Building Bridges: Reflections on the problem of transfer of learning in mathematics

The takeup of opportunities for applying formal learning outside the school is often disappointing – to teachers, parents, employers, and many pupils. Not surprisingly, there is much controversy among researchers in mathematics education and related fields, as to the reasons. Here I argue that neither traditional nor constructivist views, with their simplistic faith in the basic continuity of knowledge across contexts, nor currently popular ‘insulationist’ views such as the strong form of situated cognition, which claims that transfer is basically not possible, are adequate. Instead, I analyse why transfer is problematical in principle, and undependable in practice. I recommend an alternative approach for building bridges between practices, based on analysing the discourses involved as systems of signs, and looking for appropriate points of inter-relation between them. In this reconceptualisation of the ‘problem’ of transfer, the role of affective factors, previously under-examined in the literature, is highlighted.