WRITING MATHEMATICALLY: The Discourse of Investigation. By Candia Morgan. Falmer Press. Pounds 14.95.
It is 10 years since the introduction of GCSE coursework in mathematics and now nearly all pupils are assessed, in part, on the basis of their written accounts of mathematical activities they have undertaken.
It is therefore surprising that little attention has been paid to students' use of writing in maths.
Candia Morgan, in this latest in the Studies in Mathematics Education series, draws on established linguistic theories to explore the nature of mathematical writing in various forms, including professional academic research reports, school textbooks and students' accounts of investigations. She analyses in some detail the investigation write-ups of a sample of pupils and looks at the way their teachers have interpreted this evidence.
The author makes clear that the factors which influence the choices writers make in constructing their accounts are complex, as are those which influence the reader's interpretation of them. There are many concerns to which we as teachers ought to pay attention. How do we offer pupils models of mathematical writing which help them gain an understanding of appropriate conventions? Textbooks, after all, do not model investigation write-ups. Do we always make the purpose and audience clear when we ask pupils to produce written accounts? Is it helpful or, as the author suggests, sometimes confusing for pupils to suggest a fictitious audience ("write as if you were explaining to a pen-friend in America")? She highlights tensions that arise from the dual purpose of much of the writing pupils produce for GCSE:is it a log which helps them keep track of their ideas or an account by which they will be formally assessed? There are similar concerns arising from the dual role of teachers: mentor and guide versus monitor and judge.
The author was motivated in her research by the recognition that many pupils may not truly reflect their mathematical ability through this form of assessment. The book convincingly synthesises academic findings, personal research and teachers' anecdotal accounts. It does not provide simple answers for teachers but does convincingly makes the case for further research.
Linton Waters is Shropshire adviser for mathematics