Book · January 994 citations 110 reads 2,264 authors

particular on the strategies and skills of what can be read (Borasi & Siegel,
1990). Part of reading facility involves constructing meaning from written
texts, a task that becomes increasingly central as students progress through
the educational system (see Laborde, 1991, for an interesting account).
One current theme of research on writing involves looking at the issue of
student journal writing as an aid to learning mathematics. Some discussion
of this issue can be found in Borasi and Rose (1989). Waywood (1990,
1992) has formulated an initial classification of types of secondary school
mathematics journal writing as a framework for analysing how journals
might provide a vehicle for student learning. His proposed triple, sequential
categorization of use is: recount (narrative), summary description, dialogue
(between ideas). His aim is one of reflection on learning, and from this
work he has generated the hypothesis that the mode of journal writing
reflects the stance towards learning on the part of the student.
3. COMMUNICATING MATHEMATICALLY IN CLASSROOMS
Since Aiken’s seminal research review in 1972, entitled Language factors
in learning mathematics, the area of mathematical classroom language has
exploded dramatically in the subsequent 20 years, and a comprehensive
bibliography would now run to hundreds of entries. In part, this phenomenal
growth has paralleled the increasing interest in the role of language and so-
cial factors in schooling in general, after decades of relative under-emphasis
during what might be called "the Piagetian years." A contemporary Western
revival of interest in the work of Vygotsky on the one hand (see, e.g.,
Edwards & Mercer, 1988, discussed further below) and the specific exami-
nation of the classroom as a discourse context by linguists on the other (see
Sinclair & Coulthard, 1975; Stubbs, 1983) have altered the research arena
considerably.
In general, since the mid-1970s, techniques of discourse analysis have
been used to examine aspects of classroom discourse, among other linguis-
tic contexts, and to highlight certain normative aspects of language use in
these particular speech settings. One early "finding" by Sinclair and
Coulthard (1975) was the almost incessant repetition of the sequence
DAVID PIMM
161

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I(nitiation) – R(esponse) – F(eedback) in teacher-student exchanges. (In the
excerpt that follows (Yates, 1978), T is the teacher, P refers to any pupil
(student), and they are discussing the problem of finding a means of com-
municating what is on the blackboard (a route map of major cities and mo-
torway links in England) to someone in the next room. I have added my
suggested codings.
P: Morse Code. (R)
T: Morse code, well that is not necessary. We can speak to him – he is only the
other side of the door. (F)
P: Coordinates. (R)
T: Coordinates would be one way of doing it. That would be a very good way of
doing it. What do you mean by coordinates? (F then I)
P: Say five across and down this way. (R)
T: Well that is a very good idea, it is one I had certainly not thought of. Any other
bright ideas? (F then I)
P: Hold up a mirror. (R)
T: Hold up a mirror – it cannot go through a solid door. . . . (F)
A more detailed, analytic account of this I–R–F sequence and some tran-
scripts from lessons in which mathematics teachers have found ways of es-
caping from it is given in Pimm (1987).
However, there has been some concern about discourse analysis’ tech-
nique of ignoring content and attending only to the form of an utterance in
terms of classifying and analysing classroom language. Observations about
what discourse analysis cannot offer are made by Edwards and Mercer
(1988) in their book Common Knowledge. They comment:
It may be thought that a concern with the content of the talk rather than with its
form, and with interpreting people’s meanings rather than coding their turns at
speaking, is an altogether less rigourous and objective way of dealing with dis-
course. (p. 10)
But they then go on to offer three justifications for so doing. These are:
formal discourse analysis does not allow them to answer the questions they
want to ask; their analyses are offered in terms of the data themselves, not
data already coded; discourse analysis itself also needs an interpretative
framework in order to make judgements about coding. One interesting area
of work that I shall mention later involves situations in which mathematics