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.

Item Type:	Refereed Article
Keywords:	examples, didactic object, generalisation, learning from examples
Research Division:	Education
Research Group:	Curriculum and pedagogy
Research Field:	Mathematics and numeracy curriculum and pedagogy
Objective Division:	Education and Training
Objective Group:	Teaching and curriculum
Objective Field:	Pedagogy
UTAS Author:	Chick, H (Associate Professor Helen Chick)
ID Code:	79136
Year Published:	2011
Deposited By:	Education
Deposited On:	2012-08-20
Last Modified:	2017-11-21
Downloads:	158 View Download Statistics