Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

This paper addresses four questions: What are the effects of reducing class size? How important are these effects? How can we explain these effects? and How can we improve the outcomes when class sizes are reduced? A major aim is to provide directions for resolving the paradox as to "Why reducing class size has not led to major improvements in…