Abstract: In this article, the author, who has written extensively about mathematical
problem solving over the past 40 years, discusses some of his current thinking about the
nature of problem-solving and its relation to other forms of mathematical activity. He
also suggests several proficiencies teachers should acquire in order for them to be
successful in helping students become better problem solvers and presents a framework
for research on problem-solving instruction. He closes the article with a list of principles
about problem-solving instruction that have emerged since the early 1970s.