Strategies and Conceptual Understanding of Permutation Operations : Focused on the Understanding of Symmetrical Relationship

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  • 順列操作の実行的理解と概念的理解 : 「対称性の理解」を中心に
  • ジュンレツ ソウサ ノ ジッコウテキ リカイ ト ガイネンテキ リカイ タイショウセイ ノ リカイ オ チュウシン ニ

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The present study investigated the development of permutation operations in terms of both strategies for making permutations and conceptual understanding of permutations. In Study 1, 19 kindergartners, 21 2^<nd> graders, 21 4^<th> graders, 20 6^<th> graders, and 20 8^<th> graders performed tasks such as making permutations and predicting the number of possible permutations and the symmetrical relations (Nakagaki, 1979) of permutations. The results showed that conceptual understanding of permutations gradually develops as a generalized strategy for making permutations across various kinds of problems. In Study 2, the subjects were 47 5^<th> graders. The results of Study 1 were re-examined, and the results of Study 2 confirmed those of Study 1. In previous research, differences in performance across various kinds of permutation problems were explained by quantitative differences in information processing capacity, but the present study explained them in terms of qualitative differences in conceptual understanding.

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