Language and Mathematics
Starting points for thinking about the role of language in mathematics learning
Key Stage suitability • Explanation
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There is an increasing number of teachers of mathematics who know not only that the language in the classroom matters in general, but that there are peculiarly mathematical language problems. Eventually we may be familiar enough to dare to use the word ‘semiotic’ to refer to these idiosyncratic matters. Meanwhile it would be mistaken to attempt a premature unification of some slowly gathering insights.
So this report is not a conclusive and comprehensive survey of the language issue in mathematics teaching. Rather it is a miscellaneous collection of bits of work in progress by a group of members of the Association of Teachers of Mathematics temporarily articulated as a holding form.
A miscellaneous collection of pieces, this book is a useful stimulus for starting discussions on language, or for background reading for students and teachers studying for initial or inservice education awards.
Starting points for thinking about the role of language in mathematics learning.
ISBN 0 90095 31 8
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Mathematics is an introspective activity -- the mathematician follows the working of his own mind and tries to describe the process. Hence it is inevitable that mathematics teachers will be involved in discussions of thought and language.
The teacher of English, conscious of language, becomes concerned with its vehicular nature. Language is common to all and we should be concerned with its manifestations. Teachers o{ mathematics attend first to the mathematical activity and incidentally recognise the issues of language as communication problems increase. The more widely we believe mathematical activity can be practised the more pressing become communication problems.
There is an increasing number of teachers of mathematics who know not only that the language in the classroom matters in general, but that there are peculiarly mathematical language problems. Eventually we may be familiar enough to dare to use the word `semiotic' to refer to these idiosyncratic matters. Meanwhile it would be mistaken to attempt a premature unification of some slowly gathering insights.
So this report is not a conclusive and comprehensive survey of the language issue in mathematics teaching. Rather it is a miscellaneous collection of bits of work in progress by a group of members of the Association of Teachers of Mathematics temporarily articulated as a holding form.
It has been the practice in ATM for many years to publish work as a group.
Individual contributions are drafted and submitted to group discussion; in some sense the authors take joint responsibility for what is finally written. At the same time the Association does not publish representative reports which arc then supposed in some way to reflect the views of all members. This publication is offered in the same spirit; it offers some current thoughts from a working group of some ATM members.
Contents
How We Started - an extract from some written work by a twelve-year old after a class discussion.
Path Algebra- an extract from some written work by a twelve-year old in response to a printed workcard.
From Words To Mathematics - discussion of the differences in written work arising from different invitations to work.
Questions - observation of a class of children taking a standardised attainment test.
On Clarity- comments arising from some work done with a group of teachers using geoboards.
Towards A Language Of Struggle - young children’s encounter with mathematics compared with their mastery of language.
Comments On Language In The Classroom - different ways of interpreting events in the classroom illustrate different forms and uses of language.
Thoughts On Mathematics And Language - criticises the common assertion that mathematical language can be and should he well- defined and unambiguous.
Words Or Things -suggests that in mathematics the sign may be relatively unimportant and that the signified can be communicated by image or action.
Sign, Symbol And Form - considers the distinction between sign and symbol in the context of a mathematical conversation.
Some References - not a comprehensive bibliography but a list of work done over the last ten years by members of the Association of Teachers of Mathematics.
Authors
Bill Brookes
John Dichmont
Eric Love
Judy Morgan
Dick Tahta
Jim Thorpe
