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Qualities of examples in learning and teaching
journal contributionposted 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.
Publication titleZDM : The International Journal of Mathematics Education
Department/SchoolFaculty of Education
Place of publicationGermany
Rights statementCopyright 2010 FIZ Karlsruhe The final publication is available at www.springerlink.com