Educational Studies in Mathematics

, Volume 58, Issue 1, pp 77–100 | Cite as

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

  • Lara Alcock
  • Adrian Simpson


This paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoning, 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.


advanced mathematical thinking beliefs convergence definitions proof real analysis representations sequences series symbolic reasoning 


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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Lara Alcock
  • Adrian Simpson

There are no affiliations available

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