Visit by Tommy Dreyfus
On May 10-15, 2013, Tommy Dreyfus from Tel Aviv University visited Umeå Mathematics Education Research Centre (UMERC). During his visit, he participated in different seminars and worked together with members of UMERC, in particular with research students.
Tommy Dreyfus' research interests include mathematical thinking, concept formation, processes of abstraction, and various aspects of learning and teaching about proof, as well as theoretical and methodological issues of research in mathematics education. In teaching, he aims to convey how mathematical meaning grows out of the connectivity of concepts, processes and representations of mathematical objects.
Tuesday, May 14
"How can we know whether it is a proof?"
Proof is arguably what distinguishes mathematics most markedly from other domains of knowledge. Is it obvious what a proof is? This question has been discussed among mathematicians and philosophers and mathematics educators for many years, but research results on students’ conceptions of proof remain inconsistent. While elementary students are already capable of deductive reasoning, most high school students have a vague notion of proof, at best, and many teachers are uncertain about the status of non-algebraic arguments such as verbal, visual and generic ones. The audience for this talk is mathematics teachers at all levels, from school mathematics to university mathematics. We will explore our biases for what counts as a proof and discuss how how the community of mathematics educators deals with some of the issues raised above.