Does the problem-solving literature have anything of value to guide instructional decision making? The answer is that, although the literature on problem-solving instruction presents ambiguous messages, five results stand out:
1. Students must solve many problems in order to improve their problem solving ability.
2. Problem solving ability develops slowly over a prolonged period of time.
3. Students must believe that their teacher thinks problem solving is important in order for them to benefit from instruction.
4. Most students benefit greatly from systematically planned problem-solving instruction.
5. Teaching students about problem-solving strategies and heuristics and phases of problem solving (e.g. Polya’s, 1945/1973, four-stage problem-solving model) does little to improve students’ ability to solve general mathematics problems.
Source: “From Problem Solving to Modeling,” Frank Lester and Paul Kehle, in Beyond Constructivism.