precise and accurate mathematical language.
In another study, Koh (2006) observed that 27 PPSMI teachers who were using teachingcourseware became so engrossed that there were hardly much interaction between
teachers and students. He quoted an example that a teacher was teaching the topic ofpolygon using a teaching courseware provided by the government. The teacher wasobserved to use only the passive click and show approach without using any further
examples or communication with the students.
All the above reviews, thus, signify the needs to promote more mathematicalcommunication in the mathematics classroom even though it was not just the issue ofmathematics but also the bilingual challenges.

A proposal to promote mathematical thinking and mathematical communication
through lesson study
To gain full benefit of the APEC lesson study project, we have proposed a local study todevelop mathematical thinking and communication in three Malaysian primary schools
based on the APEC project framework. We argue that mathematical thinking andmathematical communication are inter-related and they should be promoted hand-in-hand.
We also rationale that from the review of local studies (see Lim and Hwa, 2006) showthat mathematical thinking has not yet explicitly implemented in many Malaysian schools
due to time constraints and mathematics teachers’ lack of understanding and awarenessabout mathematical thinking. Likewise, as we have discussed in the earlier section, there
is considerably lack of mathematical communication between Malaysian students andteachers. Therefore, there is an urgent need to develop mathematical thinking andcommunication among mathematics teachers before they can foster these two skills
among their students.
To develop mathematical thinking, teachers must provide students with opportunities toacquire mathematical knowledge and skills through mathematical activities such asproblem solving, reasoning and proof, communication, connection and representation- LIM, Chap Sam & CHEW, Cheng Meng 5 -(National Council of Teachers of Mathematics [NCTM], 2000). To implement suchactivity-based learning in mathematics classroom, teachers must plan lessons andteaching approaches that develop and promote mathematical thinking andcommunications in mathematics.
However, as pointed out by Takahashi (2007), “one of the reasons for teachers’ hesitation
to provide activities that cause students to develop mathematical thinking might be thatthe teachers themselves have rarely experienced such lessons when they learned
mathematics themselves” (p.56). Hence, by allowing teachers to experience themselves
activities that foster mathematical thinking and communication through workshops isdeemed an effective way of enhancing teachers’ confidence and competence inmathematical thinking.
To provide enactive experiences, all participating teachers will play the role of students
carrying out the hands-on activities that promote mathematical thinking andcommunication. These activities will be adapted from some Japanese research lessons
and other relevant resources.
In view of the busy working schedule of the school teachers, the workshop will beconducted in a manner of 2-3 hours in alternative weekends or after school hours in weekdays. The workshop activities are distributed in such a way so as to allow time forteachers to absorb and reflect on the new experiences.
The first two workshops aim to provide and develop mathematical thinking andcommunication experiences for the teachers. After all these teachers have acquired a
substantial conceptual understanding and know-how, each school team will
collaboratively plan and design a detailed lesson plan that foster pupils’ mathematicalthinking and mathematical communication in the third workshop. The teaching lesson
will be observed and video-taped for reflection and documentation. This process will be
repeated for at least 3 times to ensure both teachers and pupils have gained sufficientexperience of mathematical thinking and mathematical communication.
We hope to share more about the experiences and outcome of the above study in the next
APEC-Khon Kaen conference.

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