Development of teacher training programs focused on "knowledge and skills for mathematical thinking"

• Project/Area Number: 26350231
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Science education
• Research Institution: Shinshu University
• Principal Investigator: ITOH Takehiro 信州大学, 教育学部, 名誉教授 (00015827)
• Co-Investigator(Kenkyū-buntansha): 茅野 公穗 信州大学, 学術研究院教育学系, 教授 (20400658) ; 松澤 泰道 信州大学, 学術研究院教育学系, 助教 (60645620) ; 昆 万佑子 信州大学, 学術研究院教育学系, 准教授 (70507186)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数学的に考える力 / 教員養成

Outline of Final Research Achievements

The purpose of this research is to develop a teacher training program focused on "knowledge and skills for mathematical thinking". To achieve this objective, we developed and implemented provisional programs, identified the improvement points of the programs, and reflected them in the programs. As results of this research, three secondary school mathematics teacher training programs and two elementary school teacher training programs were developed to make it possible to deepen "knowledge and skills for mathematical thinking" through problem solving.

Research Products

• [Journal Article] 3-dimensional real hypersurfaces with η-harmonic curvature (2017)
  • Author(s): Mayuko Kon
  • Journal Title: The 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds Volume: 印刷中
• [Journal Article] Ricci tensor of real hypersurfaces (2016)
  • Author(s): Mayuko Kon
  • Journal Title: Pacific Journal of Mathematics Volume: 281 Issue: 1 Pages: 103-123
  • DOI: 10.2140/pjm.2016.281.103
  • Peer Reviewed
• [Journal Article] Non-Hopf hypersurfaces in 2-dimensional complex space forms (2016)
  • Author(s): Mayuko Kon
  • Journal Title: Tokyo Journal of Mathematics Volume: 39(2) Pages: 373-387
  • Peer Reviewed
• [Journal Article] 課題探究として証明することのカリキュラム開発: 領域「図形」のカリキュラム開発枠組みの精緻化 (2016)
  • Author(s): 茅野公穂，宮川健
  • Journal Title: 日本数学教育学会 第４回春期研究大会論文集 Volume: － Pages: 163-166
  • NAID: 120007100343
  • Acknowledgement Compliant
• [Journal Article] Developing a Curriculum for Explorative Proving in Lower Secondary School Geometry (2016)
  • Author(s): Miyazaki, M., Nagata, J., Chino, K., Fujita, T. Ichikawa D., Shimizu, S, & Iwanaga Y.
  • Journal Title: Proceedings of the 13th International Congress on Mathematical Education Volume: －
  • NAID: 120007100962
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] 課題探究として証明することのカリキュラム開発: 領域「数と式」，「図形」の カリキュラム開発枠組みの精緻化 (2015)
  • Author(s): 茅野公穂，佐々祐之，宮﨑樹夫，宮川健，中川裕之，岩永恭雄，松岡樂
  • Journal Title: 日本数学教育学会 第３回春期研究大会論文集 Volume: . Pages: 7-12
  • NAID: 120007100515
  • Acknowledgement Compliant
• [Journal Article] Real hypersurfaces in a 2-dimensional complex space form with transversal Killing tensor field (2015)
  • Author(s): Mayuko Kon
  • Journal Title: Proceedings of the 19th International Workshop on Hermitian-Grassmannian Submanifolds Volume: 19 Pages: 159-170
• [Journal Article] The Weyl-von Neumann Theorem and Borel Complexity of Unitary Equivalence Modulo Compacts of Self-Adjoint Operators (2015)
  • Author(s): Hiroshi ANDO and Yasumichi MATSUZAWA
  • Journal Title: The Royal Society of Edinburgh Proceedings A (Mathematics) Volume: 145 Issue: 6 Pages: 1115-1144
  • DOI: 10.1017/s0308210515000293
  • NAID: 120006459742
  • Peer Reviewed
• [Journal Article] On Borel equivalence relations related to self-adjoint operators (2015)
  • Author(s): Hiroshi ANDO and Yasumichi MATSUZAWA
  • Journal Title: Journal of Operator Theory Volume: 74 Issue: 1 Pages: 183-194
  • DOI: 10.7900/jot.2014may24.2030
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 3-dimensional real hypersurfaces and Ricci operator (2014)
  • Author(s): Mayuko Kon
  • Journal Title: Differential Geometry-Dynamical Systems Volume: 16 Pages: 189-202
  • Peer Reviewed
• [Journal Article] 「基本的な作図」において課題探究として証明することの授業化 (2014)
  • Author(s): 茅野公穂，嶋田和美，荻原啓一
  • Journal Title: 日本数学教育学会誌 数学教育 Volume: 96(9) Pages: 10-13
  • NAID: 110009857079
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 中学校数学における課題探究として証明することのカリキュラム開発：進行状況と授業化の意味・役割 (2014)
  • Author(s): 宮﨑樹夫，永田潤一郎，茅野公穂
  • Journal Title: 日本数学教育学会誌 数学教育 Volume: 96(9) Pages: 2-5
  • Peer Reviewed
• [Presentation] Groups of unitaries without property (FH) (2017)
  • Author(s): 松澤泰道
  • Organizer: 日本数学会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-26
• [Presentation] 3-dimensional real hypersurfaces with η-harmonic curvature (2016)
  • Author(s): 昆万佑子
  • Organizer: The 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds
  • Place of Presentation: Kyungpook National University (Korea)
  • Year and Date: 2016-07-29
  • Int'l Joint Research
• [Presentation] Real hypersurfaces in a 2-dimensional complex space form with transversal Killing tensor fields (2015)
  • Author(s): Mayuko Kon
  • Organizer: The 19th International Workshop on Hermitian-Grassmannian Submanifolds and Its Applications
  • Place of Presentation: NIMS, Daejeon, South Korea
  • Year and Date: 2015-10-27
  • Int'l Joint Research
• [Presentation] 無限次元群の話 (2015)
  • Author(s): 松澤泰道
  • Organizer: 作用素論作用素環論研究集会
  • Place of Presentation: KKR妙高高原白樺荘（新潟県妙高市）
  • Year and Date: 2015-10-25
  • Invited
• [Presentation] 中学校数学における課題探究として証明することの授業化: 第１学年の小単元「基本的な作図」 (2015)
  • Author(s): 茅野公穂, 清水あかね
  • Organizer: 日本科学教育学会 第39回年会
  • Place of Presentation: 山形大学
  • Year and Date: 2015-08-23
• [Presentation] Weyl-von Neumann同値関係の複雑さ (2015)
  • Author(s): 松澤泰道
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-22
• [Presentation] Shape operator of real hypersurfaces in a 2-dimensional complex space form (2015)
  • Author(s): Mayuko Kon
  • Organizer: The 9th OCAMI-KNUHGRG Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2015-02-13
• [Presentation] 量子力学に於ける時間作用素について (2014)
  • Author(s): 松澤泰道
  • Organizer: Nagahama Workshop "From Quantum to Life"
  • Place of Presentation: 長浜バイオ大学
  • Year and Date: 2014-11-15
• [Presentation] Weyl-von Neumannの定理の複雑さ (2014)
  • Author(s): 松澤泰道
  • Organizer: 量子場の数理とその周辺（RIMS研究集会）
  • Place of Presentation: 京都大学
  • Year and Date: 2014-10-06
• [Presentation] Hilbert-Schmidt群のFock空間上での表現 (2014)
  • Author(s): 松澤泰道
  • Organizer: 札幌数理物理研究集会
  • Place of Presentation: 北海道大学
  • Year and Date: 2014-09-01
• [Presentation] 中学校図形領域における課題探究として証明することの授業化: 第１学年の内容「基本的な作図」と「空間図形」 (2014)
  • Author(s): 茅野公穂，嶋田和美，荻原啓一
  • Organizer: 日本数学教育学会 第2回春期研究大会
  • Place of Presentation: 東京学芸大学
  • Year and Date: 2014-06-29
• [Book] History of lesson study to develop good practice in Japan. In M. Inprasitha, M. Isoda, B.-H. Yeap, & P. Wang-Iverson (Eds.), Lesson Study: Challenges in Mathematics Education (2015)
  • Author(s): Shimizu, S. & Chino, K.
  • Total Pages: 392
  • Publisher: World Scientific