“The Language of Mathematics”: Towards a Critical Analysis of Mathematics Texts by CANDIA MORGAN

In this paper I will suggest an approach to the analysis of mathematical texts that makes use of linguistic theory to provide insights into how the language of a text may influence the ways in which its readers make sense of it, in particular the ways in which teacher readers may make sense of texts produced by students.

This draws on Halliday’s ideational/experiential, interpersonal and textual functioning.

Ideational

A similar function is performed by the use of representational
objects (i e tables, graphs, diagrams, etc.) as
actors in verbal processes, e.g the table show,s that .rather
than I have shown in the table that. , which obscures the
writer’s presence as author as well as mathematician. The
use of passive rather than active forms of verbs is a further
way of obscuring agency that is much used in academic
writing and is even seen as the “correct”, “objective” way of
writing. As Halliday and Martin [1993] point out, there is a
difference between objectification and objectivity but, in the
rationalisations for their practices provided by scientists and
other academic writers, the two are often confused. p. 4

Fot example, in
an academic mathematical paper previously established
facts (labelled by numbers and hence further distanced from
the activity which originally established them) are presented
as causes of other facts without any intervening activity:
By (4). (6) the other Brianchon point of the former edge is
(1, -I), I)
In contrast, a Year 9 student’s rough work shows mathematical
facts and relationships to be dependent upon human
action:
whenever there is one dot inside and you count up the
perimeter and the area will be exactly half it
The importance of explanation and proof in mathematics is
also to be seen in the frequency with which expressions of
causality occur in a text. p. 5

Her paper then argues for paying attention to:

  • types of processes, in particular the uses made of the equals sign and the types of processes used in the expression of generalisations
  • the types of participants in these processes;
  • the portrayal or suppression of agency through nominalisations, non-human actors, the non-active forms of verbs;
  • the nature and extent of the expression of casual relationships
  • symbolisations

Interpersonal

She talks about pronouns, and the use of ‘we’

suggesting that the author is not speaking alone
but with the authority of a community of mathematicians
While such uses of the first person may draw attention to
the activity and authority of the author, we may also be used
in an inclusive way to imply that the reader is also actively
involved in the doing of mathematics.p. 5

And the specific and generic ‘you’

By including the words ‘you will notice’ it appears that the
author is addressing an individual reader personally and
directing her attention with a degree of authmity; it also
suggests that the reader ought to be interested in the details
of the mathematics presented in the text. On the other hand,
some uses of you appear to be attempts to provide expressions
of general processes rather than being addressed to
individual readers. This seems to be the case particularly
where children are struggling both to formulate generalisations
and to communicate them. p. 6

And the imperative

The use of imperatives and of other conventional and specialist
vocabulary and constructions characteristic of
academic mathematics marks an author’s claim to be a
member of the mathematical community which uses such
specialist language and hence enables her to speak with an
authoritative voice about mathematical subject matter. p. 6

Textual

the presence in a report of
mathematical activity of a large number of themes expressing
reasoning (e.g, hence, therefore, by Theorem I, etc)
would serve to consttuct the text as a deductive argument… On the other hand, a predominance of temporal themes ( e g ,
first, next, then, etc) would construct a story or report
recounting what happened.

Mmtin [1989] points out that reasoning can be expressed
through the use of conjunctions (because, so), nouns (the
reason is. ), verbs (X causes Y) or prepositions (by, because
o!J It may also be expressed less explicitly through the simple
juxtaposition of casually related statements. p. 7

She then outlines how these factors might influence interpretation of a student’s text.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s