Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role |
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Authors: | Lara Alcock Adrian Simpson |
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Institution: | (1) Rutgers University, USA;(2) University of Warwick, UK |
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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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | advanced mathematical thinking beliefs convergence definitions grounded theory proof real analysis representations sequences visualization |
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