Educational Studies in Mathematics

, Volume 57, Issue 1, pp 1–32 | Cite as

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

  • Lara Alcock
  • Adrian Simpson


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.

advanced mathematical thinking beliefs convergence definitions grounded theory proof real analysis representations sequences visualization 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Lara Alcock
    • 1
  • Adrian Simpson
    • 2
  1. 1.Rutgers UniversityUSA
  2. 2.University of WarwickUK

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