Exemplifying definitions: a case of a square |
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| Authors: | Rina Zazkis Roza Leikin |
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| Institution: | (1) Faculty of Education, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada;(2) Faculty of Education, University of Haifa, Haifa, 31905, Israel |
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| Abstract: | 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. |
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| Keywords: | Examples Learner-generated examples Example spaces Definitions Necessary and Sufficient conditions Prospective teachers Secondary mathematics teachers |
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