This article is the third in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". In this article the author focuses on what learners have to understand and learn in order to do secondary mathematics well in general terms. She is assuming a…

Describes "World Class Tests in Mathematics and Problem-Solving," developed with the belief that creativity is worth nurturing and can be nurtured. (KHR)

Describes the idea of teaching as active learning and defines direction in mathematics teaching as action and perception. Presents an example of a mathematics classroom activity in which students are centered. (KHR)

In preparing to teach speed to a Y10 intermediate class in a multicultural secondary modern, the author was aware of the difficulty in getting students not only to follow a complex logical argument, but also to be able to reproduce it in a variety of different problem situations. Normally one would set out the working out of the problem as a…