This chapter describes my investigation into what a regular class of students and a group of gifted students “know” about problem solving. My goal was to identify whether discrepancies exist in implicit and explicit knowledge within or between the two student groups. The chapter begins with a brief outline of problem solving as the educational psychology literature describes it, then provides a problem-solving framework to comprehensively represent and chart problem-solving phases.

The study's research participants came from four schools in the same metropolitan area. They included a class of regular students from one school and students judged to be academically gifted from three other schools. Both groups were interviewed about their views of problem solving and were then observed as they carried out a problem-solving task. Descriptions of problems and problem solving given by students in the regular class and the gifted students were examined to identify similarities and differences. I argue that explicit discussion of problem-solving phases has the potential to improve students’ knowledge of the language of problem solving, and can assist teachers and students to explicitly discuss problem-solving strategies for solving problems. To this end, the Problem Solving Guidance Framework is presented as a useful instrument for structuring explicit teaching and learning of problem solving.