L.J. Alcock
Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role
Alcock, L.J.; Simpson, A.P.
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.
Citation
Alcock, L., & Simpson, A. (2004). Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role. Educational Studies in Mathematics, 57(1), 1-32. https://doi.org/10.1023/b%3Aeduc.0000047051.07646.92
Journal Article Type | Article |
---|---|
Publication Date | 2004-07 |
Deposit Date | Jan 10, 2007 |
Journal | Educational Studies in Mathematics |
Print ISSN | 0013-1954 |
Electronic ISSN | 1573-0816 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 57 |
Issue | 1 |
Pages | 1-32 |
DOI | https://doi.org/10.1023/b%3Aeduc.0000047051.07646.92 |
Keywords | Advanced mathematical thinking, Beliefs, Convergence, Definitions, Grounded theory, Proof, Real analysis, Representations, Sequences, Visualization. |
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