Teaching Mathematics as the Contextual Application of Mathematical Modes of Enquiry

Abstract

Teachers whose lessons make a significant difference to students’ understanding of mathematical ideas appear to adapt mathematical modes to the restricted frames of school mathematics. We explored one of these frames, the preparation of teaching resources, to investigate our hypothesis about the central role of mathematical modes of enquiry. We set up an artificial resource preparation exercise amongst a group of knowledgeable mathematics educators and recorded their collaboration. We found that our personal mathematical modes were transforming, and the results of this process were embedded into our planning. We argue that teachers’ fluency with mathematical modes is the basis of their unique contribution in providing something that a textbook or annotated website cannot provide.