Research on Development and Utilization of Instruments of Potential Ability for Learning Mathematics (V) : The Effect of Teaching of Potential Ability on Mathematical Thinking Ability

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  • 潜在的な数学的能力の測定用具の活用化に向けた開発的研究(V) : 思考力に対する潜在力指導の効果の検討
  • 潜在的な数学的能力の測定用具の活用化に向けた開発的研究(5)思考力に対する潜在力指導の効果の検討
  • センザイテキ ナ スウガクテキ ノウリョク ノ ソクテイ ヨウグ ノ カツヨウカ ニ ムケタ カイハツテキ ケンキュウ(5)シコウリョク ニ タイスル センザイリョク シドウ ノ コウカ ノ ケントウ

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Abstract

The purpose of this research is to develop instruments to measure pupils' potential ability for learning mathematics and to study theoretically and empirically the ways to utilize the instruments for improving mathematics education. In the previous study (Nakahara et al., 2010), we found that teaching of potential ability to 4th graders had a positive effect on improvement of potential ability. Following the study, the purpose of this study is to investigate the effect of the teaching of potential ability on a certain kind of mathematical thinking ability that is roughly defined as problem solving ability for textbook-level "process problems" (Charles & Lester, 1982). In this study, firstly, 4 sets of three worksheets for teaching of potential ability were constructed according to the theoretical framework of potential ability. Each set of three worksheets was related to one of the four factors of the "mathematical thinking" of potential ability (i.e., pattern, logic, operation, flexibility of thinking), and each worksheet had one or two mathematical problem(s). For experimental group, the classroom teacher conducted 15 minutes teaching in the morning per a week using the worksheet. And, before and after the 12 week teaching period, we conducted mathematical thinking ability test for both experimental (N=121) and control (N=121) groups. The two-way ANOVA showed significant interaction between the teaching of potential ability and the improvement of mathematical thinking ability. Including the result of our previous study, the positive effect of teaching potential ability on both the potential ability itself and mathematical thinking ability was found. Finally, we discussed how the teaching of potential ability could influence the improvement of mathematical thinking/problem-solving ability and how to consider alternative ways of teaching to improve it reflecting results of our studies.

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