Teaching to See Like a Mathematician

Walter J. Whiteley

I will report on two types of Lab experiences Ifrom a geometry course and a first year seminar on Information in Visual Form: (A) Computer based visual illustrations for the basic themes that: (i) We create what we see; (ii) You do not see what I see; (iii) That what we see matters to our thinking processes; (iv) We can change what we see - and this is worth doing.

(B) Issues of 3-D symmetry in multiple contexts and the connections between representations used, interactions which are offered to users; and the mix of kinesthetic and visual reasoning which arises in these situations. Some issues of current concern include: (i) Practice in 2-D does not support 3-D visual skills; (ii) Student's abilities in 3-D are likely to decrease as they pass through the system; (iii) 3-D visual skills are important in a number of areas outside of mathematics; (iv) 3-D visual skills involve a number of distinct cognitive processes which require distinct supports for learning.

I will also present, briefly, a recent SIGGRAPH Report on Visual Learning in Science and Engineering: http://www.siggraph.org/education/vl/vl.htm which addresses these themes and many others of interest in this context.