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Example-Generation as Indicator and Catalyst of Mathematical and Pedagogical Understandings

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Transforming Mathematics Instruction

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This chapter examines the activities of example-generation and example-verification from both the teaching and learning perspectives. We closely examine how engaging learners in generating and verifying examples of a particular mathematical concept as a group activity serves both as an indicator of learners’ understandings and a catalyst for enhancing their understanding and expanding their example space that is associated with the particular concept. We present two cases that illustrate how the mathematics instruction may look when classroom activities and discussions build on example-generation and example-verification – the first case focuses on the concept of an irrational number and the second on the notion of a periodic function. The learners in these cases are in-service secondary mathematics teachers (MTLs), and the teacher is a mathematics teacher educator (MTE). We show how this kind of learning environment lends itself naturally to genuine opportunities for learners to engage in meaningful mathematics, to share and challenge their thinking, and to sense the need for unpacking mathematical subtleties regarding definitions and ideas. For practicing and prospective mathematics teachers, engaging in such activity and experiencing the potential learning opportunity that it offers is also likely to convince them to implement this approach in their classrooms.

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Author information

Authors and Affiliations

  1. New York University, 2 Washington Square Village, Apt. 9B, New York, NY, 10012, USA

    Orit Zaslavsky

  2. Technion – Israel Institute of Technology, Technion City, Haifa, 32000, Israel

    Orit Zaslavsky

  3. Technion – Israel Institute of Technology, 11 HaEshel Street, 12864, Nesher, 36860, Israel

    Iris Zodik

Authors
  1. Orit Zaslavsky
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  2. Iris Zodik
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Correspondence to Orit Zaslavsky .

Editor information

Editors and Affiliations

  1. Department of Teaching, Learning and Culture, Texas A&M University, College Station, Texas, USA

    Yeping Li

  2. School of Education, University of Michigan, Ann Arbor, Michigan, USA

    Edward A. Silver

  3. Dept. of Mathematics, East China Normal University, Putuo, China

    Shiqi Li

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Zaslavsky, O., Zodik, I. (2014). Example-Generation as Indicator and Catalyst of Mathematical and Pedagogical Understandings. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_28

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