In this chapter, I want to consider the problematical relationship between the mathematics learned in the mathematics classroom and the “math” which is used in practical situations outside the school. I shall examine traditional and “alternative” views of the relationship between the two kinds of mathematics – according to their conceptions of the context of mathematical thinking, and of the relationship between cognition and context. I set out the features that need to be considered in a more satisfactory account of thinking-in-context. I then expand on this notion of contexted cognition and illustrate its use in research on numerate thinking and affect among adult students, using in-depth consideration of a case study. Finally, I put forward some conclusions about the ways that the problem of transfer should be considered by mathematics educators.

Two views of mathematics and transfer

The “transfer” of learning can be considered to refer in general to the use of ideas and knowledge from one context in another. It often is used particularly for the “application” of knowledge from academic contexts to work or everyday activities. This is clearly a central problem of training, and also for most conceptions of education. It is especially important for mathematics. Of all the subjects taught and learned at school, it is one of those claimed to have the widest applicability outside school. However, at the same time, it is perhaps the subject in which the classroom at school (as opposed to outside activities) provides the context for the greatest part of children's learning and problem solving – though not for all of it.