Prof Yoshinori Shimizu
University of Tsukuba, Japan

Title: Defining, extending, and creating: key experiences in mathematics

Abstract

In mathematics a definition is simply an agreement that makes clear the meaning attached to a certain word or symbol. It plays critical roles in understanding concepts, in reasoning, in problem solving, and in communicating with others. Moreover, examining a definition of a mathematical term at the phase of extending the meaning of a concept or creating a new concept for going into an expanded system are key experiences in mathematics. However, our students seem to have some difficulties in using definitions in various contexts of learning mathematics, while they have few experience of extending the existing world of mathematics. In this workshop, a series of tasks, mostly at the level of junior or senior high school, will be given and discussed to illustrate rich experiences in defining, extending, and creating in mathematics. The participants are invited to work on examining and creating definitions of various mathematical objects, including familiar quadrilaterals such as a kite and "boomerang", and on extending meanings of numbers in certain number systems to experience the process of extending and creating a world of mathematics.