COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Seminars

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Seminar: Learning to See Like a Mathematician: Lets look at mathematics a different way

2003-11-10

12:10p.m. Neill Hall 5W

Walter Whiteley

Abstract: Experts, teachers, and novices all see a diagram, a manipulative, or lines of algebra in different ways. In mathematical situations, we see what we have learned to see: selecting, shifting ourfocus, and interpreting according to experience and learned conventions, in our imaging and imagining. We will offer some examples to illustrate how we create what we see and that what we see makes a difference to how we think and solve problems. We will give some special attention to seeing symmetry and the fundamental role of symmetry in geometry. To explore a common area of confusion in elementary texts, and for elementary teachers, we will investigate the classification of quadrilaterals through symmetry and inclusive definitions, using paper folding, dynamic geometry software, and other activities. In contradiction of the two column proofs which many high school curricula present as geometry, we will consider the fundamental role of transformations and geometric reasoning with visual and kinaesthetic processes at all levels of mathematics, from growing toddlers to advanced research in geometry. We will also consider some consequences of the presence or absence of support for visual reasoning to the inclusion of a broad range of students in the mathematics classroom.