### Writing to develop mathematical understanding

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STOP PRESS, AUTUMN 2014: Franco Vivaldi's *Mathematical Writing* book is now published by Springer. View details here.

The notion that understanding can be tested in and developed through (written) verbal expression (i.e. the link between thinking and writing) has been a key idea in the practice developed by colleagues in the School of Mathematical Sciences at QMUL.

The ground was laid by Professor Wilfrid Hodges (now retired) who, with Edmund Harriss, developed 'Logic 1: mathematical writing' . The module contained regular exercises which required students essentially to do 2 things: to identify or define things, and to prove things. There was an emphasis on writing explanations 'in role', for particular audiences and particular purposes - and the use of mathematical symbols and notation was often ruled out in favour of the struggle to make mathematical understanding explicit in words. (Read about an experimental course in mathematical writing).

Professor Franco Vivaldi shared Wilfrid's interests and further developed them into a larger second year 'Mathematical Writing' module, which is supported by an extensive web book Mathematical Writing for undergraduates. Franco has also contributed to Thinking Writing's STEM Wishees site where you can listen to him explaining the strengths and weaknesses of three student responses to questions requiring them a) to describe a graph and b) to summarise a text book account of 'the scalar product'.

Thinking Writing supported the development of both these courses, and in 2007-2008 conducted an evaluation (funded by the Maths, Statistics and OR Network (MSOR)) which looked in some depth at the students' experiences of the approach, focusing particularly on whether the writing tasks increased students' conceptual understanding of mathematics. Data was collected through:

- a focus group with Mathematical Writing students
- interviews with students and tutors
- ethnographic observations of lectures and tutorials
- samples of the writing tasks

**Read collaboratively written reports** of the evaluation findings: Beyond templates, and Beyond templates 2.

Look at some examples (from Logic 1) of imaginative short writing tasks which ask students to practice putting their thinking into words, often to a particular audience, or within the constraints of a particular form or word length.

Edmund Harriss is now a professor at the University of Arkansas where he continues to be interested in mathematics and communication.