順列・組合せ問題の解答プロセスにおけるメタ認知の役割

抄録

When solving a mathematical problem, in spite of mastering knowledge and formula necessary for the solution, we sometimes encounter a situation where we cannot reach the correct answer. The reason can be contributed to the lack in metacognitive abilities. Metacognitive abilities consist of comparing the difficulty of problem with own ability, proper plan of solution process, and conscious monitoring and control of solution process. The role and importance of metacognitive ability in mathematical problem solving of permutations and combinations was explored. Participants were required to solve five problems related to permutations and combinations. For each problem, the solution process was divided into (1) recognition of mathematical problem, (2) plan of solution, and (3) execution of solution. Participants were required to rate the anticipation whether they can solve it or not, and to rate the confidence of their own answer. According to the total score of five problems, the participants were categorized into the group of the higher test score and the group of the lower test score. As a result, at the plan and the execution processes, statistically significant differences were detected between the high and low score groups. As for the rating on the anticipation of result and the confidence of own answer, no significant differences were found between both group. Moreover, the relationship between the score of plan process and the score of execution process was statistically correlated. In other words, the more proper the plan process was conducted, the more proper solution the participants reached. In such a way, the importance of metacognitive ability in the solving process, especially the plan ability was suggested.