Improving of Mathematical Problem-Solving: Some New Ideas from Old Resources

Abstract

The main focus of this chapter is on improvement of teaching of problem-solving. In the introduction important and to some extent neglected issues of teaching problem-solving will be presented and discussed. On this background the following questions and possible answers will be addressed: o How to combine the traditional mathematical curriculum with problem-solving, understanding, and creativity? o Pupils can construct rules for calculating with fractions themselves, conjectures as well as proofs of the Pythagorean and related theorems. o How history might help to better understand and foster mathematical problem-solving processes? o Observed problem-solving processes of pupils involved in well-known problems from calculating the area of a circle, fractions and calculus can be interpreted as reinvention of old and important heuristic strategies. o Finally, some recommendations are made for teacher education and teachers.