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Study of the Effect of Using Interactively Manipulable 3D Objects on the Students' Understanding of Linear Algebra

Research Project

Project/Area Number 24501077
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Science education
Research InstitutionNational Institute of Technology, Toyota College

Principal Investigator

Nishizawa Hitoshi  豊田工業高等専門学校, 電気・電子システム工学科, 教授 (40249800)

Co-Investigator(Kenkyū-buntansha) YOSHIOKA Takayoshi  豊田工業高等専門学校, 電気・電子システム工学科, 教授 (30270268)
NIWA Takahiro  八戸工業高等専門学校, 総合科学科, 准教授 (50611349)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords自然科学教育 / 線形代数 / 空間図形 / ベクトル方程式 / 理解度 / インタラクティブ / Web学習システム / 三角関数 / 国際研究者交流(フィンランド)
Outline of Final Research Achievements

Learning the connection between symbolic and visual representations is a key to conceptual understanding of three-dimensional (3D) vector equations. Such a connection is especially valuable for the introductory stage, where students will have an overview of the subjects and start learning them with some confidence. With the overview and confidence, even slow learners tended to avoid black-box approach, where they memorized key formulas blindly and concentrated on the repeated trainings of calculation. The interactive learning contents using 3D objects, however, did not deepen the learners’ understanding automatically even if they motivated the learners to learn more meaningfully. Calculating exercises with paper and pencil were still necessary.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (15 results)

All 2015 2014 2013 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (7 results) (of which Int'l Joint Research: 2 results) Remarks (3 results)

  • [Journal Article] 数学・物理の概念的学習を即すWebベースコンテンツの開発と試用2015

    • Author(s)
      丹羽隆裕、西澤一
    • Journal Title

      高専教育

      Volume: 38 Pages: 410-415

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Interactive worksheets for connecting symbolic and visual representations of 3D vector equations2014

    • Author(s)
      H. Nishizawa, K. Kimura, W. Ohno, T. Yoshioka
    • Journal Title

      Teaching Mathematics and Its Applications

      Volume: 33 Issue: 1 Pages: 52-64

    • DOI

      10.1093/teamat/hru005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Increasing Reality and Educational Merits of a Virtual Game2013

    • Author(s)
      H. Nishizawa, K. Shimada, W. Ohno, T. Yoshioka
    • Journal Title

      Procedia Computer Science

      Volume: 25 Pages: 32-40

    • DOI

      10.1016/j.procs.2013.11.005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Learning Linear Algebra by Combining a Virtual Game in Class and Web-based Learning Activities2013

    • Author(s)
      H. Nishizawa, K. Shimada, T. Yoshioka
    • Journal Title

      Proc. of the IASTED International Conference on Web-based Education

      Volume: 1 Pages: 844-850

    • DOI

      10.2316/p.2013.792-016

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Interactive Worksheets for Learning the Connection Between Graphic and Symbolic Object Representations2012

    • Author(s)
      H. Nishizawa, T. Yoshioka, M.E. Pesonen, A. Viholainen
    • Journal Title

      Proc. of the 17th Asian Technology Conference in Mathematics

      Volume: 1 Pages: 236-245

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Real and Virtual Helixes for the Introduction of Trigonometric Functions2015

    • Author(s)
      Nishizawa, H., Ohno, W., Yoshioka, T.
    • Organizer
      12th International Conference on Technology in Mathematics Teaching
    • Place of Presentation
      Faro, Portugal
    • Year and Date
      2015-06-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Handling 3D Graphic Objects Directly for the Learning of Vector Equations2015

    • Author(s)
      Ohno, W., Nishizawa, H.
    • Organizer
      12th International Conference on Technology in Mathematics Teaching
    • Place of Presentation
      Faro, Portugal
    • Year and Date
      2015-06-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Locating Points in 3D Graphic Space As More Direct Interface to the Learning Contents of Vector Equations2014

    • Author(s)
      Ohno, W., Shimada, K. Nishizawa, H., Yoshioka, T.
    • Organizer
      19th Asian Technology Conference in Mathematics, Yogyakarta, Indonesia
    • Place of Presentation
      Yogyakarta, Indonesia
    • Year and Date
      2014-11-26 – 2014-11-30
    • Related Report
      2014 Research-status Report
  • [Presentation] 低学年物理のためのwebベースコンテンツの開発と試用2014

    • Author(s)
      丹羽隆裕、西澤一
    • Organizer
      H26年度全国高専教育フォーラム教育研究活動発表会
    • Place of Presentation
      金沢市
    • Year and Date
      2014-08-26 – 2014-08-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 図形と数式を関連づけるインタラクティブ空間ベクトル学習コンテンツ

    • Author(s)
      西澤一、丹羽隆裕
    • Organizer
      H25年度全国高専教育フォーラム教育研究活動発表会
    • Place of Presentation
      豊橋技術科学大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 図形と数式を関連づけるインタラクティブ数学学習コンテンツ

    • Author(s)
      西澤一、丹羽隆裕
    • Organizer
      H24年度全国高専教育フォーラム教育研究活動発表会
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Related Report
      2012 Research-status Report
  • [Presentation] Virtual Game in Classroom for Introducing 3D Vector Operations

    • Author(s)
      2) H. Nishizawa, K. Shimada, T. Yoshioka
    • Organizer
      17th Asian Technology Conference in Mathematics
    • Place of Presentation
      Suan Sunandha Rajabhat University, Bangkok, Thailand
    • Related Report
      2012 Research-status Report
  • [Remarks] 数学学習支援システム

    • URL

      http://orchard.ee.toyota-ct.ac.jp

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
  • [Remarks] 数学学習支援システム

    • URL

      http://orchard.ee.toyota-ct.ac.jp

    • Related Report
      2013 Research-status Report
  • [Remarks] 数学学習支援システム

    • URL

      http://orchard.ee.toyota-ct.ac.jp

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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