均衡化理論に基づく数学的概念の一般化における理解過程に関する研究 : 「包含除」の一般化における理解過程

• 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 Process in Generalization of Mathematical Concepts Based on the Equilibration Theory : Understanding Process in Generalization of Quotitive Division

抄録

Multiplication and division of decimal fraction is one of the most difficult contents for 5th graders in the primary school. This study focuses on the division of decimal fraction, especially on the generalization from quotitive division to first application of ratio. The purpose of this study is to clarify the understanding process in generalization of quotitive division, especially the factors of difficulties in understanding the division of decimal fraction and the factors for overcoming the diffuculties. The main results are folloing; 1. The generalization of quotitive division is made by extending the idea of 'measurement'. 2. In the generalization, it is effective to use the operative material that can generalize the idea of measurement and that function as the semi-concrete material for number-line expression. 3. The primitive model on quotitive division include the properties of 'quotient is integer' and 'dividend is larger than divisor'. 4. Children feels difficulties in such situations that quotient is decimal fraction and that dividend is smaller than divisor. These situations are related with primitive model. 5. The stages that the idea 'how many times' is abstracted from how many pieces 'are folloing; (a) The idea of 'how many times' is primitively constructed in such a division that dividend is larger than divisor and quotient is decimal fraction. (b) The idea of 'how many times' is realized in such a division that dividend is smaller than divisor. (c) The merit of the idea of 'how many times' is realized when all division of decimal fraction is conceived by the idea.

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 2 (0), 91-100, 1996

  全国数学教育学会

キーワード

• 包含除の一般化
• 暗黙モデル
• 理解モデル

詳細情報

• CRID: 1390845713038931072
• NII論文ID: 110009498358
• DOI: 10.24529/jasme.2.0_91
• 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