図形の論理的位置づけの初期の様相について : 論証への移行を目指した中学1年『平面図形』のデザイン実験(1)

• 高本 誠二郎

  上越教育大学大学院

• 岡崎 正和

  上越教育大学

書誌事項

タイトル別名

• Initial Aspects of Logical Justification in Learning Geometric Figures : Design Experiment of 7th Grade Unit "Plane Geometry" towards the Transition to Geometric Proof (1)

抄録

We conducted the design experiment in the teaching unit "plane geometry" which was concieved as the transitional material from geometry in primary mathematics to geometric proof in secondary school, and designed as three subunits of (1) the discovery game of geometric figures, (2) the jintori game, and (3) the discovery game of geometric constructions. This paper reprorts 7th grade students' initial aspects of logical justification of geometric figures in the first subunit "the discovery game of geometric figures". The findings in this paper are the following four points. ・Students first tended to attend to the larger figures visually in the hemp leaf situation of the discovery game of geometric figures. However, when they began to consider the criticism by others and the counter examples in their minds, they could change their object of justification to the smaller figures, with their consciousness of insufficiency of the empirical explanations. They then developed their idea of trying to justify the constituent geometric figures by using the smaller figure (the right triangle). ・Therefore, we may indicate that the idea of placing the constituent figures by the right triangle was produced in the situation of formulation in which the assumption of the others' criticism was added to the situation of action. ・When students tried to justify the constituent figures by one geometric figure (right triangle), they began to consider the order of placing the figures and the justification of the right triangle itself. The justification could be successful when they reconstructed steps of geometric construction as conditions of proof. Furthermore, we suggest that the logical proof was produced as a feedback of the others' criticism and based on the logic of justification of the right triangle. ・We also found students' tendencies of complementing their logical explanation with the empirical means and of approving the empirical explanation in some cases, although they enhanced their abilities of explaining the geometric figures in the logical manner.

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 14 (0), 41-50, 2008

  全国数学教育学会

キーワード

• 論理的正当化
• 経験的説明
• 図形

詳細情報

• CRID: 1390564238066260864
• NII論文ID: 110009498611
• DOI: 10.24529/jasme.14.0_41
• 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