Development and Evaluation of Curriculum for Algebraic Thinking and its Representation in Elementary and Secondary Education

• Project/Area Number: 17H02693
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Education on school subjects and activities
• Research Institution: Tokyo Gakugei University
• Principal Investigator: FUJII Toshiakira 東京学芸大学, 教育学部, 名誉教授 (60199289)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000); Fiscal Year 2021: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2020: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2018: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2017: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
• Keywords: 擬変数 / 初等代数 / 教材開発 / 授業研究 / 研究授業 / 問題解決型授業 / 文字式 / 代数的思考 / 数学的表現 / 数学的思考 / カリキュラム / 代数滝思考 / 教授可能性 / 文字の式 / 数字の式 / 式をよむ / 式に表す / 式の形式的処理 / 数学教育学 / 代数的表現 / カリキュラム開発

Outline of Final Research Achievements

At the elementary and secondary education level, there is an assumption that "literal symbols such as a,x " can express generality, while "numerical symbols " using numbers cannot. However, looking at the history of mathematics, before the development of written notation, "numerical formulas" were used to imply generality and to develop arguments. In this study, we named the numbers that imply generality in "numerical expressions" as "quasi-variables," focused on the function of quasi-variables, developed new teaching materials, and at the same time, examined and improved existing teaching materials from the viewpoint of quasi-variables to construct a curriculum proposal for algebraic thinking and expression. Furthermore, we conducted a comprehensive survey of students and teachers after the experimental lessons and evaluated the curriculum.

Academic Significance and Societal Importance of the Research Achievements

国の内外を問わず、中等教育段階において、文字a,xなどを用いた「文字式」の学習は、算数から数学へ飛躍する際の壁であり、ここで多くの生徒が困惑し、数学嫌いになっている。にも拘わらずこの学習困難性に対してこれまで明確な改善指針が提言されていない。
本研究では、数学史において、文字表記が充実する前では、一般性を含意して論を展開する際には、「数字式」が用いられている事実に着目し、このような数を擬変数(quasi-variable)と命名し、擬変数を視点に新しい教材を開発した。また、既存のカリキュラムを精査・改良し、「数字式」から「文字式」に至るカリキュラム試案を構築した点が成果である。

Research Products

• [Journal Article] Roles of Quasi-variables in the Process of Discovering Mathematical Propositions (2022)
  • Author(s): Toshiakira FUJII
  • Journal Title: Proceedings of 16th International Conference of The Mathematics Education for the Future Project Volume: Vol.1 Pages: 100-106
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] 擬変数の役割と機能：命題の発見過程に焦点を当てて (2020)
  • Author(s): 藤井斉亮
  • Journal Title: 学芸大数学教育研究 Volume: 32号
  • NAID: 120007046323
  • Peer Reviewed
• [Journal Article] 数学的問題解決における日米共通調査再考-「マッチ棒の問題」の解決における式表現と擬変数に焦点を当てて- (2018)
  • Author(s): 藤井斉亮 成田慎之介 清野辰彦
  • Journal Title: 日本数学教育学会誌 Volume: 100 Pages: 2-15
  • NAID: 130007937372
  • Peer Reviewed
• [Presentation] Roles of Quasi-variables in the Process of Discovering Mathematical Propositions (2022)
  • Author(s): Toshiakira FUJII
  • Organizer: 16th International Conference of The Mathematics Education for the Future Project
  • Int'l Joint Research
• [Book] 数学教育学の礎と創造 (2017)
  • Author(s): 藤井斉亮先生ご退職記念論文集編集委員会
  • Total Pages: 358
  • Publisher: 東洋館出版社
  • ISBN: 9784491034447