Educational Studies in Mathematics

, Volume 68, Issue 3, pp 195-208

What makes a counterexample exemplary?

  • Rina ZazkisAffiliated withFaculty of Education, Simon Fraser University Email author 
  • , Egan J. ChernoffAffiliated withFaculty of Education, Simon Fraser University

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In this paper we describe two episodes of instructional interaction, in which examples are used in order to help students face their misconceptions. We introduce the notions of pivotal example and bridging example and highlight their role in creating and resolving a cognitive conflict. We suggest that the convincing power of counterexamples depends on the extent to which they are in accord with individuals’ example spaces.


Cognitive conflict Conceptual change Pivotal example Bridging example Example space Proof scheme