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Convergence of sequences and series: interactions between visual reasoning and the learner's beliefs about their own role

Alcock, L.J.; Simpson, A.P.

Authors

L.J. Alcock



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.