Educational Practice on More Meaningful Teaching/Learning of Linear Algebra Starting from Real-Life Applications

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20500767
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Science education
• Research Institution: Toyota National College of Technology
• Principal Investigator: NISHIZAWA Hitoshi Toyota National College of Technology, 電気・電子システム工学科, 教授 (40249800)
• Project Period (FY): 2008 – 2011
• Keywords: ものづくり / 線形代数 / 有意味学習 / 空間図形 / ベクトル方程式

Research Abstract

本研究では、線形代数、特に空間図形のベクトル方程式の理解度が低迷している原因が、学習内容が現実事象から切り離された抽象的な記号処理に終始していることにあると考えた。このことが、学生に現実感を喪失させ、学習の表面化を助長していることに注目、工学系学生に身近な「ものづくり」の事例を出発点に、学生が現実感を持って学べる学習体系の構築をめざした。具体的には、空間図形のベクトル方程式を題材に、
(1)学生に身近な「ものづくり」の事例から抽出した応用例からの導入し、
(2)実体模型と3次元グラフィックスを用いたモデル化の方法を検討し、
(3)3次元グラフィックスを用いた仮想実験とWebシステムへの実装を行い、
(4)ベクトル表現のしくみ理解に注力した授業を実践、
(5)この教育体系による教育実践の効果を、科目試験成績と手書き答案で分析するだけでなく、授業終了10ヶ月後に行われる全国高専学習到達度試験(到達度試験)でも測定して、効果を検証、表面学習に流れやすい線形代数における有意味学習のモデルを構築することを目指した。

Research Products

• [Journal Article] Virtual Game for Deepening Students' Conceptual Understanding of 3D Vector Operations (2011)
  • Author(s): Nishizawa, H., Yamada, Y., Yoshioka, T.
  • Journal Title: Proc.International Conference Virtual and Augmented Reality in Education Pages: 30-34
  • Peer Reviewed
• [Journal Article] A System of Helping Concept-Building in 3D Linear Algebra by Connecting Graphics, Symbolic, and Verbal Representations (2010)
  • Author(s): Nishizawa, H., Zgraggen, B., Yoshioka, T.
  • Journal Title: Proc.The Electronic J. of Mathematics and Technology 4-2 Pages: 175-183
  • Peer Reviewed
• [Journal Article] A Proposal to Teach 3D Vector Operations in a Role-Playing Game (2008)
  • Author(s): Nishizawa, H., Yoshioka, T.
  • Journal Title: Proc.13th Asian Technology Conference in Mathematics Pages: 364-369
  • Peer Reviewed
• [Presentation] The Tournament : Virtual Game Using 3D Vectors (2011)
  • Author(s): Yamada, Y.
  • Organizer: International Conference "Virtual and Augmented Reality in Education"
  • Place of Presentation: Vidzeme University of Applied Sciences, Latvia.
  • Year and Date: 2011-03-18
• [Presentation] MATHEMATICA module Showing Dynamic Link of 3D Graphic Objects and Vector Equations (2010)
  • Author(s): Nishizawa, H.
  • Organizer: 15th Asian Technology Conference in Mathematics
  • Place of Presentation: University of Malaya, Malaysia.
  • Year and Date: 2010-12-19
• [Presentation] Cabri 3D Module to Visualize the Construction of 3D Vector Equation (2009)
  • Author(s): Asano, T.
  • Organizer: 14th Asian Technology Conference in Mathematics
  • Place of Presentation: Beijin Normal University, China.
  • Year and Date: 2009-12-19
• [Presentation] Software Module Showing Dynamic Link of 3D Graphic Objects and Vector Equations (2009)
  • Author(s): Kishi, N.
  • Organizer: 14th Asian Technology Conference in Mathematics
  • Place of Presentation: Beijin Normal University, China.
  • Year and Date: 2009-12-19
• [Presentation] Constructing a Game for Introducing 3D Vector Operations (2009)
  • Author(s): Yamada, Y.
  • Organizer: 14th Asian Technology Conference in Mathematics
  • Place of Presentation: Beijin Normal University, China.
  • Year and Date: 2009-12-19
• [Remarks] 線形代数学習システム「ぷにぷにベクトル」
  • URL: http://orchard.ee.toyota-ct.ac.jp