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Qualities of examples in learning and teaching

journal contribution
posted on 2023-05-17, 12:56 authored by Watson, A, Helen ChickHelen Chick
In this paper, we theorise about the different kinds of relationship between examples and the classes of mathematical objects that they exemplify as they arise in mathematical activity and teaching. We ground our theorising in direct experience of creating a polynomial that fits certain constraints to develop our understanding of engagement with examples. We then relate insights about exemplification arising from this experience to a sequence of lessons. Through these cases, we indicate the variety of fluent uses of examples made by mathematicians and experienced teachers. Following Thompson’s concept of “didactic object” (Symbolizing, modeling, and tool use in mathematics education. Kluwer, Dordrecht, The Netherlands, pp 191–212, 2002), we talk about “didacticising” an example and observe that the nature of students’ engagement is important, as well as the teacher’s intentions and actions (Thompson avoids using a verb with the root “didact”. We use the verb “didacticise” but without implying any connection to particular theoretical approaches which use the same verb.). The qualities of examples depend as much on human agency, such as pedagogical intent or mathematical curiosity or what is noticed, as on their mathematical relation to generalities.

History

Publication title

ZDM : The International Journal of Mathematics Education

Volume

43

Pagination

283-294

ISSN

1863-9690

Department/School

Faculty of Education

Publisher

Springer Netherlands

Place of publication

Germany

Rights statement

Copyright 2010 FIZ Karlsruhe The final publication is available at www.springerlink.com

Repository Status

  • Restricted

Socio-economic Objectives

Pedagogy

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