
06494756
a
2015f.00435
Singer, Florence Mihaela
Voica, Cristian
Is problem posing a tool for identifying and developing mathematical creativity?
Singer, Florence Mihaela (ed.) et al., Mathematical problem posing. From research to effective practice. New York, NY: Springer (ISBN 9781461462576/hbk; 9781461462583/ebook). Research in Mathematics Education, 141174 (2014).
2014
New York, NY: Springer
EN
D50
C40
problem posing
creativity
cognitive flexibility
development of creativity
doi:10.1007/9781461462583_7
Summary: The mathematical creativity of fourth to sixth graders, high achievers in mathematics, is studied in relation to their problemposing abilities. The study reveals that in problemposing 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 problemposing context, students' mathematical creativity manifests itself through a process of abstractiongeneralization based on small, incremental changes of parameters, in order to achieve synthesis and simplification. This approach results from a tension between the students' tendency to maintain a builtin cognitive frame, and the possibility to overcome it, which is constrained by their need to devise mathematical problems that are coherent and consistent.