id: 06494756
dt: a
an: 2015f.00435
au: Singer, Florence Mihaela; Voica, Cristian
ti: Is problem posing a tool for identifying and developing mathematical
creativity?
so: Singer, Florence Mihaela (ed.) et al., Mathematical problem posing. From
research to effective practice. New York, NY: Springer (ISBN
978-1-4614-6257-6/hbk; 978-1-4614-6258-3/ebook). Research in
Mathematics Education, 141-174 (2014).
py: 2014
pu: New York, NY: Springer
la: EN
cc: D50 C40
ut: problem posing; creativity; cognitive flexibility; development of
creativity
ci:
li: doi:10.1007/978-1-4614-6258-3_7
ab: Summary: The mathematical creativity of fourth to sixth graders, high
achievers in mathematics, is studied in relation to their
problem-posing abilities. The study reveals that in problem-posing
situations, mathematically high achievers develop cognitive frames that
make them cautious in changing the parameters of their posed problems,
even when they make interesting generalizations. These students display
a kind of cognitive flexibility that seems mathematically specialized,
which emerges from gradual and controlled changes in cognitive framing.
More precisely, in a problem-posing context, studentsâ€™ mathematical
creativity manifests itself through a process of
abstraction-generalization based on small, incremental changes of
parameters, in order to achieve synthesis and simplification. This
approach results from a tension between the studentsâ€™ tendency to
maintain a built-in cognitive frame, and the possibility to overcome
it, which is constrained by their need to devise mathematical problems
that are coherent and consistent.
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