The Explanatory Power of Examples in Mathematics: Challenges for Teaching

I use the term “instructional example,” to refer to an example offered by a teacher within the context of learning a particular topic. The important role of instructional examples in learning mathematics stems firstly from the central role that examples play in mathematics and mathematical thinking. Examples are an integral part of mathematics and a significant element of expert knowledge (Rissland, 1978). In particular, examples are essential for generalization, abstraction, and analogical reasoning. Furthermore, from a teaching perspective, there are several pedagogical aspects of the use of instructional examples that highlight the significance and convey the complexity of this central element of teaching.