Abstract
In this largely theoretical article, we discuss the relation between a kind of
affect, behavioural schemas and aspects of the proving process. We begin
with affect as described in the mathematics education literature, but soon
narrow our focus to a particular kind of affect – nonemotional cognitive
feelings. We then mention the position of feelings in consciousness because
that bears on the kind of data about feelings that students can be expected
to be able to report. Next we introduce the idea of behavioural schemas as
enduring mental structures that link situations to actions, in other words,
habits of mind, that appear to drive many mental actions in the proving
process. This leads to a discussion of the way feelings can both help cause
mental actions and also arise from them. Then we briefly describe a design
experiment – a course intended to help advanced undergraduate and
beginning graduate mathematics students improve their proving abilities.
Finally, drawing on data from the course, along with several interviews,
we illustrate how these perspectives on affect and on behavioural schemas
appear to explain, and are consistent with, our students’ actions.