Geometric Construction as a Threshold of Proof : The Figure as a Cognitive Tool for Justification

• Iwasaki Hideki

  International Development and Cooperation at Hiroshima University

• Okazaki Masakazu

  Joetsu University of Education.

抄録

Geometric construction is usually considered as the procedure of drawing a figure bounded by a straightedge ruler and a compass. It, however, could be didactical intermediate between a cause-effect and an assumption-conclusion explanation because it is not only a series of systematic activities using only two tools but also mathematical proof of existence in itself. We, therefore, consider it as a educational threshold of proof in system although most mathematics teachers emphasize its procedural aspect. We analyzed the justification of the geometric constructions made by seventh grade students in the classroom lessons in terms of image schema. Image schema was developed for a meaning-making function by Dörfler(1991). It was made available for us to clarify the logical or cognitive base of the students' justification and change of thought. This research finally showed some factors for the transition from construction to proof in geometry.

収録刊行物

• International Journal of Curriculum Development and Practice

  International Journal of Curriculum Development and Practice 3 (1), 57-64, 2001

  日本教科教育学会

詳細情報

• CRID: 1390001205782287360
• NII論文ID: 110007969897
• DOI: 10.18993/jcrdaen.3.1_57
• ISSN: 24241415
• ISSN: 13444808
• 本文言語コード: en
• 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