On the Teaching Situation of Irrational Numbers : Epistemological Considerations as the Basis of Designing for Conceptual Change

• SHINNO Yusuke

  Mathematics Education Department, Graduate School of Education, Hiroshima University

抄録

Generally we can point out two different ways in introducing new kinds of numbers as follows. The first is to represent a result of measurement The second is to solve algebraic equations. Although the relation between these two ways might have been overlooked in any teaching situations, this can be didactically explicit in the teaching situation of irrational numbers from the conceptual change perspective. The purpose of this paper is to derive some didactical implications for a conceptual change situation by focusing on a knowing of "incommensurability" that can be an essential aspect of irrationals. For attaining this purpose, the epistemological considerations take place in three contexts: curricular contents, history and teaching experiment. In conclusion, three points as didactical implications are shown: 1) problematic situation regarding the representation of number; 2) eliminating the tendency to cling to the "concrete"; 3) shifting attitudes toward the mathematical knowledge.

収録刊行物

• International Journal of Curriculum Development and Practice

  International Journal of Curriculum Development and Practice 10 (1), 67-76, 2008

  日本教科教育学会

詳細情報

• CRID: 1390282680759629952
• NII論文ID: 110007969935
• DOI: 10.18993/jcrdaen.10.1_67
• 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