Teacher Feature...
Classrooms as Discourse Communities
by Daniel Chang
Communication is an outward extension of thought. It helps in the process of arranging thought, linking one idea to another. Often communication gives access to information or alternative ideas that help understanding, as in discussion, in listening to someone else or in reading a book.
Communication includes both verbal and non-verbal forms. Verbal, that is, language in written and spoken form; and non-verbal, that is, language in conventional symbols and ways of representation through drawings and diagrams.
Griffiths and Clyne (1994) categorised communication modes as:
- Spoken language (speaking and listening)
- Written language (reading and writing)
- Graphic representation (diagrams, pictures, graphs)
- The 'active' mode (performing, demonstrating and physical involvement)
Each mode is said to have 2 aspects namely, receptive mode, that is, involving the interpretation of someone else's communication; and expressive mode, that is, using one's own familiar language.
Discourse is a form of communication either in spoken or written form. The types of discourse are such as, discussion, asking and answering questions, story telling, genres, novels and debates. Discourse in a classroom can be divided into 4 structures namely, initiation-response-evaluation (IRE), instructions, probing questions and argumentation. IRE may possess a traditional pattern of discourse such that the teacher asks a question, the student answers and the teacher evaluates. The teacher continues to ask another question and so the sequence continues. The students' responses are usually brief and the main concern of the students is to provide the answer that is expected by the teacher. The teacher's role is to ask questions in order to pursue the desired answer but only a few students are actively involved.
Giving instructions is another type of discourse, which is monopolised by the teacher. The teacher gives either directive or informative statements. The students do not respond verbally, however, they understand the statements as instructions by following them physically.
The next discourse structure is probing questions. It is a more complex structure with less-well defined rules. The teacher asks referential questions or thinking questions and the students are encouraged to give longer answers through their thinking. Their answers may challenge the teacher's position. However, evaluation does not come immediately after the students' responses. The teacher may express praise for the process the students have followed and he does not pursue the correct aggressively.
Argumentation is more or less like probing questions where the teacher challenges the student in order to have him to justify his reason. The questions asked are normally referential questions, which try to invoke predictions, explanations and clarification from the student. The argumentation may be in question or statement forms.
According to the Professional Standards for Teaching Mathematics, communication and discourse are taken into account for the current trend of teaching mathematics (NCTM 1989,1991). The Standards define discourse as the ways of representing, thinking, talking, agreeing and disagreeing that students and teachers engage in as they do mathematics. The discourse of the classroom is shaped by the tasks, environment, teachers and students.
The Standards identify three of the six standards of the teaching mathematics, which discuss the notions of classrooms as discourse communities and of teachers as facilitators of mathematical discourse. The three sections are Teacher's Role in Discourse, Student's Role in Discourse, and Tools for Enhancing Discourse.
The teacher of mathematics, for example, has a central role in orchestrating the oral and written discourse in ways that contribute to students' understanding of mathematics. The teacher will ask questions and give tasks that elicit, engage and challenge the students' thinking. The teacher's role is not the same as the traditional mathematics instruction where, the teacher transmits knowledge, corrects students' mistakes and expects students to learn alone in silence.
It is important for the teacher to take interest of the students' ideas and ask them to clarify and justify their ideas either in oral or written form. This will establish a discourse centred on reasoning if the teacher continuously encourages students to explain and elaborate their ideas, without too much criticising and giving negative evaluations. The teacher himself also has to be a good listener and accept the ideas contributed. However, the teacher should know how to pick up the important points and filter out unnecessary ones, in order to promote favourable student learning. At the same time, teachers can provide information that the students might need to know. It is also the teacher's decision when to lead and to let students struggle in order to make sense of an idea or a problem without much help from the teacher; when to ask leading questions and when to tell students something directly. These are some of the teacher's roles in order to orchestrate a productive classroom discourse.
The teacher should also monitor and engage every student to participate in discussions either in small groups or whole class. Students who always volunteer to talk and good at expressing themselves should not be called upon all the time. Every student should be encouraged and given chances to participate. The teacher should think of a variety of ways for students to contribute their ideas using means like, written or pictorial forms, concrete objects as well as orally.
The nature of the classroom discourse can influence what the students learn. The student's role is to listen to, respond to, and question one another while working in small or large groups. In other words, students should be the audience for one another's comments. It is necessary for the students to contribute their own ideas and try to convince others to accept it.
Besides talking to one another, students should respond to the teacher. The flow of ideas and knowledge is mainly only from the teacher to students if the teacher talks the most. Ideas and knowledge will be developed collaboratively when students make public conjectures and reason with others about certain problems.
In a mathematics class, for example, the students should engage in making conjectures, proposing ways to solve the problems and arguing about the validity of particular claims. They should learn to verify, revise, and discard claims on the basis of mathematical evidence and use a variety of mathematical tools.
To enhance the discourse in the classroom, a teacher should encourage and accept the use of a variety of tools and other technology devices. In a mathematical class, the teacher should help students learn to use calculators and computers as tools for mathematical discourse. A mathematics teacher should encourage students to use drawings, diagrams, tables, graphs, invented symbols and analogies as means for communicating about mathematics. Students should be allowed to choose the means they find most useful for working on or discussing a particular mathematical problem. At other times, teacher may specify the means the students are to use in order to develop the students' repertoire of mathematical tools.
Take for example an activity where the teacher gives a graph to the students in small groups. Their task is to write a creative story about a person having a bath that 'fits' the given graph (Ellerton & Clements, 1991). The teacher has enhanced the discourse of the students by asking them to write a story through interpretation of the graph, provided the students have already a clear concept about graphs. Then the students are asked to present their story orally in whole group. The teacher may ask a different group to dramatise their story. Through such activities, this will broaden and deepen the students' understanding in using the 'expressive language' (Del Campo & Clements, 1987).
The classroom discourse pattern may be worrying in Brunei Darussalam. Most of the discourse is likely to be monopolised by the teachers in the upper primary levels. Primary 4, for instance, is a transition level where there is a switch of instruction. The medium of communication used is English for most of the subjects taught. Students may find it difficult to adapt to a sudden change of instructions mostly in English. As a result, the teachers are the ones who will probably do most of the talking, and students tend to keep quiet and just listen to the teachers. The students may become less expressive with their ideas in words in fear of using the English Language incorrectly. Consequently, the introduction of the BBC (Bruneian Bilingual Child) Project since 1998 (Ferrer, Lampoh & Chong, 1999) will help to expose the students to both Malay and English languages in the lower primary classes. Teachers use code-switching method so that the students may learn both languages at the same time. This project may probably help the students to be confident in using the English Language when they are promoted to Primary 4.
The idea of using code-switching during the mathematics lesson in a discourse can be considered. This is because according to Setati (1996,1998), code-switching enables learners to interact mathematically with one another. She argued that if the language of a learner was not used regularly in mathematical discourse, then, almost certainly, mathematics would remain formal and procedural for that learner.
Then again the teacher should not only use mathematical symbols and terminology types of language in teaching of mathematics. Sierpinska (1994) stated that teachers should employ a mixture of everyday spoken language, didactical jargon and technical mathematical terms in their communication with the students. This would probably help the students to have a better understanding of the lesson.
In order to develop an effective discourse community in the classroom, the reform vision discussed by the Professional Standards for Teaching of Mathematics (NCTM, 1989, 1991) namely, the Teacher's Role in Discourse, the Student's Role in Discourse and Tools for Enhancing Discourse, could be implemented in the mathematics class in Brunei Darussalam. As one of the aims given in the Mathematics Syllabus for the Upper Primary Schools of Brunei Darussalam (1992) stated that "To encourage socialization (through interaction and communication)", it is important for the teachers of mathematics to encourage the pupils to carry out proper discourse while learning the subject.
In conclusion, it is not an easy task to "build up" a successful discourse community in a classroom overnight. Teachers have to undertake many challenges in order to create a classroom environment that is conducive for interaction among the students, and teacher with the students where thinking and speaking are involved. To prompt students to speak in a mathematics class, for instance, the teacher should not criticise if the students make mistakes. A sensitive teacher will always apply his or her knowledge of educational psychology to correct and the students' errors, so that the students will not become withdrawn and stop participating in other discourse activities.
At the same time, teachers also help to build up collaborative communities where students learn to work in groups. They will learn to help one another in solving problems, and not becoming self-centred in the learning of mathematics.
However, many teachers might probably be confronted with dilemmas and difficulties with such ideas of promoting discourse communities in the classroom. The main reason is that teachers may have limitations associated with the ways in which they have learned the formal mathematics they know. In order to lead a successful discourse community, teachers need to have broad, deep, flexible knowledge of content and pedagogical alternatives. Also teachers need to be supported by their colleagues and supervisors, so that they will feel that they can operate in a safe and supportive environment.
References
Ball, G. (1990). Talking And Learning: Primary Maths for the National Curriculum. Great Britain: Simon & Schuster Education.
Brissenden, T. (1988). Talking About Mathematics. Great Britain: Basil Blackwell Ltd.
Del Campo, G., & Clements, M. A. (1987). A Manual for the Professional Development of Teachers of Beginning Mathematics. Melbourne: Catholic Education Office of Victoria and Association of Independent Schools of Victoria.
Ellerton, N. F., & Clements, M. A. (1991). Mathematics in Language: A Review of Language Factors in Mathematics Learning. Geelong, Victoria: Deakin University Press.
Ferrer, L. M., Abdullah, L., & Chong, N. (1999) 'Promoting Language and Collaboration in Science and Mathematics Classroom' in Leong Yong Pak & M.A. Clements (Eds.) Proceedings of the Fourth Annual Conference of Science and Mathematics Education. Brunei: UBD.
Griffths, R., & Clyne, M. (1994). Language in the Mathematics Classroom. Armadale, Victoria: Eleanor Curtain Publishing.
Mousley, J., & Marks, G. (1987). Discourses in Mathematics. Geelong, Victoria: Deakin University Press.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards For School Mathematics. Reston, Va.: National Council of Teachers of Mathematics.
_______. (1991). Professional Standards for the Teaching of Mathematics. Reston, Va.: National Council of Teachers of Mathematics.
Setati, M. (1996). Code-switching and mathematical meaning in a senior primary class of Second language learners. M.Ed. research report, University of the Witwatersrand.
_______. (1998). 'Code-switching in a senior primary class of second-language mathematics learners' in For the Learning of Mathematics, 18(1), pp.34-40.
Sierpinska, A. (1994) Understanding in Mathematics. London: The Falmer Press.
Silver, E. A., & Smith, M.S. (1996). 'Building Discourse Communities in Mathematics Classrooms: A Worthwhile but Challenging Journey in Elliot, P.C., & Kenney, M. J. (Eds.) Communication in Mathematics, K-12 and Beyond, NCTM Yearbook. Reston, Va: National Council of Teachers of Mathematics.
(1992). Mathematics Syllabus: Upper Primary Schools. Curriculum Development, Ministry of Education. Brunei Darussalam.
http://eric-web.tc.columbia.edu/
monographs/ti17_issues.html
http://www.nctm.org/corners/researchers/
research/rme_clip_discourse.html
http://standards.nctm.org/Previous/
ProfStds/TeachMath_discourse.html
| 
