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Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner's Beliefs about Their Own Role

Lara Alcock and Adrian Simpson
Educational Studies in Mathematics
Vol. 57, No. 1 (2004), pp. 1-32
Published by: Springer
Stable URL: http://www.jstor.org/stable/4150313
Page Count: 32
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Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner's Beliefs about Their Own Role
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Abstract

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior.

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