Departing from Black Box Approach in Linear Algebra with the Help of a Web-System

H. Nishizawa and T. Yoshioka (Japan)


Meaningful learning, real world application, Web-system, and linear algebra


Black box approach has been spreading among Japanese students in learning linear algebra. Led by the approach, students memorize numerous formulas and solving processes, but do not relate them to graphic objects or actual phenomena in the real world. They do not examine the mechanisms of the formulas by themselves, and the isolated knowledge vanishes in a short while. In this paper, the authors analyze the weakness of conventional lessons of linear algebra in Japanese educational institutions, propose a new lesson plan, and report the result of experimental lessons according to the plan. The plan blends traditional lectures and exercises with Web-based activities. It introduces linear algebra with its application in the real world, lets the students do experiments to connect mathematical ideas with real and graphic objects, and then leads them into the lectures and exercises in the classroom and on the Web. The experimental lessons have enriched our students’ learning in linear algebra.

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