Mr. Frog Challenged by Mathematical Conjectures: Fermat’s Last Theorem and Twin Primes

Abstract

Is it possible to communicate abstract mathematical thinking to children? This is what the Danish picture books “Fermat’s last theorem” and “Twin primes” attempt to do. This chapter discusses their educational potential from both a literary and a didactical perspective, basing the latter on the Danish framework for mathematical competencies and its characterization of mathematical overview and judgement. On the one hand, the books serve an aesthetic purpose by combining conventional elements of a picture book with colourful illustrations and the narrative structure of a fairy-tale and unconventional mathematical content. On the other hand, they contravene traditional norms for children’s books by introducing complex problems with no solution. This unexpected turn invites the reader to engage in mathematical and philosophical thinking, abstract reflection and dialogue, which may contribute to the development of the critical child. Without even mentioning Fermat’s last theorem, the first book’s application of mathematical formulations, considerations and methods to a non-mathematical problem, as well as the implicit example (Fermat) of the historical development of mathematics, presents the nature and characteristics of mathematics as a discipline. The second book, “Twin primes”, is more traditional in the context of subject-oriented children’s books as it is explicitly stated that the narrative is used to communicate a mathematical topic. Both of the books have the potential to develop children’s mathematical overview and judgement. However, if the invitation to engage in abstract thinking is to be accepted and exercised, the rather complex content needs to be mediated by a qualified adult.