Jeff Boats - On using computer tutorials to tailor linear algebra for secondary teachers

An integral part of a mathematics student's education involves developing an intuition about underlying structures and relationships. Even more so for the future mathematics educator, who will need to illustrate these insights. The courses in a mathematics education program should be crafted to develop such intuition.

The linear algebra student, in particular, must develop the ability to visualize the properties of vectors and vector spaces. But while an abstract understanding of vector spaces benefits the mathematician, the secondary mathematics teacher requires a more concrete visualization. The goal, then, is to provide resources with which the future math educator may improve his visualization.

Properly-designed computer tutorials can be used to decompose the standard problems of linear algebra into simpler, more digestible forms. These tutorials generally involve exercises in construction, and take full advantage of the computer's speed and efficiency, avoiding the pitfall of computer-empowerment.

This talk briefly describes the motivation of computer tutorials, explains how they differ from the computer exercises of most textbooks, and provides an example or two.