Mathematics Education Research journal 1996, Vol. 8, No. 1, 1-3

Editorial

Communication: Assumptions and Responsibilitiesof Mathematics Education Researchers

Nerida F. Ellerton

Few would disagree that communication is of fundamental importance to mostpeople, regardless of their role in society. Further, the nature, quality and length ofspecific communication between individuals and groups can vary widely.

Communication can also be implicit or explicit. The teacher who is quoted assaying "This is wrong, you have to calculate it over ágain" (Alro & Skovsmose,1996) is communicating explicitly via a direct command to a student. In addition,the teacher's philosophy about mathematics is being communicated immiplicitly viathe same statement.

We communicate the results of mathematics education research explicitly in theform of journal papers, conference presentations, and in books and chapters inbooks. We present seminars to various audiences, and we discuss different aspectsof research with our students. But implicit in each person's mode ofcommunication is that person's underlying philosophy of mathematics educationresearch.

Freudenthal (1981) pointed out that "education problems are problems of lifearising from changing needs, moods and whims of a changing society" (p. 133). Sonot only are we, as researchers, communicating our research in explicit and implicitways, but we are being influenced in this process by "a changing society."

Communication as a Two-Way Process

Communication, by definition, has both an initiator and a receiver. Thus notonly does the philosophy of the initiator affect the way in which thecommunication is presented, but the philosophy of the receiver effectively filterswhat is being communicated. A process which can be superficially assumed to besimple—person A communicating with person B—is actually an extremelycomplex process.

Why am I concerned about this complexity? I believe that, because of differentphilosophies of communicator and communicatee, we are actually, often, not really"communicating" at all! Thus when we think we are sharing the results of ourresearch with others, we are actually only sharing the ideas with a very limitednumber of "receivers" who share similar education philósophies to ourselves. Ineffect, the question which needs to be asked is whether we are really onlycommunicating with a very small group of researchers rather than the largercommunity of mathematics educators. And if this is the case, then how can thiscommunication net be broadened?

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Language and Cultural Factors in Mathematics Education Research

I shall illustrate what I am talking about by referring to the literature on"language factors in mathematics learning." Whát are the implications ofconsidering language factors in the communication of mathematics educationresearch? I have chosen three themes in the language and mathematics teachingand learning area to provide a framework.

Words and meaning: It was Brune (1953) who talked of words as "links in thechain of communication" (p. 160), and of mathematical words often representing"mental constructs rather than tangibles" (p. 161). Thus when we considermathematics education research, we are likely to be dealing with mental constructsof mental constructs. Perhaps it is this notion which inspired Freudenthal (1981) towrite:

Both in mathematical and educational research, production is high. The difference isthat the retrieval of good and relevant research is easy in mathematics and almostimpossible in education. (p. 149)

Freudenthal was very critical of what he called "wasting the vast resources ofhuman experience" (p. 135).

The meaning of words is often context specific. The difficulty encountered bysome students in understanding mathematical language is often attributed to alack of understanding (and sometimes confusion over the meaning) of specificwords when they are used in a mathematical context. In a similar way, I believe, weare in danger of developing specialised languages within the broad framework ofmathematics education research which are used to communicate with and betweenonly a narrow range of people who use the same genre. In the previous section Ispoke of difficulties in communication which may arise because of differentphilosophies of communicator and communicatee; here it is the use of differentgenres which may cause similar difficulties.

Writing in mathematics education research. It is one thing to hear about theresearch which others are conducting; it is another to talk about your research (orthe research of others). What opportunities do mathematics education researchershave to explain their attempts at research in the appropriate language register?Most of the time, mathematics education researchers are reading what others havewritten, or listening to presentations by those experienced in research.Opportunities for expression are sometimes quite limited, especially for those newto mathematics education research. Synthesising what one has read and applying itto one's own unique context is non trivial. This points to an area of professionaldevelopment which I believe is seriously neglected in the postgraduate area—thatof delving beyond the superficial reporting of what others write in the literature,and of starting to form links between what different researchers write fromdifferent perspectives.

Bruner. (1996) included a chapter in his book titled "Narratives of science." Hetalked about "good science teachers" who put the emphasis on "live science"rather than on "the achieved remains of, so to speak, already accomplishedscience" (p. 127). He also proposed narrative "as a mode of thinking, as a structurefor organising our knowledge, and, as a vehicle in the process of education"

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(p. 119). In mathematics education research, I believe we are in danger of losingsight of the importance of narrative in the fabric of our lives—we have lost the artof telling a story. Rather than describing the "sequence of events" and the "impliedevaluation of the events recounted" which Bruner articulates as the centralelements of a "story" (p. 121), the reporting of research can slip into an economy ofwords and an efficiency of reporting that is neither particularly informative norinspirational.

How often have you picked up a research article which you found hard to putdown because of the way it captured your interest? Bruner (1996) pointed out theinherent ambiguity in our lives: we dedicate huge eifort into the teaching ofscientific approaches and rational thinking—yet "we live most of our lives in aworld constructed according to the rules and devices of narrative" (p. 149).

The culture of mathenuztics education research. Our very existence in the worlddepends largely on effective communication between different cultures.Mathematics education research is not culture free as has often been assumed.Communication between the difference "cultures" of mathematics educationresearch is essential if the different cultures are to survive.

Cultural difference is a feature of our world which helps to distinguish us asindividuals, yet it is individuals who continue - to mould culture. Clearly, then,there is a tension between the apparent need for us to identify with a particularculture, and the importance of communicating effectively across cultures.

This, I suggest, is one of the greatest barriers to moving mathematics educationresearch out of the rut of self-complacency. Many pockets of research havedeveloped established "cultures" which self-generate new members. But it isdifficult to step outside any particular culture and ask whether the combined"mini-cultures" within mathematics education research are really making adifference to the teaching and learning of mathematics in schools.

Unless we, as mathematics education researchers, take up challenges such asthese, however, we are likely to continue to talk only to each other, and listen toeach other, but never really communicate with each other in the truest sense of theword.

ReferencesAlro, H., & Skovsmose, O. (1996). On the right track. For the Learning of Mathematics,

16(1),2-8, 22.Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies 111

Mathematics, 12(2),133-150.Brune, J. H. (1953). Language in mathematics. In H. F. Fehr (Ed.), The learning of Inathernatics:

Its theory and practice (pp. 156-191). Washington, DC: National Council of Teachers ofMathematics.

Bruner, J. (1996). The culture of education. Cambridge: Harvard University Press.