In a college of technology in Japan, many students have suffered lower performance in three-dimensional linear algebra for a long time. It is partially because they have learned linear algebra as a set of symbolic procedures isolated from graphical or verbal representations, and also from real world applications. Procedural knowledge without understanding the concept seems to evaporate just after the examinations.
To help students build conceptual knowledge of linear algebra, we have been constructing a learning system, which shows the dynamic relations of three representations: vector equations, 3D graphic objects represented by the equations, and verbal explanations of the features of equations and graphic objects. The system serves a series of activities, where students are able to touch or transform some parts of the graphic objects in virtual space, observe animated transformations of the graphic objects and simultaneous changes of symbolic expressions, and connect them to a list of verbal explanations. By experiencing the activities in the system, the students are expected to recognize the links between the three representations in 3D linear algebra.
The system is a combination of several software programs including web-browser/server, a database management system, a dynamic geometry software, and a computer algebra system. The structure and several activities of the system are described in this paper.