Abstract
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.
Highlights
I want to highlight some constraints in teaching and research of mathematical problem solving
Because of space-limitation, a more detailed analysis of norms and values in mathematics education cannot be given here. Such analysis was started in more detail several years ago in connection with an attempt to develop a metatheory of mathematics education (Zimmermann 1979, 1981, 1983)
There should be better strategies to implement research on problem solving into the teaching of problem solving
Summary
I want to highlight some constraints in teaching and research of mathematical problem solving. Teachers as well as researchers should be much more aware of possible limits and constraints of their respective enterprise. Such awareness might help to improve the planning and effectuation of their teaching or research project as well as its appropriate evaluation. Because of space-limitation, a more detailed analysis of norms and values in mathematics education cannot be given here. Such analysis was started in more detail several years ago in connection with an attempt to develop a metatheory of mathematics education (Zimmermann 1979, 1981, 1983). To some aspects of this point I will relate later
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