The identity of problem solving

This paper raises issues motivated by considering the “identity” of problem solving. This means that we are concerned with how other mathematics education topics impinge on problem solving, and with themes that naturally arise within the problem-solving agenda. We claim that some of these issues need more attention by educational research, while for others, the coverage they have in the literature requires reappraisal in certain ways. In particular, the following themes are discussed: problem solving vis-à-vis proof; conceptualization; structure and representations; raising questions and posing; the significance to problem solving of techniques; application of knowledge; exploration; and the reading of mathematical texts.