中学生の証明問題解決過程の分析

概要

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The performance of geometric proof problems were analyzed using a think aloud procedure. Ten ninth graders participated in the investigation, five students were high achievers in mathematics and other five were low achievers. Their views of proof were also investigated. The results of protocol analysis showed that high achievers generated more information and more frequently made use of it. Especially they frequently reread the problem sentences. Geometric proof problem is performed based on a figure attached to the problem. The figure includes not only premise but also conclusion of the problem. Since successful performance of the proof needs to separate the premise, conclusion and other terms generated during the performance of the proof, it is required to reread the problem sentence so as to monitor her/his own process of the performance. The high achievers were to show superior ability to monitor. They regarded the purpose of proof as the verification of inference and anticipation, and the means to develop their logical thinking ability. On the other hand the low achievers regarded it as the explanation and the indication of their understanding to others. According to these findings, some issues of teaching proof are discussed.
全国数学教育学会の論文