Teacher Tasks for Mathematical Insight and Reorganization of What it Means to Learn Mathematics

The mathematics-for-teachers tasks we discuss in this chapter have two qualities: (1) they offer teachers opportunities to experience the pleasure of mathematical insight; and (2) they aim to disrupt and reorganize teachers\u27 views of what it means to do and learn mathematics. Given that many future and inservice elementary teachers fear and dislike mathematics, it is perhaps not too far-fetched to suggest that there is a need for “math therapy.” We believe that a form of mathematics therapy may involve new and different experiences with mathematics. Such experiences, considered broadly to include questions or prompts for mathematical exploration, draw attention to deep mathematical ideas and offer the potential of experiencing the pleasure of significant mathematical insight. In our work with teachers we have developed and used a variety of mathematics tasks as opportunities for experiential therapy. The tasks aim to challenge some of the mathematical myths that future teachers believe to be true and are typically assumed by them in mathematics classrooms. The tasks have potential to disrupt teachers\u27 view of mathematics, and to start the process for reorganizing their thinking about what mathematics is and what it means to do and learn mathematics. In this chapter we describe and discuss four of the mathematics tasks which involve non-routine mathematics problems that we use in our mathematics-for-teachers program. This program is offered annually to our 440 future elementary school (K-8) teachers, who generally lack confidence in mathematics and often fear and/or dislike the subject. It is also offered to inservice teachers through a series of mathematics-for-teachers courses. A student response summarizes the effects of our approach