Revised Version

COMMUNICATION IN MATHEMATICS: THE ROLE 0F
LANGUAGE AND ITS CONSEQUENCES FOR ENGLISH AS
SECOND LANGUAGE STUDENTS
Madihah KhalidMohd Khairul Amilin Tengah
Universiti Brunei Darussalam
This paper will look at the emphasis on communication in the new Brunei mathematics curriculumfor primary schools, the components of mathematics communication to be developed and theapproaches to develop communication among Bruneian students as stated and suggested in the newcurriculum document. This paper will also present problems pertaining to Bruneian students interms of communicating using a second language because mathematics is taught in English inBrunei while most of the students are second language users of English.

INTRODUCTION
Renewed emphasis on communication was apparent in recent years as open-endedteaching and the teaching of mathematics via problem solving becomes more popular.
This kind of teaching processes requires a look at language in mathematics education.
The importance of language in the learning of mathematics has always been
underestimated as mathematics has always been thought of as a solitary subject, andthe belief that mathematics is mechanical, not creative. However, this thinking isslowly changing in tandem with the emphasis on process-based teaching approach
represented by communication in the classroom. Developing classroom
communication is important because it helps in the development of thinking ability(first announcement, 2007). Mathematics is the most appropriate subject to develop
communications because both mathematical way of communication andmathematical thinking is necessary for students to achieve success in life especiallywhen working in real-life.
Brunei Darussalam employs English as a medium of instruction for teachingmathematics from elementary to tertiary level. Mathematics used to be taught in theNational Language in the first three years of the elementary level. However, fromnext year onwards, mathematics will be taught in English starting from the lowestlevel. As a second or third language for many students and with the greater emphasison communication, it is a wonder if this will affect students’ performance inmathematics. If so, then what is the best strategy to minimize this effect?
WHY DO WE FOCUS ON MATHEMATICAL COMMUNICATION?
With the adoption of a constructivist philosophy, mathematics educators now
advocate more active learning on the part of students and a more facilitative role forteachers. A key component of most new instructional strategies is that students are- Madihah Khalid 1 -Revised Version

expected to discuss mathematics with their peers and their teachers. This newemphasis upon mathematical communication is a challenge for teachers and students
in classrooms everywhere. Esty (1992), citing Kaput (1988), regarded the language
used in mathematics as both a means of communication and an instrument of thought.
The new Brunei Primary Mathematics Curriculum specifically mentioned
communication as one of the processes that need to be developed with the teaching ofmathematical content. In fact, together with mathematical thinking, the ability tocommunicate findings and provide explanations is considered as an important
outcome of education (CDD, 2006). Figure 1 shows the role of communication in theteaching and learning of mathematics as shown in the conceptual framework of the
new mathematics primary curriculum of Brunei Darussalam.

According to the document, mathematics provides a powerful means ofcommunication which can be used to present information in figures, tables, charts,graphs and symbols (CDD, 2006, p. 2) and the process of communication is to be
developed at the same time with the teaching of mathematics content together withother skills such as mathematical skills and problem solving.
Among the main aims stated in the mathematics curriculum is to develop children’sability to interpret and communicate mathematical ideas. In addition, the document- Madihah Khalid 2 -Revised Version

also stated that among the main objective of the curriculum is to provide learners
with the opportunity to develop the ability to communicate mathematical ideas
clearly and work with others and value their contribution (CDD, 2006, p.3).
The emphasis of communication in the syllabus is also reflected in the suggested
assessment and evaluation method. Continuous school-based assessment is supposed
to include assessment tasks that have the communication component and are as
follows:• Class discussions or oral presentations• Written assignments• Creative work
• Use of ICT(CDD, 2006, p.3 )WHAT ARE YOUR COMPONENTS OF MATHEMATICALCOMMUNICATION TO DEVELOP?
The first announcement (2007) for this conference mentioned that communication inmathematics can be in the form of argumentation as well as communication whereargumentation involves knowing what mathematical proofs are, while the latter
involves expressing oneself. The sub-processes of communication mentioned in theBruneian primary mathematics curriculum are written communication, oral
communication and using ICT (CDD, 2006, p. 5). It can be contended that we needboth oral and written communication to argue and communicate about mathematics
and with the presence and popularity of the new technology, ICT can be brought in to
help make communication effortless. I am excited with the prospect and current
situation of ICT in helping our children to communicate better especially for students
with English as a second language.
As mentioned before, language is considered as an instrument of thought, and manystudies have shown that the interaction of the procedural knowledge and language
facility in mathematics significantly contribute to conceptual development (Aiken,1972). Therefore, communication through language would benefit students to makesense of topics in mathematics taught by teachers through procedural knowledge.
Mathematics teaching style in Brunei has been critiqued as very procedural andalgorithmic and students resort to rote memorization in preparation for examination(Clements, 2002). Communicating in mathematics classes is supposed to change thissituation and make students learn with better understanding. Conceptual
understanding develops when students reason out or justify their thinking using thelanguage of mathematics, which is made up of the everyday language used together
with a set of special vocabulary, symbols, tables, graphs etc.
In the instructional approach section of the primary mathematics curriculum for
Brunei Darussalam (CDD, 2006), among the six modes of representation strongly- Madihah Khalid 3 -Revised Version

recommended is the verbal representation and this mode refers to thinking about, andcommunicating mathematical ideas, where children need to be able to interpretstatements made by others, state their own ideas, clarify meanings and constructsimple arguments (CDD, p. 7). Other representations such as concrete, diagrams,
real-world, ICT and symbolic will help in clarifying meanings and makecommunication more varied.
From the social constructivist perspective, cognitive development of mathematics ina classroom is socially constructed by students from their past experiences and fromteachers through communication. It is therefore necessary for students to participate
actively in a conversational interaction that goes in a mathematics classroom to beable to “make sense” of mathematics. For Vygotsky (1978), “thought is not merely
expressed in words; it comes into existence through them” (p. 218). A student
working alone on a problem depends entirely on self-mediation of previously
appropriated mathematical knowledge, while another student working with friends
and employing teachers’ help receives additional help from interactive mathematicalmeaning mediation. Vygotsky (1978) again stressed that learning takes place when
the learner first collaborates with an adult or more competent peer to accomplish atask just beyond the learner's level of independent functioning, within the "zone ofproximal development."
The question remains as to what is the implication of the social constructivist
philosophy to students studying mathematics in a second language and what are thebest approaches for them to feel comfortable communicating.
WHAT KINDS OF APPROACH WILL YOU PREFER TO DEVELOP THECOMMUNICATION IN CLASSROOM?
In any mathematics lesson, communication cannot be separated from problem
solving and mathematical thinking. In a problem solving process, besides playing arole as an instrument for thinking mathematically, language is also important forverbal representations, and together with other representations such as diagrams,
concrete materials, symbols, and ICT, students should be communicating effectively.
However, this kind of scenario is not happening in Brunei. Students are reluctant tospeak in class and this is recognized by Martin (1996) when he said that apart fromthe choral chanting, there is very little verbal output by students in Brunei classroom,
which to him is a disturbing feature. He added that when there is verbal output it isvery often in the form of simple verbal recall statements. Single word responses
generally do not promote students’ thinking ability. Is it the language that isabstaining our students from speaking up or is it the culture? Salleh (2005) suggeststhat despite being very expressive, pupils in the Bruneian culture are not used togiving their views in a classroom setting. Therefore, what is the best model toenhance communication in mathematics in the Bruneian context?
The document from Curriculum Development Department (CDD, 2006) suggests
classroom layout and seating arrangement as in Figures 2A and 2B. This kind of- Madihah Khalid 4 -Revised Version

seating arrangement favors small group discussion and I think is a good way toencourage communication between students. Small group format is also favored byBrenner (1998), who thinks that for many language minority students in California, it
may prove to be a comfortable and culturally appropriate instructional format. This isalso the format for cooperative learning, which can be a recommended learningteachnique for students in Brunei.

Peers working together are able to describe their problem solving processes. They arealso able to reflect upon them or otherwise support each others' problem solving
performance. In addition to benefiting from peer interactions because peers can be asource of help, other work suggests that students benefit from hearing a variety ofdifferent perspectives about a problem solving situation. The normal seating
arrangement in traditional classrooms sometimes prevents students from participating
in classroom discussions. They feel intimidated or uncomfortable when spotlighted
and would prefer to keep quiet rather than make mistakes. These classroom
arrangements are also suitable for large group instruction when the teacher feels theneed to address everybody in the classroom.
Another approach that can encourage communication in the classroom is by giving
more open a problem. It is said that the more open-ended a problem is, the more
students would communicate, because students would come up with multiple
strategies or multiple solutions to discuss about. Nowadays, teachers have no excuse
in finding open-ended problem since it is quite easy for them to source for openended problems from books and internet.
Communication during teaching should mirror the authentic communication in thereal world (Noraini, 1999) and with the curriculum’s emphasis on real world
representation, problems posed in problem solving classes need to be as close to thereal world as possible. This is another aspect of problem selection that teachers needto take into consideration. The ability to communicate is not exclusively dependent
on linguistic competence but may rely extensively on external factors and- Madihah Khalid 5 -Revised Version

conceptions such as students’ understanding of concept, procedures, social dynamics,
prior knowledge and experience etc. Successful communication depends on theanalysis of what is particular about the activity and setting. Communication for aparticular lesson fails when students just ask other students for answers or when thechatter that is heard is about something else other than the topic that is being
discussed or not about mathematics at all.
Lastly, besides writing reports for projects and presenting them, writing aboutmathematics should be made a regular feature in the mathematics classroom, either inthe form of essay or journal writing for reflection and for the purpose of assessment.
LANGUAGE AND ITS CONSEQUENCES TO SECOND LANGUAGE USERS
Brunei has adopted English as a medium of instruction in almost every subject fromelementary to tertiary levels. However, with limited English proficiency, pupils in
Brunei usually have difficulty in trying to understand their teacher and evenmathematics word problems found in books and tests. Teachers are more comfortablecode-switching between English and Malay in the classroom or when speaking innormal circumstances. Many times, they take the easy way out by translating theproblems into Malay and end up having students (especially those in the lower abilityclasses) expecting teachers to translate all problems before they start working on it. A
major reason cited for students’ poor performance in solving word problems is thatstudents are not able to understand the problems. Some teachers resort to teaching
using key words and this has been known to bring detrimental consequences (Sainah,1998; Clements, 1999). If too much weight is placed on key words, students arelikely to become confused.
Classes in Brunei are still highly teacher-centred. According to Brenner (1998) where
she quoted Cohen and Tellez (1994), teachers who have a transmissionist philosophy,
i.e., the belief that students need to be told academic content in lieu of constructing it,
are unlikely to use small groups in their classes, and in most of the lessons that I haveobserved in Brunei, teachers have the tendency to spoon-feed (telling everything or
sometimes explain) rather than question or ask students to give reasons. Students
seldom ask questions and would answer teachers’ questions with one word answer,
and teachers seemed happy to get chorus answers.
Salleh (2005) suggested that the direct effect of code-switching from English to
Malay has led to the expansion of the English vocabulary not being emphasized,
despite it being essential to cope with the demands of the curriculum. Since thequality of student teacher interaction influences students’ mathematicalunderstanding, then it is not surprising for students to resort to rote learning to passexaminations.
The study by Brenner (1998) found that ESL students in her study were observed tocommunicate in the computer lab when they were not seen to be communicating
mathematically during the large group instruction or in small group discussions. In
the lab setting of the study, students were paired up to work on limited number of- Madihah Khalid 6 -Revised Versioncomputers. The students had to rely more upon their own resources rather than
external help because it was difficult to attract teacher’s attention. The computer itself
seemed to be engaging for the students. Unlike most class days, the students talked
about mathematics for the entire class period with little irrelevant talk interspersed.
This is an encouraging sign for Brunei since ICT is one of the modes ofrepresentations that are emphasized in the new curriculum and the ministry ofeducation has taken the initiatives to equipped schools with computers. The mostrecent innovation by the ministry is the introduction of MOBITEL (mobile notebookswith LCD projector), where each secondary and primary school in Brunei is provided
with forty and twenty computers respectively.
According to Brenner (1998) again, other authors including Hoyles, Sutherland andHealy (1991) have also noted that working on the computer tends to increase thequantity and quality of student discussion. It has already been suggested in this paperthat the altered participant structure in the computer lab made inter-student
communication more necessary since there were fewer sources of help from outside
the student group. More speculatively, it is possible that the computer also provides
support for students who are just beginning to communicate about mathematics. One
challenge for students who are learning to talk about mathematics is that they must
learn to externalize cognitive processes which they previously accomplished assolitary activities while doing individual seatwork. The computer makes more of thisvisible as students monitor each others' keystrokes and the subsequent outcomes on
the computer screen. The resultant discussion may also seem like less of a discussion
about an individual's private thoughts, since the computer appears to do some of the`cognitive' work (Brenner, 1998). She then quoted Dixon (1995) who has shown thatstrategic use of the computer in mathematics classes can also enhance theachievement of LEP students in classes with English-speaking peers.
DISCUSSION AND CONCLUSION
Anyone who has paid attention to the direction that math has taken over the last
several years will notice that it is highly verbal. Teachers should take note of thechanges and try to apply the suggestions written in the curriculum document,
otherwise pupils who are not used to giving their views in class won’t communicate
in mathematics lessons. Teachers play a big role in encouraging and determining thesuccess of communication in any class. They should encourage students to makeconjectures, to generate generalizations, or to compare alternative solutions. However,in order to do this, teachers need training and support from the appropriate people.
Training in the form of teacher professional development should be held every now
and then by the Curriculum Development department and Sultan Hassanal BolkiahInstitute of Education of Universiti Brunei Darussalam.
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Brenner, M.E (1998). Development of mathematical communication in problem solving
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