Rina Zazkis and Roza Leikin have written an article that was published online in Educational Studies in Mathematics last week. The article is entitled Exemplifying definitions: a case of a square, and here is the abstract:
In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.