Mathematical Problem Solving - On Some Constraints in Teaching and Research

Teaching of problem solving as well as research in problem solving are subjected to many different constraints and hidden assumptions. Many of the constraints for teaching hold as well for research in these areas. The detection and the analysis of such issues are carried out on the background of concrete elucidating examples (“proofs of existence”). We conclude with some theses, related to such constraints as “As well teachers as researchers should be much more aware on their respective belief-system” and “There should be more analysis and reflection about possible constraints and limits on own studies on problem-solving and metacognition.” Some own reflections on possible constraints of this study are presented as well.Teaching of problem solving as well as research in problem solving are subjected to many different constraints and hidden assumptions. Many of the constraints for teaching hold as well for research in these areas. The detection and the analysis of such issues are carried out on the background of concrete elucidating examples (“proofs of existence”). We conclude with some theses, related to such constraints as “As well teachers as researchers should be much more aware on their respective belief-system” and “There should be more analysis and reflection about possible constraints and limits on own studies on problem-solving and metacognition.” Some own reflections on possible constraints of this study are presented as well