初等代数の問題解決過程における推論スキーマの役割 : 数学的概念に基づく推論スキーマ

• 益子 典文

  鳴門教育大学学校教育学部

書誌事項

タイトル別名

• The Role of Reasoning Schemata in Generalized Arithmetic Problem Solving Processes : Reasoning Schemata based on Mathematical Concepts

抄録

The existence and identification of functions of mathematical concepts reasoning schemata in problem solving processes are proposed in this paper. Firstly, the existence of reasoning schemata that are based on characteristics of mathematical concepts in simple reasoning problems is pointed out. Problem space of mathematical problem solving processes is not only defined by simple operators like chess, but also include rich mathematical concepts. The existence and the role of such mathematical concepts reasoning schemata have been discussed in three research papers understanding of generalized arithmetic. These are (1) student-professor problem (Clement 1982), (2) CSMS algebra test problems (Kuchemann 1981), and (3) "conceptual entity" in problem solving processes (Greeno 1982). Secondly, functions of mathematical concepts reasoning schemata in problem solving processes are identified through several concrete problems. The results show that, mathematical concepts reasoning schemata (1) help using mathematical structures in problem solving processes, (2) connect different knowledge in problem solving processes as cognitive glue (Lesgold 1988), and (3) produce elegant methods in problem solving. These results are applied to research into task analysis of nonroutine problems and task sequencing.

収録刊行物

• 科学教育研究

  科学教育研究 19 (2), 67-77, 1995

  一般社団法人 日本科学教育学会

キーワード

• mathematics education
• cognitive science
• problem solving
• reasoning schemata
• generalized arithmetic

詳細情報

• CRID: 1390282680728515968
• NII論文ID: 110002704636
• NII書誌ID: AN00036978
• DOI: 10.14935/jssej.19.67
• ISSN: 21885338
• ISSN: 03864553
• 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