数学的概念の一般化における理解過程に関する研究 : 平行四辺形概念の一般化

• 岡崎 正和

  広島大学大学院

書誌事項

タイトル別名

• Research on the Understanding Processes in Generalization of Mathematical Concepts : Generalization of Parallelogram

抄録

In this research we approach to the understanding processes in generalization of mathematical concepts based on the "Optimizing Equilibration Model of Mathematical Understanding". In this paper, in particular, we will clarify the processes through which children understand inclusion relations between quadrilaterals and generalize their schema of parallelogram. Difficulties in understanding inclusion relations are not consisted in mathematical logic, but in such children's tacit property that each angle of rectangle is not 90°. We have discussed means that they overcome the difficulties and understand inclusion relations, and indicated that the following means are effective. 1. conceiving geometrical figures dynamically by manipulating on operative material and seeing continual transformations from parallelogram to rectangle or rhombus 2. understanding conservation of properties in the transformations 3. understanding negative properties in the transformations 4. analogy to the inclusion relation between parallelogram and rhombus 5. analogy to the inclusion relation between rhombus and square We also clarified that after understanding the content, children's schema of parallelogram becomes to be in the states of the followings. 1. Properties of a geometrical figure are organized, and children can define a geometrical figure by using those properties. 2. Children conceive properties of a geometrical figure as common properties between geometrical figures. 3. A geometrical figure is a bearer of their properties. These states are effective for children to learn proof in lower secondary school. Therefore, children should learn inclusion relations between quadrilaterals in primary school.

収録刊行物

• 数学教育学研究 : 全国数学教育学会誌

  数学教育学研究 : 全国数学教育学会誌 3 (0), 117-126, 1997

  全国数学教育学会

詳細情報

• CRID: 1390001288112850176
• NII論文ID: 110009498374
• DOI: 10.24529/jasme.3.0_117
• ISSN: 24333034
• ISSN: 13412620
• 本文言語コード: ja
• データソース種別:
  • JaLC
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可