Development of teaching materials for facilitating students' action proof in mathematical inquiry

2011 Fiscal Year Final Research Report

• Project/Area Number: 22830035
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Education on school subjects and activities
• Research Institution: Shinshu University
• Principal Investigator: KOMATSU Xingkotaro 信州大学, 教育学部, 准教授 (40578267)
• Project Period (FY): 2010 – 2011
• Keywords: 数学教育 / 証明 / 操作的証明 / 数学的探究 / 教材開発

Research Abstract

Proof and proving are at the core of mathematical activities, and therefore should be the center of students' mathematical experiences at all grades. However, mathematics education researches have revealed that many students feel difficulties in learning proof and proving. In order to improve this learning situation, this study focuses on a notion of" action proof", and aims to explore how we can encourage students to utilize action proof in mathematical inquiry. In particular, this study derives some guidelines for developing teaching materials which intend to facilitate students' activities, by examining the existing researches, analyzing materials, and conducting and analyzing teaching-experiments with fifth and ninth graders.

Research Products

• [Journal Article] ラカトシュの可謬主義から見た数学的探究とその教育的意義 (2011)
  • Author(s): 小松孝太郎
  • Journal Title: 『科学教育研究』(日本科学教育学会) Volume: 第35巻第3号 Pages: 272-286
  • Peer Reviewed
• [Journal Article] How do studentsgeneralize a conjecture throughproving?: The importance of boundarycases between example andcounterexample. In B. Ubuz(Ed.) (2011)
  • Author(s): Komatsu, K.
  • Journal Title: Proceedings of the 35th Conference ofthe International Group for thePsychology of Mathematics Education Volume: Vol.3 Pages: 89-96
  • Peer Reviewed
• [Journal Article] 数学的探究におけるaction proofの活用の促進:事例研究を通して (2010)
  • Author(s): 小松孝太郎
  • Journal Title: 日本数学教育学会誌数学教育学論究 Volume: 第93号 Pages: 3-29
  • Peer Reviewed
• [Presentation] How do students generalize a conjecture through proving?: The importance of boundary cases between example and counterexample. (2011)
  • Author(s): Komatsu, K.
  • Organizer: The 35th Conference of the International Group for the Psychology of Mathematics Education
  • Place of Presentation: Ankara, Turkey
  • Year and Date: 2011-07-14
• [Presentation] An assessment framework for students' abilities/competencies in proving. (2010)
  • Author(s): Chino, K., Fujita, T., Komatsu, K., Makino, T., Miyakawa, T., Miyazaki, M., Mizutani, N., Nakagawa, H., Otsuka, S., & Tsujiyama, Y.
  • Organizer: The 5th East Asia Regional Conference on Mathematics Education
  • Place of Presentation: Tokyo, Japan
  • Year and Date: 2010-08-21
• [Book] 数学の学習論・学習者論,教科教育の理論と授業II (2012)
  • Author(s): 小松孝太郎
  • Total Pages: 71-84
  • Publisher: 東京:協同出版