This article is written from our perspective as both researchers and mathematics teacher educators, and describes how our knowledge has grown as we engage concurrently in both teaching and research. Reflection-on-action is a means for us of approaching the relationship between theory and practice that comes out of the development of our work as…

This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of epsilons. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by…

Our approach to emotion in school mathematics draws on social semiotics, pedagogic discourse theory and psychoanalysis. Emotions are considered as socially organised and shaped by power relations; we portray emotion as a charge (of energy) attached to ideas or signifiers. We analyse transcripts from a small group solving problems in mathematics…