Development of teaching method for linear algebra based on cognitive science

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K12392
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Science education
• Research Institution: Osaka Prefecture University
• Principal Investigator: Kawazoe Mitsuru 大阪府立大学, 高等教育推進機構, 教授 (10295735)
• Co-Investigator(Kenkyū-buntansha): 岡本 真彦 大阪府立大学, 人間社会システム科学研究科, 教授 (40254445)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 数学教育 / 認知科学 / 線形代数

Outline of Final Research Achievements

In the previous research, it has been believed that students have sufficient intuitive understanding on geometric vectors. However, our study revealed that there are many learners who have difficulty in imagining the space generated by three vectors, and that those learners have difficulty in recognizing that four spatial vectors are linearly dependent. Based on the result of the qualitative analysis, we hypothesized that the cognitive process in imagining a space generated by three vectors can be captured by "Basic Metaphor of Infinity" introduced by Lakoff and Nunez, and tried to improve students' understanding by helping students' geometric way of thinking. We obtained results suggesting that geometrical understanding is related to deep understanding of linearly independence, but we could not confirm the effect of the instruction which is aimed to help students' geometric way of thinking.

Free Research Field

数学教育

Academic Significance and Societal Importance of the Research Achievements

本研究は，従来研究が3次元空間までの概念は直観的に理解可能と暗黙のうちに前提していたことについて，３次元空間での幾何ベクトルに関しても直観的理解には限界があることを明らかにした。本研究の成果は，３次元までの直観的理解を前提とした指導がこれまで十分な効果を上げられなかったことの要因の説明を可能にする。この意味で，本研究の成果は，今後の線形代数の教育研究の基礎となりうるものである。