Tim Rowland has written an article about The purpose, design and use of examples in the teaching of elementary mathematics. This article was recently published (online) in Educational Studies in Mathematics. The article describes an interesting study that featured video recordings of 24 lessons that were taught by prospective teachers. Here is the abstract of the article:

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.