Mathematical Pedagogy

Many learners of mathematics seem to take a passive stance towards their studies, at best assenting to a sequence of definitions and theorems. The notion of personal example spaces will be developed as a setting for pedagogical strategies which can be used to provoke learners into an active (assertive) stance as generators and re-constructors of mathematical objects and meaning. Various constructs arising from mathematics education will be used to try to make sense of the endemic tension between learners' and teachers' conceptions of learning mathematics.