Development of task design principles for promoting mathematical activity involving assumptions in school mathematics

• Project/Area Number: 18K18636
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Review Section: Medium-sized Section 9:Education and related fields
• Research Institution: University of Tsukuba (2021-2022); Shinshu University (2018-2020)
• Principal Investigator: Komatsu Kotaro 筑波大学, 人間系, 准教授 (40578267)
• Project Period (FY): 2018-06-29 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000); Fiscal Year 2020: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 算数・数学 / 前提追究 / 教材開発

Outline of Final Research Achievements

This research project aimed to develop task design principles for promoting mathematical activity involving assumptions in school mathematics. I specified learning goals targeted in this project from the perspective that truth in mathematics depends on assumptions and used the literature to construct a preliminary version of task design principles. I then implemented tasks designed based on these principles in primary and secondary schools and analysed the implementation to refine the preliminary principles. From this project, I showed that the refined principles can underpin the design of tasks for achieving the intended learning goals.

Academic Significance and Societal Importance of the Research Achievements

従来の数学教育では，前提が明確な状況で推論を積み重ねる論理的思考力の育成が志向されてきたが，日常社会では条件が明確な問題に直面することは少ない。そこで本研究では前提追究活動に着目し，真に生きて働く力を算数・数学科で育成することを目指した。さらに，個々の具体的な課題を設計することよりも，そうした課題設計を裏付ける一般的な設計原理を開発した。これにより，原理に基づいて，研究で開発した課題以外にも多くの課題を設計できるようになることが期待される。

Research Products

• [Int'l Joint Research] University of Cambridge/University of Oxford(英国)
• [Int'l Joint Research] University of Cambridge/University of Oxford(英国)
• [Int'l Joint Research] University of Cambridge/University of Oxford(英国)
• [Int'l Joint Research] University of Cambridge/University of Oxford(英国)
• [Journal Article] 学校数学における課題設計原理の開発に関する研究の枠組み (2023)
  • Author(s): 小松孝太郎
  • Journal Title: 日本数学教育学会誌数学教育 Volume: 105(1) Pages: 2-13
  • Peer Reviewed / Open Access
• [Journal Article] The discovery function of proving by mathematical induction (2023)
  • Author(s): Komatsu, K.
  • Journal Title: Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] Toulmin analysis of meta-mathematical argumentation in a Japanese grade 8 classroom (2022)
  • Author(s): Reid, D., Shinno, Y., Komatsu, K., & Tsujiyama, Y.
  • Journal Title: Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education Volume: 1 Pages: 234-241
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Teachers’ Assessment Factors of Students’ Non-Cognitive Skills: Analysis of a Survey in the Area of “Data Handling” in Junior High School Mathematics (2022)
  • Author(s): 青山和裕・辻山洋介・小松孝太郎・永田潤一郎・吉川厚
  • Journal Title: Journal of Science Education in Japan Volume: 46 Issue: 1 Pages: 91-103
  • DOI: 10.14935/jssej.46.91
  • ISSN: 0386-4553, 2188-5338
  • Peer Reviewed / Open Access
• [Journal Article] Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning (2022)
  • Author(s): Komatsu, K., & Jones, K.
  • Journal Title: Educational Studies in Mathematics Volume: 109(3) Issue: 3 Pages: 567-591
  • DOI: 10.1007/s10649-021-10086-5
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Toulmin analysis of meta-mathematical argumentation in a Japanese grade 8 classroom (2021)
  • Author(s): Reid, D., Shinno, Y., Komatsu, K., & Tsujiyama, Y.
  • Journal Title: Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Interplay between paper-and-pencil activity and dynamic-geometry-environment use during generalisation and proving (2020)
  • Author(s): Komatsu, K., & Jones, K.
  • Journal Title: Digital Experiences in Mathematics Education Volume: 6(2) Issue: 2 Pages: 123-143
  • DOI: 10.1007/s40751-020-00067-3
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] The Role of “Opportunity to Learn” in the Geometry Curriculum: A Multilevel Comparison of Six Countries (2019)
  • Author(s): Bokhove Christian、Miyazaki Mikio、Komatsu Kotaro、Chino Kimiho、Leung Allen、Mok Ida Ah Chee
  • Journal Title: Frontiers in Education Volume: 4:63
  • DOI: 10.3389/feduc.2019.00063
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Curriculum development for explorative proving in lower secondary school geometry: Focusing on the levels of planning and constructing a proof (2019)
  • Author(s): Miyazaki, M., Nagata, J., Chino, K., Sasa, H., Fujita, T., Komatsu, K., & Shimizu, S.
  • Journal Title: Frontiers in Education Volume: 4(31)
  • DOI: 10.3389/feduc.2019.00031
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Task design principles for heuristic refutation in dynamic geometry environments (2019)
  • Author(s): Komatsu, K., & Jones, K.
  • Journal Title: International Journal of Science and Mathematics Education Volume: 17(4) Issue: 4 Pages: 801-824
  • DOI: 10.1007/s10763-018-9892-0
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Task design for developing students’ recognition of the roles of assumptions in mathematical activity (2019)
  • Author(s): Komatsu, K., Stylianides, G. J, & Stylianides, A. J.
  • Journal Title: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Secondary school students’ appraisal of mathematical proofs (2018)
  • Author(s): Komatsu, K., Yamazaki, M., Fujita, T., Jones, K., & Sue, N.
  • Journal Title: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education Volume: 3 Pages: 227-234
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Domain-specific frameworks for curriculum development of explorative proving in junior high school mathematics (2018)
  • Author(s): Miyazaki, M., Nakagawa, H., Chino, K., Iwata, K., Komatsu K., & Fujita, T.
  • Journal Title: School mathematics curriculum reforms: Challenges, changes and opportunities (ICMI Study 24 conference proceedings) Volume: - Pages: 269-276
  • Peer Reviewed / Open Access
• [Presentation] 学校数学における課題設計原理の開発に関する研究 (2022)
  • Author(s): 小松孝太郎
  • Organizer: 日本数学教育学会第10回春期研究大会
• [Presentation] 学校数学における課題設計原理の開発に関する研究の枠組み (2022)
  • Author(s): 小松孝太郎
  • Organizer: 日本数学教育学会第10回春期研究大会
• [Presentation] Approaches to analysing classroom argumentation (2022)
  • Author(s): Komatsu, K., & Jones, K.
  • Organizer: The 44th Conference of the International Group for the Psychology of Mathematics Education
  • Int'l Joint Research
• [Presentation] 前提の役割に関する生徒の認識を育成するための課題設計 (2019)
  • Author(s): 小松孝太郎・Andreas J. Stylianides・Gabriel J. Stylianides・和田聖国
  • Organizer: 日本数学教育学会第52回秋期研究大会
• [Presentation] 授業過程の研究手法としてのアーギュメンテーション分析 (2019)
  • Author(s): 真野祐輔・David A. Reid・小松孝太郎・辻山洋介
  • Organizer: 日本科学教育学会第43回年会
• [Presentation] 科学教育の内容・活動に固有な非認知的スキルの評価法の開発：領域「データの活用」における調査結果の考察 (2019)
  • Author(s): 辻山洋介・青山和裕・小松孝太郎・永田潤一郎・吉川厚
  • Organizer: 日本科学教育学会第43回年会
• [Presentation] The role of ‘opportunity to learn’ in the geometry curriculum: A multilevel comparison of six countries (2019)
  • Author(s): Bokhove, C., Miyazaki, M., Leung, A., Mok, I., Komatsu, K., & Chino, K.
  • Organizer: 2019 American Educational Research Association Annual Meeting
  • Int'l Joint Research
• [Presentation] Task design with DGEs: The case of students’ counterexamples (2019)
  • Author(s): Jones, K., & Komatsu, K.
  • Organizer: The Eleventh Congress of the European Society for Research in Mathematics Education
  • Int'l Joint Research
• [Presentation] 課題探究として証明することを実現する指導法の開発：領域「データの活用」に焦点をあてて (2018)
  • Author(s): 小松孝太郎・永田潤一郎・辻山洋介
  • Organizer: 日本数学教育学会第6回春期研究大会
• [Presentation] 科学教育の内容・活動に固有な非認知的スキルの評価法の開発：領域「データの活用」における調査内容について (2018)
  • Author(s): 永田潤一郎・青山和裕・小松孝太郎・辻山洋介
  • Organizer: 日本科学教育学会第42回年会
• [Book] B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of digital resources in mathematics education (Intertwined use of physical and digital tools in mathematics teaching and learning) (2023)
  • Author(s): Komatsu, K., & Fujita, T.
  • Publisher: Springer
• [Book] M. Danesi (Ed.), Handbook of cognitive mathematics (Teaching and learning authentic mathematics: The case of proving) (2022)
  • Author(s): Stylianides, A. J., Komatsu, K., Weber, K., & Stylianides, G. J.
  • Total Pages: 1406
  • Publisher: Springer
  • ISBN: 3031039440
• [Book] 礒田正美・影山和也（編著），『中等数学科教育（新・教職課程演習第19巻）』（Q31 数学的な見方・考え方および態度とは何かを述べなさい，Q32 中学校数学科の問題解決において数学的な見方・考え方が働く場面を示しなさい，Q33 高等学校数学科の問題解決において数学的な見方・考え方が働く場面を示しなさい） (2021)
  • Author(s): 小松孝太郎
  • Total Pages: 201
  • Publisher: 協同出版
  • ISBN: 4319003608
• [Book] 蒔苗直道・松浦武人（編著），『初等算数科教育（新・教職課程演習第13巻）』（「Q11算数科で用いる記号や式について説明しなさい，Q14空間観念の育成とはどのようなことか説明しなさい，Q27図形の求積公式の指導について説明しなさい」の執筆） (2021)
  • Author(s): 小松孝太郎
  • Total Pages: 201
  • Publisher: 協同出版
  • ISBN: 4319003543
• [Book] 礒田正美・影山和也（編著），『中等数学科教育（新・教職課程演習第19巻）』（「Q31数学的な見方・考え方および態度とは何かを述べなさい，Q32中学校数学科の問題解決において数学的な見方・考え方が働く場面を示しなさい，Q33高等学校数学科の問題解決において数学的な見方・考え方が働く場面を示しなさい」の執筆） (2021)
  • Author(s): 小松孝太郎
  • Publisher: 協同出版
• [Book] G. Hanna, D. A. Reid, & M. de Villiers (Eds.), Proof technology in mathematics research and teaching (Virtual manipulatives and students’ counterexamples during provingの執筆) (2019)
  • Author(s): Komatsu, K., & Jones, K.
  • Total Pages: 379
  • Publisher: Springer
  • ISBN: 9783030284831
• [Book] 初等算数科教育（第５章執筆） (2019)
  • Author(s): 吉田武男（監修）清水美憲（編著）
  • Total Pages: 200
  • Publisher: ミネルヴァ書房
  • ISBN: 9784623086023
• [Book] 新版算数科教育研究（第２章第５節執筆） (2019)
  • Author(s): 算数科教育学研究会（編）
  • Total Pages: 218
  • Publisher: 東洋館出版社
  • ISBN: 9784491036816
• [Book] Proof technology in mathematics research and teaching（Part IVの１節執筆） (2019)
  • Author(s): G. Hanna, D. Reid, & M. de Villiers (Eds.)
  • Publisher: Springer
• [Funded Workshop] 証明の指導と学習に関する国際研究集会（International Seminar of Research on Teaching and Learning Mathematical Proof） (2019)