A study on designing lessons and teaching units for developing advanced geometrical thinking in mathematics education

• Project/Area Number: 23730829
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Education on school subjects and activities
• Research Institution: Hiroshima University
• Principal Investigator: KAGEYAMA Kazuya 広島大学, 教育学研究科(研究院), 准教授 (60432283)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 高次の幾何的思考 / 身体的認知 / 身体的認知理論 / 質的研究 / 変換幾何 / 投影的な見方

Research Abstract

The aim of this study is to improve and develop teaching geometry in secondary school for developing advanced geometrical thinking. For this aim this study clarifies students' geometrical thinking through both theoretical and empirical considerations.
This study descrived a process of geometrical thinking from the viewpoint of formalization of mathematics and setting definitions based on findings of its recursive nature and embodiment theory. Especially actual geometrical thinking is consisted of complex interactions between cognition and conception. This study presented the descriptive framework having this both aspects and argued that mathematical rules let this interactions enhance mathematically.

Research Products

• [Journal Article] 図形的概念形成への新たな認知論的接近 (2013)
  • Author(s): 影山和也
  • Journal Title: 日本数学教育学会『数学教育学論究臨時増刊』 Volume: 第95巻 Pages: 97-104
  • NAID: 130008019008
  • Peer Reviewed
• [Journal Article] Sensuous experience and mathematical conceptions. Heinze, A. (Ed.) (2013)
  • Author(s): Kazuya Kageyama
  • Journal Title: Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. Kiel, Germany : PME Volume: 3 Pages: 121-128
  • Peer Reviewed
• [Journal Article] Improving teaching practices through group activities with problem posing. Inprasitha, M. (Ed.) (2013)
  • Author(s): Mitsunori Imaoka, Kazuya Kageyama and Hideaki Kida
  • Journal Title: Proceedings of the 6th East Asia Regional Conference on Mathematics Education.Phuket, Thailand : ICMI Volume: 3 Pages: 192-201
  • Peer Reviewed
• [Journal Article] 図形的概念形成への新たな認知論的接近 (2013)
  • Author(s): 影山和也
  • Journal Title: 数学教育学論究 臨時増刊 Volume: 95 Pages: 97-104
  • NAID: 130008019008
  • Peer Reviewed
• [Journal Article] Student's initial concepts of geometric transformations and underlying cognitive abilities. Tai-Yih Tso. (Ed.) (2012)
  • Author(s): Kazuya Kageyama
  • Journal Title: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education.Taipei, Taiwan : PME Volume: 3 Pages: 3-10
  • Peer Reviewed
• [Journal Article] 図形の動的な見方の構造について : 比喩的認識の視点から (2012)
  • Author(s): 岡崎正和・岩崎秀樹・影山和也・和田信哉
  • Journal Title: 日本教科教育学会,『日本教科教育学会誌』 Volume: 第35巻,第2号 Pages: 53-62
  • NAID: 110009844848
  • Peer Reviewed
• [Journal Article] Geometrical thinking identified in 'static geometry environments'. Sung Je Cho. (Ed.) (2012)
  • Author(s): Kazuya Kageyama
  • Journal Title: Proceedings of the 12th International Congress on Mathematical Education. Soul, Korea : ICMI Pages: 2232-2241
  • Peer Reviewed
• [Journal Article] 図形の動的な見方の構造について：比喩的認識の視点から (2012)
  • Author(s): 岡崎正和，岩崎秀樹，影山和也，和田信哉
  • Journal Title: 日本教科教育学会誌 Volume: 35 Pages: 53-62
  • NAID: 110009844848
  • Peer Reviewed
• [Journal Article] Development of student's ability to construct unit(s) for tessellating a plane with figures. Ubuz, B. (Ed.) (2011)
  • Author(s): Kazuya Kageyama
  • Journal Title: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education. Ankara, Turkey : PME Volume: 1 Pages: 329-329
  • Peer Reviewed
• [Journal Article] 潜在的な数学的能力の測定用具の活用化に向けた開発的研究(V)－思考力に対する潜在力指導の効果の検討－ (2011)
  • Author(s): 中原忠男，山田篤史，清水紀宏，山口武志，影山和也，小山正孝，飯田慎司，植田敦三
  • Journal Title: 数学教育学研究 Volume: 17 Pages: 65-74
  • NAID: 110009616211
  • Peer Reviewed
• [Presentation] Sensuouscognition論からみた図形的概念形成 (2013)
  • Author(s): 影山和也
  • Organizer: 全国数学教育学会第38回研究発表会
  • Place of Presentation: 香川大学
• [Presentation] Sensuous experience and mathematical conceptions (2013)
  • Author(s): 影山和也
  • Organizer: International Group for the Psychology of Mathematics Education
  • Place of Presentation: Kiel, Germany
• [Presentation] Sensuous cognition論からみた図形的概念形成 (2013)
  • Author(s): 影山和也
  • Organizer: 全国数学教育学会
  • Place of Presentation: 高松市
• [Presentation] Improving teaching practices through group activities with problem posing (2013)
  • Author(s): 今岡光範，影山和也，喜田英明
  • Organizer: The 6th East Asia Reginal Conference on Mathematics Education
  • Place of Presentation: Thailand
• [Presentation] 数学教育における高次の幾何的思考に関する基礎的研究-定義をする活動の位置- (2012)
  • Author(s): 影山和也
  • Organizer: 日本数学教育学会,『第45回数学教育論文発表会論文集』,611-616
  • Place of Presentation: 奈良教育大学
• [Presentation] Student's initial concepts of geometric transformations and underlying cognitive abilities (2012)
  • Author(s): 影山和也
  • Organizer: the 36th Conference of the International Group for the Psychology of Mathematics Education
  • Place of Presentation: Taiwan
• [Presentation] 数学教育における高次の幾何的思考に関する基礎的研究－定義をする活動の位置－ (2012)
  • Author(s): 影山和也
  • Organizer: 第45回数学教育論文発表会
  • Place of Presentation: 奈良教育大学
• [Presentation] Geometrical thinking identified in 'static geometry environments' (2012)
  • Author(s): 影山和也
  • Organizer: The 12th International Congress on Mathematical Education
  • Place of Presentation: Korea
• [Presentation] 数学教育における高次の幾何的思考に関する基礎的研究-数学の形式性に着目して- (2011)
  • Author(s): 影山和也
  • Organizer: 日本数学教育学会,『第44回数学教育論文発表会論文集』, 471-476
  • Place of Presentation: 上越教育大学
• [Presentation] 数学教育における高次の幾何的思考に関する基礎的研究－数学の形式性に着目して－ (2011)
  • Author(s): 影山和也
  • Organizer: 第44回数学教育論文発表会
  • Place of Presentation: 上越市
• [Presentation] Development of student's ability to construct unit(s) for tessellating a plane with figures (2011)
  • Author(s): 影山和也
  • Organizer: the 35th Conference of the International Group for the Psychology of Mathematics Education
  • Place of Presentation: Ankara,Turkey