Improving of mathematical problem-solving: some new ideas from old resources. (English)

Felmer, Patricio (ed.) et al., Posing and solving mathematical problems. Advances and new perspectives. Cham: Springer (ISBN 978-3-319-28021-9/hbk; 978-3-319-28023-3/ebook). Research in Mathematics Education, 83-108 (2016).

Summary: 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:{ }How to combine the traditional mathematical curriculum with problem-solving, understanding, and creativity?{ }Pupils can construct rules for calculating with fractions themselves, conjectures as well as proofs of the Pythagorean and related theorems.{ }How history might help to better understand and foster mathematical problem-solving processes?{ }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.{ }Finally, some recommendations are made for teacher education and teachers.