id: 06675739
dt: a
an:
au: Zimmermann, Bernd
ti: Improving of mathematical problem-solving: some new ideas from old
resources.
so: 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).
py: 2016
pu: Cham: Springer
la: EN
cc: D50
ut:
ci:
li: doi:10.1007/978-3-319-28023-3_6
ab: 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.
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