Speaking Mathematically

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Mathematically speaking: the importance of language in the learning of mathematics Kerry O’Regan Flexible Learning Centre, University of South Australia The genesis of this paper was a study which set out to explore the part played by emotion in the learning of mathematics, and which encountered a number of other things along the way. Part of the data from that study comprised transcripts of discussions involving three groups: university mathematics lecturers and secondary and primary education students. One of the themes emerging from the discussions (which focussed on learning experiences of the participants) was the importance of verbalising mathematical concepts, relationships and processes in order to construct meaning and make sense of them. This finding stimulated the author to delve into the literature of psycholinguistics from the classic writings of the middle of the century to recent studies of the place of language in learning, particularly the learning of mathematics. The paper documents this exploration and ends up by posing the question of how the critical process of making meaning through language can be accommodated, not only in traditional face-to-face teaching/learning environments, but also in settings that are increasing remote and electronic. Talking is a wonderful smoother-over of difficulties. When I come upon anything – in Logic or any other hard subject – that entirely puzzles me, I find it a capital plan to talk it over, aloud, even when I am alone. (Lewis Carroll. Introduction to Symbolic Logic. 1896)

Introduction Traditionally, mathematics and language-based subjects have resided on opposite sides of a great divide. This has been typified in, for example, the nature of tutorials within these two discipline areas. Language-based subjects have a tradition of language-based tutorials in which students are expected and encouraged to talk and work together collaboratively, using language to construct and articulate their ideas. Mathematics tutorials, on the other hand, represent a very different learning culture. Here the tradition is that students will, before coming to the tutorial, have attempted a prescribed set of mathematical problems, preferably working alone and independently (after all ‘collaboration skates very close to the supreme academic sin, plagiarism’ (Bruffee 1993, p.27)). The main purpose of the tutorial is for them to be provided with ‘the solutions’ so that they can check that they were on the ‘right’ track and have an opportunity to ask for guidance if their track was wrong. However, this divide may be inappropriate and may actually inhibit learning. Real mathematicians, such as Charles Dodgson (alias Lewis Carroll) and Niels Bohr (Schrage 1995) made mathematical meaning through talking. And everyday mathematicians and mathematics students report a similar process. This paper had its beginnings in a study (Ingleton & O’Regan 1998) of the part played by emotion in the learning of mathematics. That study used a technique of Memory Work in which the participants reflected on, wrote about and then discussed positive and negative experiences that had been part of their mathematics learning. The 16 participants in the study comprised a group of university lecturers in mathematics, and two groups of education students who were prospective teachers of mathematics at primary and secondary level respectively. The 32 written narratives and the discussion transcripts provided a rich source of data which initially was analysed primarily in relation to the emotions associated by the participants with their learning. However

HERDSA Annual International Conference, Melbourne, 12-15 July 1999

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O’Regan

other patterns emerged as well. One which stood out for the present author was a recurrent reference to the importance for the participants of language in their learning of mathematics, an aspect that had not been sought or predicted by the study. This paper follows the author’s...
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