Investigation of cognitive and affective factors that lead students to produce incomplete proof at junior high school level

• Project/Area Number: 22730700
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Education on school subjects and activities
• Research Institution: Utsunomiya University
• Principal Investigator: MAKINO Tomohiko 宇都宮大学, 教育学部, 准教授 (10450157)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 各教科の教育(算数・数学) / 未完成な証明 / 認知的要因 / 情緒的要因 / 推論過程 / 中学校数学 / 架橋過程

Research Abstract

This study aims to explore cognitive and affective factors that lead to incomplete proof, focusing on students' reasoning in the process that they produce it. This study divided into some types of incomplete proof produced by students, identified cognitive and affective factors that lead to each type and inferred students' thinking hidden behind each factor of incomplete proof. Focusing on the proving process by students who can successfully construct geometrical proof, this study clarifies the characteristics of mathematical cognition in their proving process and suggests cognitive factors lead to incomplete proof based on them.

Research Products

• [Journal Article] 中学校数学での証明の「架橋過程」における生徒の認知的困難 (2012)
  • Author(s): 牧野智彦
  • Journal Title: 日本科学教育学会研究会研究報告 Volume: 26巻, Vol.5 Pages: 25-30
• [Journal Article] 中学生の証明の構成過程における推論の特質-成功的証明者による「架橋過程」に焦点を当てて- (2010)
  • Author(s): 牧野智彦
  • Journal Title: 第43回日本数学教育学会論文発表会論文集 Volume: 2巻 Pages: 699-704
  • Peer Reviewed
• [Journal Article] An Assessment Famework 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 Volume: Vol.2 Pages: 416-423
  • Peer Reviewed
• [Journal Article] 証明の本質の理解を促す指導の開発研究 (2010)
  • Author(s): 牧野智彦
  • Journal Title: 第34回日本科学教育学会年会論文集 Pages: 85-86
• [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 Volume: 2 Pages: 416-423
  • Peer Reviewed
• [Presentation] 中学校数学での証明の「架橋過程」における生徒の認知的困難 (2012)
  • Author(s): 牧野智彦
  • Organizer: 平成23年度第5回日本科学教育学会研究会
  • Place of Presentation: 筑波大学
  • Year and Date: 2012-04-07
• [Presentation] 中学生の証明の構成過程における推論の特質-成功的証明者による「架橋過程」に焦点を当てて- (2010)
  • Author(s): 牧野智彦
  • Organizer: 第43回日本数学教育学会論文発表会
  • Place of Presentation: 宮崎大学
  • Year and Date: 2010-11-14
• [Presentation] 証明の本質の理解を促す指導の開発研究 (2010)
  • Author(s): 牧野智彦
  • Organizer: 第34回日本科学教育学会年会
  • Place of Presentation: 広島大学
  • Year and Date: 2010-09-11
• [Presentation] An assessment framework for students' abilities/competencies in proving (2010)
  • Author(s): Chino, K.
  • Organizer: 第5回東アジア数学教育国際会議
  • Place of Presentation: 国立オリンピック記念青少年総合センター
  • Year and Date: 2010-08-21
• [Book] 新教職教育講座 第6巻 教科教育の理論と授業II 理数編 (2012)
  • Author(s): 大高泉, 清水美憲, 蒔苗直道, 高橋等, 小松孝太郎, 牧野智彦, 銀島文, 伊藤伸也, 辻宏子, 高橋聡, 郡司賀透, 内ノ倉真吾, 山下修一, 片平克弘, 稲田結美, 山本容子, 鈴木宏昭, 畑中敏伸
  • Total Pages: 310
  • Publisher: 協同出版