Alf Coles (Graduate School of Education, University of Bristol): A relational view of the concept of number; pedagogical, neuroscientific, and philosophical considerations

In this seminar, I will move from pedagogical to neuroscientific to philosophical considerations of the concept of 'number'. Two sources of evidence converge to bring into question the orthodoxy that learning mathematics entails a movement from the concrete to abstract. The first source comes from reflection on commonalities across the pedagogy of three of the great mathematics educators of the twentieth century (Caleb Gattegno, Vasily Davydov and Bob Davis). The second source is recent neuroscientific research into number sense and the previously unacknowledged role of ordinality (cf the work of Ian Lyons). Drawing these sources together suggests the potential, for children's learning, of approaching number as a relation, which then leads to philosophical implications for what numbers are.