REVIVING LINEAR ALGEBRA COURSE WITH THE HELP OF TECHNOLOGY

Linear algebra is an important but poorly understood field of mathematics for Japanese engineering students. They learn little from the lesson that starts with definitions and stays in symbolic manipulations because it lacks the reality and tends to lead the students only to surface learning. As the result, their performance in linear algebra usually stays lower than the ones of other fields. To overcome this situation, we designed lessons that started from a real-world application, moved to handling graphical objects in virtual space, and arrived at symbolic manipulations at last. In the former two stages, we fully used three-dimensional graphics produced by dynamic geometry software and/or computer algebra software. We expect such activities help our students to feel the reality in 3D vectors and understand them deeper. LOWER PERFORMANCE IN LINEAR ALGEBRA The authors have been used a Web-based exercise system of symbolic manipulations (Yoshioka, Higuchi & Nishizawa, 2000), analysed error-patterns in students’ manipulations, and added diagnosis of typical errors to the system (Nishizawa, Yoshioka, Fuchs, & Dominik, 2003). The effort helped to improve our students