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Didactics of Mathematics as a Scientific Discipline, 159-169.
© 1994 Dordrecht: Kluwer Academic Publishers. Printed in the Netherlands.
David Pimm
Milton Keynes

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Frye (1963) has written:". . . the language of mathematics, which is really
one of the languages of the imagination, along with literature and music."
However, in this chapter, after a few broader illustrations of the area in gen-
eral, I shall focus particularly on issues of mathematics classroom language
– though it is an interesting open question concerning how the fact that it is
mathematics that is under discussion shapes and influences all of the lan-
guage forms and functions that are customarily employed.
2. CHANNELS OF MATHEMATICAL COMMUNICATION
The teaching and learning of mathematics involves the activities of reading
and writing, listening and discussing. Each of these linguistic aspects of
classrooms has engendered considerable work. A few items in each activity
are mentioned here.
Since the early 1980s, discussion in mathematics classrooms and teacher
gambits to promote and facilitate it have moved onto the educational agen-
das in some Western countries (e.g., in the UK, with the Cockcroft report,
DES, 1982; in the US, with the publication of the NCTM Standards docu-
ment, 1989). Various attempts to specify which parts of classroom talk are
to count as mathematical discussion have been proposed. For instance, Pirie
and Schwarzenberger (1988, p. 461) offer: "It [mathematical discussion] is
purposeful talk on a mathematical subject in which there are genuine pupil
contributions and interaction."
However, there is still the vexed question of the particular contributions
that talk of this kind (and whose "purposes" and whose decisions about the
"genuine" nature of the interactions) can make to the specific learning of
mathematics. I indicate below an example of teachers choosing to ignore the
meaning in favour of attending to the form of an utterance: One possibility
here is to find situations in which the teacher is making such judgements
and endeavour to study them.
I have looked at the situation of reporting back on a range of open-ended
or problem-solving activity and explored a number of questions about active
listening, as well as the linguistic demands placed on all participants when
engaged in reporting back to the rest of the class. More specific questions
include: How can students develop the linguistic skills of reflection and
selection of what to report? How can they work on acquiring a sense of
audience? To whom is the reporter talking? (For more on this topic, see
Pimm, 1992.)
Finally, a current general orientation to classroom talk (arising from
ethnographic research) invokes the notions of representativeness and voice:
Who gets to speak? Whom do we hear from in classrooms, and how? And
about what? Who remains silent, how and why? (Are they silenced or do
they silence themselves?) One result of the disciplined ways of looking that
many fields develop may be that the same voice (or voices) gets replicated
over and over. These questions are worth asking of mathematics
MATHEMATICS CLASSROOM LANGUAGE
160

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classrooms. One focus might be on representativeness of the voices of the
two genders, or the various ethnic or social groups, while another might be
more on the form and structure of spoken interactions between mathematics
teachers and students in general.
There are important differences between speech and writing, not least
with regard to relative permanence and linear or non-linear flow in time, as
well as being able to see the whole discourse when written down (an aid for
reflection). There has been much research on reading in mathematics. Early
work focused primarily on the problematic notion of "readability indices,"
which objectified the phenomena of interest and located it as a property of
the text alone. Subsequently, some more interesting work has been done, in