ABSTRACT
Recent research in cognitive psychology and artificial intelligence (collectively called cognitive science) has made impressive progress in revealing the varieties and intricacies of mathematical problem solving. However, the connections between studies of mathematical problem solving and the practice of teaching mathematics are not always clear. That is to be expected. Due to the very nature of scientific inquiry, studies of problem solving must focus on questions of limited scope with simplified hypotheses, if only to provide a filter with which to separate signal from noise.
