Curriculum design for reflecting on proofs and proving in mathematics education

• Project/Area Number: 22530960
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Education on school subjects and activities
• Research Institution: Shinshu University
• Principal Investigator: CHINO Kimiho 信州大学, 教育学部, 准教授 (20400658)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 学校数学 / 証明 / カリキュラム

Research Abstract

This research has constructed a preliminary framework for curriculum design, which will enrich students’ not only planning and constructing proofs but also reflecting on proofs and proving. In order to achieve intentional and planned guidance of students' learning activities, the framework is equipped with the hierarchy matching required activities for reflecting on proofs and proving.

Research Products

• [Journal Article] 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.
  • Journal Title: Proceedings of the 5th East Asia Regional Conference on Mathematics Education (EARCOME5) Volume: Vol. 2 Pages: 416-423
• [Journal Article] 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
  • Journal Title: Proceedings of the 5th East Asia Regional Conference on Mathematics Education (EARCOME5) Volume: Vol.2 Pages: 416-423
• [Presentation] 学校数学における証明することの学習に関する研究: 証明することをふりかえる側面で必要な活動に焦点をあてて (2012)
  • Author(s): 茅野公穂
  • Organizer: 日本数学教育学会 第45回数学教育論文発表会
  • Place of Presentation: 奈良教育大学.
  • Year and Date: 2012-11-10
• [Presentation] Reflecting on geometrical proofs: What do students produce by reflecting on a proof? (2012)
  • Author(s): Kimiho Chino
  • Organizer: The 12th International Congress on Mathematical Education
  • Place of Presentation: COEX, Seoul, Korea.
• [Presentation] 学校数学における証明することの学習に関する研究: 証明することをふりかえる側面で必要な活動に焦点をあてて (2012)
  • Author(s): 茅野公穂
  • Organizer: 日本数学教育学会 第45回数学教育論文発表会
  • Place of Presentation: 奈良教育大学
• [Presentation] Reflecting on geometrical proofs: What do students produce by reflecting on a proof? (2012)
  • Author(s): Kimiho Chino
  • Organizer: The 12th International Congress on Mathematical Education
  • Place of Presentation: COEX, Seoul, Korea
• [Presentation] 学校数学における証明や証明することをどう捉えるか (2011)
  • Author(s): 茅野公穂
  • Organizer: 日本科学教育学会 第35回年会
  • Place of Presentation: 東京工業大学.
  • Year and Date: 2011-08-23
• [Presentation] 学校数学における証明や証明することをどう捉えるか (2011)
  • Author(s): 茅野公穂
  • Organizer: 日本科学教育学会 第35回年会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-08-23
• [Presentation] 学校数学での理由の説明・証明を捉える枠組み (2010)
  • Author(s): 茅野公穂
  • Organizer: 日本科学教育学会 第34回年会
  • Place of Presentation: 広島大学
  • Year and Date: 2010-09-11
• [Presentation] 学校数学での理由の説明・証明を捉える枠組み (2010)
  • Author(s): 茅野公穂
  • Organizer: 日本科学教育学会第34回年会
  • Place of Presentation: 広島大学
  • Year and Date: 2010-09-11