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Educational Studies in Mathematics

, Volume 87, Issue 3, pp 323–349 | Cite as

Analyzing the teaching of advanced mathematics courses via the enacted example space

  • Timothy Patrick Fukawa-Connelly
  • Charlene Newton
Article

Abstract

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in Educational Studies in Mathematics 69:77–79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the concept of an example space (Mason & Watson, 2008) and variation theory (Runesson in Scandinavian Journal of Educational Research 50:397–410, 2006) to create a lens to study how examples are used for pedagogical purposes in undergraduate proof-based instruction. We adapted the construct of an example space and extended its application to the constructs of example neighborhood, methods of example construction, and the functions of examples. We explained how to use our new lens to analyze the collection of examples and non-examples that the students had access to. We then demonstrate our method by analyzing the collection of examples and non-examples of a mathematical group the professor of an abstract algebra class presented during lectures or assigned to students in problem sets or exams.

Keywords

Undergraduate teaching Examples Abstract algebra Variation theory 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Timothy Patrick Fukawa-Connelly
    • 1
    • 2
  • Charlene Newton
    • 1
  1. 1.The University of New HampshireDurhamUSA
  2. 2.School of EducationDrexel University, Korman CenterPhiladelphiaUSA

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