EJMT Abstract

The use of geometry (or graphics) to teach and learn linear algebra is an interesting theme. Several published works have studied it, and have illustrated that the use of graphics can be helpful. However, the results of our questionnaire survey (in Japan) and our survey on linear algebra textbooks (in Japanese and English) show that the use of graphics tends to be held off in case of linear algebra compared to the case of calculus or analytic geometry. This tendency is most remarkable in general linear algebra with which the concepts generalizable to the vector spaces other than ℝⁿ (such as the space of functions, matricies, progressions, and so on) are concerned. Persisting in the fact that linear algebra is a general theory to unify various mathematical objects seems to reduce the teachers’ incentive for using graphics. However, as shown in this paper, many topics which motivate students to learn abstract concepts of general linear algebra can be found in the geometric (Euclidean) context. Hence, the use of geometric models (or 3D-graphics) should have strongly positive effects on learning them. The aim of this paper is to illustrate that using LATEX graphics drawn with KETpic should serve a great help for students in their learning linear algebra. KETpic is a macro package of computer algebra systems (CAS) to insert high-quality graphics into LATEX documents. The 3D-graphics drawn with KETpic are equipped with high accuracy (due to the use of CAS) and rich perspectives. The educational effect of using them will be shown through the result of our students’ interview.