
06434092
a
2015c.00499
Zaslavsky, Orit
Thinking with and through examples.
Liljedahl, Peter (ed.) et al., Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education ``Mathematics education at the edge", PME 38 held jointly with the 36th conference of PMENA, Vancouver, Canada, July 1520, 2014, Vol. 1. [s. l.]: International Group for the Psychology of Mathematics Education (ISBN 9780864913609/set; 9780864913616/v.1). 2134 (2014).
2014
[s. l.]: International Group for the Psychology of Mathematics Education
EN
E50
C30
D30
D40
mathematical thinking
examples
mathematical concepts
proof
proving
Summary: In my talk I will discuss the roles that examples play (or could play) in mathematical thinking, learning, and teaching. I draw mainly on research I've been doing for over a decade that addresses this broad topic from several perspectives. In terms of learning  I look at mathematical concepts (e.g., periodic function) and metaconcepts (e.g., definition) and examine the way interacting with examples may enhance understanding of these concepts. In terms of mathematical thinking, I look at mathematical proof and proving as a site for developing mathematical thinking (here I draw on my experience in designing and implementing an undergraduate course on Mathematical Proof and Proving (MPP), on my current work with Eric Knuth and Amy Ellis on the roles of examples in learning to prove, and my previous work with Uri Leron on generic proving, and with Orly Buchbinder on the roles of examples in determining the validity of mathematical statements). In terms of teaching, I try to unpack pedagogical considerations that teachers encounter when constructing or selecting instructional examples (this work I have done mainly with Iris Zodik), and try to characterize this kind of knowledge for teaching mathematics that appears to be crafted through experience. I propose examining the field through three teaching/research settings that elicit exampleuse and examplebased reasoning: Spontaneous exampleuse, evoked exampleproduction, and exampleprovisioning (by the teacher or researcher).