Presents three schools of argument on mathematical communication: (1) cognitivist argument; (2) interactionist argument; and (3) neo-pragmatist argument. Distinguishes the mathematical versus talking about mathematics, talking mathematics versus learning the art of mathematical conversation, and the conversation of mathematicians versus students'…

Raises a number of questions about knowledge generation from mathematics education and the nature of pedagogical information in the field. Considers two main activities within the realm of mathematics education: (1) pursuing investigations to improve instruction and (2) redefining the boundaries of mathematics as a subject. (DDR)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)

Failure of most children to solve word problems beyond the simplest is seen to stem from two causes: failure to understand applied arithmetic and failure to relate problems to the real world. Relevant research is reviewed, and a route for new research is proposed. (MP)