# Problem modification as a tool for detecting cognitive flexibility in school children

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## Abstract

This paper presents the results of an experiment in which fourth to sixth graders with above-average mathematical abilities modified a given problem. The experiment found evidence of links between problem posing and cognitive flexibility. Emerging from organizational theory, cognitive flexibility is conceptualized through three primary constructs: cognitive variety, cognitive novelty, and changes in cognitive framing. Among these components, changes in cognitive framing could be effectively detected in problem-posing situations, giving a relevant indication of students’ creative potential. The students’ capacity to generate coherent and consistent problems in the context of problem modification may indicate the existence of a strategy of functional type for generalizations, which seems to be specific to mathematical creativity.

## Keywords

Problem posing Cognitive flexibility Creativity Change in cognitive framing## Mathematical Subject Classification

97C30## Notes

### Acknowledgments

The authors thank the three anonymous reviewers for their valuable comments on an early version of this paper.

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