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Developing Websites of Explorative Learning for Space Geometry with Three Dimensional Dynamic Geometry Software

Research Project

Project/Area Number 20330181
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Education on school subjects and activities
Research InstitutionShinshu University

Principal Investigator

IWANAGA Yasuo  信州大学, 教育学部, 教授 (80015825)

Co-Investigator(Kenkyū-buntansha) ITO Takehiro  信州大学, 教育学部, 教授 (00015827)
MIYAZAKI Mikio  信州大学, 教育学部, 教授 (10261760)
CHINO Kimiho  信州大学, 教育学部, 准教授 (20400658)
KOMATSU Kotaro  信州大学, 教育学部, 准教授 (40578267)
KON Mayuko  信州大学, 教育学部, 准教授 (70507186)
Research Collaborator ARAI Hitoshi  国立教育政策研究所, 調査官 (40641543)
OGIHARA Fumihiro  佐久長聖高等学校, 教諭
OGUCHI Yuichi  茨城大学, 教育学部, 教授 (70405877)
KATO Ryuhei  国立教育政策研究所, 調査官 (10618648)
KITAJIMA Shigeki  筑波大学, 附属中学校, 教諭
BABA Naoki  長野県伊那市立春富中学校, 教諭
YUMOTO Takeshi  長野県松本市立開成中学校, 教諭
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥18,330,000 (Direct Cost: ¥14,100,000、Indirect Cost: ¥4,230,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2010: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2009: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2008: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Keywords3次元動的幾何ソフト / 空間図形 / 探究的な学習 / Webサイト / カリキュラム
Research Abstract

This study developed the website of explorative learning for spatial geometry with three dimensional geometry software in order to improve the learning of spatial geometry in mathematics education. Tis site consists of the following two parts ; ELesson Recipe(Lesson designs based on the courses of explorative learning), Enjoy Mathematics in 3D(Groups of digital contents for guidance based on the lesson designs).

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (53 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (24 results) (of which Peer Reviewed: 21 results) Presentation (23 results) Book (4 results) Remarks (2 results)

  • [Journal Article] Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics2012

    • Author(s)
      Miyazaki, M., Kimiho, C., Katoh, R., Arai, H., Ogihara, F., Oguchi, Y., Morozumi, T., Kon, M., and Komatsu, K
    • Journal Title

      The International Journal for Technology in Mathematics Education

      Volume: 19(2)(in press)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics2012

    • Author(s)
      Miyazaki, M., Kimiho, C., Katoh, R., Arai, H., Ogihara, F., Oguchi, Y., Morozumi, T., Kon, M., Komatsu, K.
    • Journal Title

      The International Journal for Technology in Mathematics Education

      Volume: 19(2)(印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Supporting students to overcome circular arguments in secondary school mathematics : the use of the flowchart proof learning platform2011

    • Author(s)
      Fujita, T., Jones, K. and Miyazaki, M
    • Journal Title

      Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vol.2 Pages: 353-360

    • NAID

      120007100959

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semi-parallel CR submanifolds in a complex space form2011

    • Author(s)
      Kon, M
    • Journal Title

      Colloquium Mathematicum

      Volume: 124, no.2 Pages: 237-246

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Tanaka-Webster connection and real hypersurfaces in a complex space form2011

    • Author(s)
      Cho, J. T., Kon, M
    • Journal Title

      Kodai Mathematical Journal

      Volume: 34, no.3 Pages: 474-484

    • NAID

      130004687961

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [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

      Volume: 第35巻第3号 Pages: 272-286

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] How do students generalize a conjecture through proving?: The importance of boundary cases between example and counterexample2011

    • Author(s)
      Komatsu, K
    • Journal Title

      Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vol.3 Pages: 89-96

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Supporting students to overcome circular arguments in secondary school mathematics : the use of the flowchart proof learning platform2011

    • Author(s)
      Fujita, T., Jones, K.Miyazaki, M.
    • Journal Title

      Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education

      Volume: 2 Pages: 353-360

    • NAID

      120007100959

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] How do students generalize a conjecture through proving? : The importance of boundary cases between example and counterexample2011

    • Author(s)
      Komatsu Kotaro
    • Journal Title

      Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education

      Volume: 3 Pages: 89-96

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-parallel CR submanifolds in a complex space form2011

    • Author(s)
      Kon, M.
    • Journal Title

      Colloquium Mathematicum

      Volume: 124(2) Pages: 237-246

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Tanaka-Webster connection and real hypersurfaces in a complex space form2011

    • Author(s)
      Cho, J.T., Kon, M.
    • Journal Title

      Kodai Mathematical Journal

      Volume: 34(3) Pages: 474-484

    • NAID

      130004687961

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact minimal CR submanifolds of a complex projective space with positive Ricci curvature2010

    • Author(s)
      昆万佑子
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 33 Pages: 415-434

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A minimal real hypersurface of a complex projective space with non-negative sectional curvature2010

    • Author(s)
      昆万佑子
    • Journal Title

      Bulletin of the Australian Mathematical Society

      Volume: 81 Pages: 488-492

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • 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

      Volume: 91巻 Pages: 3-29

    • NAID

      110007609878

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact minimal CR submanifolds of a complex projective space with positive Ricci curvature2010

    • Author(s)
      昆万佑子
    • Journal Title

      Tokyo Journal of Mathematics 33巻

      Pages: 415-434

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A minimal real hypersurface of a complex projective space with non-negative sectional curvature2010

    • Author(s)
      昆万佑子
    • Journal Title

      Bulletin of the Australian Mathematical Society 81巻

      Pages: 488-492

    • Related Report
      2010 Self-evaluation Report
    • 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 91巻

      Pages: 3-29

    • NAID

      110007609878

    • Related Report
      2010 Self-evaluation Report
    • 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: 91 Pages: 3-29

    • NAID

      110007609878

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Teaching and learning a proof as an object2009

    • Author(s)
      Miyazaki, M., Yumoto, T.
    • Journal Title

      Proceedings of the 19th the International Commission on Mathematical Instruction, ICMI Study 19 Conference, Proof and proving in mathematics education 2

      Pages: 76-81

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 学校数学における証明の基礎的学習の諸相を整理する枠組みの構築:証明の構造, 証明する活動,証明の機能に焦点をあてて2009

    • Author(s)
      宮崎樹夫
    • Journal Title

      日本数学教育学会第42回数学教育論文発表会論文集

      Pages: 601-606

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 我が国の数学教育における証明研究の課題と展望2009

    • Author(s)
      宮崎樹夫, 茅野公穂, 他
    • Journal Title

      日本数学教育学会第42回数学教育論文発表会論文集

      Pages: 64-69

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Cognitive Incoherence of Students Regarding the Establishment of Universality of Propositions through Experimentation/Measurement2008

    • Author(s)
      Miyazaki, M
    • Journal Title

      International Journal of Science and Mathematics Education

      Volume: 6(3) Pages: 533-558

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cognitive Incoherence of Students Regarding the Establishment of Universality of Propositions through Experimentation/Measurement2008

    • Author(s)
      Miyazaki, M.
    • Journal Title

      International Journal of Science and Mathematics Education 6(3)

      Pages: 533-558

    • Related Report
      2010 Self-evaluation Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 中学校数学における証明の学習の諸相を整理する枠組みの構築 : 証明の構造と, 証明する活動に焦点をあてて2008

    • Author(s)
      宮崎樹夫
    • Journal Title

      日本数学教育学会第41回数学教育論文発表会論文集

      Pages: 537-542

    • Related Report
      2008 Annual Research Report
  • [Presentation] 学校数学における証明の基礎的学習に関する研究:証明の構造に基づく関係的な学習で新たに必要となる活動に着目して2011

    • Author(s)
      宮崎樹夫
    • Organizer
      日本数学教育学会第44回数学教育論文発表会
    • Place of Presentation
      上越教育大学
    • Year and Date
      2011-11-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] Supporting students to overcome circular arguments in secondary school mathematics : the use of the flowchart proof learning platform2011

    • Author(s)
      Fujita, T., Jones, K. and Miyazaki, M
    • Organizer
      the 35th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Ankara, Turkey : Middle East Technical University
    • Year and Date
      2011-07-14
    • Related Report
      2011 Final Research Report
  • [Presentation] How do students generalize a conjecture through proving?: The importance of boundary cases between example and counterexample2011

    • Author(s)
      Komatsu, K
    • Organizer
      The 35th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Ankara, Turkey : Middle East Technical University
    • Year and Date
      2011-07-14
    • Related Report
      2011 Final Research Report
  • [Presentation] Secondary school mathematics learners constructing geometric flow-chartproofs with a web-based learning support system2011

    • Author(s)
      Miyazaki, M., Fujita, T., Murakami, Y., Baba, N., Jones, K.
    • Organizer
      10th International Conference on Technology in Mathematics Teaching
    • Place of Presentation
      University of Portsmouth
    • Year and Date
      2011-07-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] On 3-dimensional compact real hypersurfaces of a complex space form2011

    • Author(s)
      Kon, M
    • Organizer
      The 15-th International Workshop on Differential Geometry
    • Place of Presentation
      Korea
    • Related Report
      2011 Final Research Report
  • [Presentation] 複素空間形の実部分多様体について2011

    • Author(s)
      昆万佑子
    • Organizer
      第5回札幌・福岡幾何学セミナー
    • Place of Presentation
      北海道
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] On 3-dimensional compact real hypersurfaces of a complex space form2011

    • Author(s)
      Kon, M.
    • Organizer
      The 15-th International Workshop on Differential Geometry
    • Place of Presentation
      Kyungpook National University, Korea
    • Related Report
      2011 Annual Research Report
  • [Presentation] 複素空間形の擬平行なCR部分多様体について2011

    • Author(s)
      昆万佑子
    • Organizer
      統計多様体の幾何学とその周辺(3)幾何学と諸科学の連携調査
    • Place of Presentation
      北海道大学
    • Related Report
      2011 Annual Research Report
  • [Presentation] 中学校数学におけるフローチャート証明の学習支援システムの開発:ディジタルコンテンツ及びその編成の特徴2010

    • Author(s)
      宮崎樹夫
    • Organizer
      日本科学教育学会第34回年会
    • Place of Presentation
      広島大学(車広島市)
    • Year and Date
      2010-09-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] 学校数学での理由の説明・証明を捉える枠組み2010

    • Author(s)
      茅野公穗
    • Organizer
      日本科学教育学会第34回年会
    • Place of Presentation
      広島
    • Year and Date
      2010-09-11
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] An assessment framework for students' abilities/competencies in proving2010

    • Author(s)
      Chino, K.
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • 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
      2010-08-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] 学校数学における証明の基礎的学習に関する研究:証明の構造に基づく関係的な学習に必要な活動に着目して2010

    • Author(s)
      宮崎樹夫
    • Organizer
      日本数学教育学会第43回数学教育論文発表会
    • Place of Presentation
      宮崎
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Students understanding of the structure of proof : Why do students accept a proof with logical circularity?2010

    • Author(s)
      Miyazaki, M., Fujita, T
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      Tokyo
    • Related Report
      2011 Final Research Report
  • [Presentation] An assessment framework for students abilities/competencies in proving2010

    • Author(s)
      Chino, K., Komatsu, K., Miyazaki, M., et al
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      Tokyo
    • Related Report
      2011 Final Research Report
  • [Presentation] Students'understanding of the structure of proof : Why do students accept a proof with logical circularity?2010

    • Author(s)
      Miyazaki, M., Fujita, T.
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      Tokyo
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] An assessment framework for students'abilities/competencies in proving2010

    • Author(s)
      Chino, K., Komatsu, K., Miyazaki, M., et al.
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      Tokyo
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] カリキュラムにおける証明の居場所を捉える枠組み2009

    • Author(s)
      茅野公穂
    • Organizer
      日本科学教育学会第33回年会
    • Place of Presentation
      京都
    • Year and Date
      2009-08-25
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 中学校数学におけるフローチャート証明の学習支援システムの開発:誤りの特徴に応じた修正促進に着目して2009

    • Author(s)
      宮崎樹夫
    • Organizer
      日本科学教育学会第33回年会
    • Place of Presentation
      同志社女子大学
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] カリキュラムにおける証明の居場所を捉える枠組み2009

    • Author(s)
      茅野公穂
    • Organizer
      日本科学教育学会 第33回年会
    • Place of Presentation
      同志社女子大学
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] 我が国の数学教育における証明研究の課題と展望2009

    • Author(s)
      宮崎樹夫,茅野穂,小松孝太郎, 他
    • Organizer
      日本数学教育学会第42回数学教育論文発表会
    • Place of Presentation
      静岡
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Teaching and learning a proof as an object2009

    • Author(s)
      Miyazaki, M., Yumoto, T.
    • Organizer
      The 19th the International Commission on Mathematical Instruction, ICMI Study 19 Conference, Proof and proving in mathematics education
    • Place of Presentation
      Taiwan
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 学校数学における証明の基礎的学習の諸相を整理する枠組みの構築:証明の構造,証明する活動,証明の機能に焦点をあてて2009

    • Author(s)
      宮崎樹夫
    • Organizer
      第42回数学教育論文発表会
    • Place of Presentation
      静岡
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 中学校数学における証明の学習の諸相を整理する枠組みの構築:証明の構造と,証明する活動に焦点をあてて2008

    • Author(s)
      宮崎樹夫
    • Organizer
      日本数学教育学会第41回数学教育論文発表会
    • Place of Presentation
      茨城
    • Related Report
      2010 Self-evaluation Report
  • [Book] The first sourcebook on Asian research in mathematics education.2012

    • Author(s)
      Miyazaki, M. & Fujita, T
    • Publisher
      Information Age Publishing
    • Related Report
      2011 Final Research Report
  • [Book] 数学の学習論・学習者論,大高泉・清水美憲(編著),『教科教育の理論と授業:数理編(新教職教育講座シリーズ第6巻)』(第I部第5章)2012

    • Author(s)
      小松孝太郎
    • Publisher
      協同出版
    • Related Report
      2011 Final Research Report
  • [Book] 『教科教育の理論と授業II:数理編』「数学の学習論・学習者論」(第I 部第5章)を執筆(大高泉・清水美憲編)2012

    • Author(s)
      小松孝太郎
    • Publisher
      協同出版
    • Related Report
      2011 Annual Research Report
  • [Book] 図形の概念と操作、『算数科教育研究』(第4章第1節)2010

    • Author(s)
      宮崎樹夫, 他
    • Publisher
      学芸図書出版
    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.schoolmath.jp/3dcontent/index.html

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.schoolmath.jp/3d/teacher/recipe/index.htm

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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