paradox and learning: implications from paradoxical psychotherapy and zen buddhism for mathematical inquiry with paradoxes

Abstract

This paper argues that paradox offers an ideal didactic context for open-ended group discussion, for the intensive practice of reasoning, acquiring dispositions critical for mathematical thinking, and higher order learning. In order to characterize the full pedagogical range of paradox, I offer a short overview of the effects of paradox, followed by a discussion of some parallels between the use of paradox in paradoxical psychotherapy and the use of the koan in Zen Buddhist spiritual training. Reasoning with paradoxes in a community of mathematical inquiry is interpreted as a comparative if not isomorphic pedagogical and cognitive phenomenon. Finally, some broad implications are drawn for mathematical inquiry with paradoxes.