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.
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: