Convergence of Sequences and Series 2: Interactions between Nonvisual Reasoning and the Learner's Beliefs about their own Role

Alcock, L.; Simpson, A.P.

Abstract

this paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoining, and tend not to incorporate visual images into their work. It examines the work of students from two parallel courses of introductory real analysis, whose reasoning ranges from those who introduce definitions appropriately and work with them competently, to those who cannot recall definitions and appear to manipulate notation without regard for its reference. It presents a theory that relates the differences to students' expectations regarding their role as learners of mathematics. Throughout, the argument is illustrated with interview data from which the theory was inductively generated.

Citation

Alcock, L., & Simpson, A. (2005). Convergence of Sequences and Series 2: Interactions between Nonvisual Reasoning and the Learner's Beliefs about their own Role. Educational Studies in Mathematics, 58(1), 77-100. https://doi.org/10.1007/s10649-005-2813-5

• Journal Article Type: Article
• Publication Date: 2005-01
• 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: 58
• Issue: 1
• Pages: 77-100
• DOI: https://doi.org/10.1007/s10649-005-2813-5
• Keywords: Advanced mathematical thinking, Beliefs, Convergence, Definitions, Proof, Real analysis, Represenatations, Sequences, Series, Symbolic reasoning.
• Public URL: https://durham-repository.worktribe.com/output/1596810