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This article aims to identify, characterize and compare the cognitive flexibility profile of the mental calculations of Brazilian students, based on the analysis of cognitive elements, namely the characteristics of the problems and the solution procedures, used during the resolution of problems. arithmetic calculations. The sample for this study included 42 second-year students (7 to 8 years old) and 42 fourth-year students (9 to 11 years old), from four public schools in Porto Alegre. Each child was encouraged to classify 12 arithmetic calculations, demonstrating their numerical knowledge by explaining the reasoning involved in solving, through a specific assessment instrument on cognitive flexibility. The results revealed that the differences in the proportions of use of numerical knowledge differentiated the profiles of cognitive flexibility: flexible, mixed or rigid.
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