Description
Developments in the practice of mathematics over the last three decades have led to new types of proof and argumentation, challenging the established norms in this area. These developments originated from the use of computers (both as a heuristic device and as a means of verification), from a new quality in the relations of mathematics to its applications in the empirical sciences and technology, and from a stronger awareness of the social nature of the processes leading to the acceptance of a proof. A large number of philosophers of mathematics have turned their attention more and more from the justificatory to the explanatory role of proof. Their central questions are no longer only why and how a proof makes a proposition true, but also how it contributes to an adequate understanding of the proposition in question and what role is played in this process by factors that go beyond logic. The use of computers has also caused a radical change in educational practices as well. In algebra, analysis, geometry and statistics, for example, computer software already provides revolutionary capabilities for visualisation and experimentation, and holds the promise of further change. At the same time, there is a stronger emphasis on communication in the classroom, an emphasis reflected in the didactics of mathematics by the idea of emphasis on justification and explanation. Thus the role of traditional notions of proof in education has changed, and new forms and types of explanation and argumentation have evolved. This book proposal is unique in that it will bring together themes of interest to both philosophy and mathematics education. Philosophers will gain by reflecting on the dimensions of mathematical proof and explanation that could be relevant to the general culture and to broadly educated adults whereas mathematics education researchers will gain by specifically eliciting the epistemological and methodological aspects relevant to teaching and learning. Thus both the fields of mathematics education and philosophy of mathematics stand to benefit from an exchange of ideas.
