具体から抽象へ向かう線形代数の理解度深化の試み [in Japanese] Deepening Students' Conceptual Understanding in Linear Algebra by Starting From Concrete Examples Towards Abstract Ideas [in Japanese]
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Linear algebra was one of underachieved strands of mathematics for the students of colleges of technologyin Japan at the annual INCT achievement tests, which were given to all the students a year after their learning oflinear algebra. The low scores at the achievement tests were partially because, in traditional lessons, theprocedures of symbolic manipulation were taught without relating to the features of associated graphical objectsor how they were used in real world applications. The isolated procedural knowledge did not accompanyconceptual understanding and must be easily forgotten just after the term-end examination. To compensate thissituation and deepen the students' conceptual understanding, we redesigned our lesson-plan to be directed fromconcrete examples towards abstract mathematical ideas, from handling graphic objects and observing theircharacteristics towards building vector equations and manipulating them symbolically. In the new lessons, severalinformation and communication technologies (ICT)-assisted activities are included to demonstrate the closerelation of graphic objects and vector equations interactively. This paper reports how the new lessons arechanging our students' learning style from black-box approach to more meaningful one. Their written answershave richer explanations than their former students who learnt in traditional lessons. Their scores in the annualINCT achievement test also increased significantly in 2010 academic year.
- Japanese colleges of technology education journal
Japanese colleges of technology education journal (35), 215-220, 2012-03
Institute of National Colleges of Technology,Japan