数学的問題解決における方略的能力に関する研究(V) : 問題解決能力に対する方略的能力の寄与率の実証的検討

The purpose of this study is to explore experimentally the role of strategic ability which is ability to make use of our mathematical resources in mathematical problem solving. In this study, strategic ability are captured by two dimension, "Ability to Use Problem Solving Strategies" and "Metacognitive Ability". The present paper aims to explore the rate of contribution of the strategic abilities and mathematical resources toward problem solving ability by multiple regression analysis. A total of 300 graders 6 in elementary school were administered the prpblems to evaluate children's problem solving ability, mathematical resources, and ability to use problem solving strategies. And, they were administered "A Questionnaire-Type Instrument for Measuring Metacognitive Ability in Mathematical Problem Solving" (Shimizu, N., 1995). The following were mainly found out through the various multiple regression analysisses. (1) The variables of Mathematical Resoure and Strategic abilities accounted for about 60% of the variance of problem solving ability. (2) The order of the variable which has higher contribution toward problem solving ability were "Mathmatical Resources", "Ability to Use Problem Solving Strategies" and "Metacognitive Ability" in turn. (3) To evaluate children's "Ability to Use Problem Solving Strategies" by all-or-nothing method seems to lead to underestimate the ability. (4) There were a gender difference with respect to the aspect of contribution toward problem solving ability, though there were not a gender difference with respect to the means and variance of the all variables significantly. Although the results of this research may be of limited generality and validity, the following are mainly suggested. (1) We Should not make light of basic mathematical resources. (2) With respect to strategic ability, first of all, we should emphasize teaching of the problem solving strategies, and second, teaching of the metacognition. (3) We should evaluate children's "Ability to Use Problem Solving Strategies" by multiple viewpoints. (4) We should consider the issue of gender difference in problem solving in detail.