台形概念の形成過程における確率的表象に関する研究
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概要
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The purpose of this study was to analyze the structure of childrens' own concept. Children in this study included 50 fifth graders who had received instruction about trapezoids during the previous year. One group, A, could not write the definition and the second group, B, could do this. Two methods of analysis, a conviction degree rating scaling method and a protocol, were applied to the data. The analysis of the data from group A (i.e. childrens' own concept) was as follows. 1. There exists 'a set of trapezoids', that was constructed with a continuous change distribution based upon the probability representation. 2. Every trapezoid was arranged according to a conviction degree rating in order. 3. When any instance was presented, it was neither recognized as a snap shot nor discriminated by definitive representation. It was recognized as a continuous change distribution by probability representation. 4. When children discriminated presented trapezoids, they retrieved the reference that was 'a set of trapezoids' that consisted of well-experienced instance, focused instance studied at the first teaching, and geometrical figure which was similar to trapezoids. Therefore, they may have mistaken the relevant instances. In contrast to the concept of group A, the analysis of the data from group B indicated that whether or not a presented instance was perceived as a trapezoid was based upon definitive representation. inconsistencies. It is the conscious of teachers on the student's individual concept of geometry that needs to be reformed.
- 全国数学教育学会の論文
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