Educational Studies in Mathematics

, Volume 69, Issue 2, pp 131–148 | Cite as

Exemplifying definitions: a case of a square

  • Rina ZazkisEmail author
  • Roza Leikin


In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.


Examples Learner-generated examples Example spaces Definitions Necessary and Sufficient conditions Prospective teachers Secondary mathematics teachers 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Faculty of EducationSimon Fraser UniversityBurnabyCanada
  2. 2.Faculty of EducationUniversity of HaifaHaifaIsrael

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