Electronic Proceedings of the 12th Asian Technology Conference in Mathematics


            Abstract for 12760

            A Graphical Explanation of Fundamental Vector Operations for

            Engineering Students

            Authors: Hitoshi Nishizawa, Takayoshi Yoshioka

            Affiliations: Toyota National College of Technology, Dept. of

            Electrical and Electronic Engineering



            At the achievement test of fundamental mathematics for third-year

            students of colleges of technology in Japan, the students in

            linear algebra was lower than the ones of calculus, trigonometry, or

            algebra. Many students failed to separate the equation of a straight

            line in 3D space from the one of a flat surface. Interviews to the

            students revealed that:

            1) they have memorized those equations just before term-end

            examinations, but

            2) they did not have the experience to relate them to graphic

            objects, so

            3) they could not explain how the change in a parameter of the

            equation affects on the position or direction of the related graphic

            object, even qualitatively.

            Their knowledge in linear algebra seems to evaporate in thin air

            because it is not related to the experiences which students feel

            more reality.


            To improve this situation, we have been building some graphical

            explanation of vector operations in 2D and 3D space with the help of

            graphic software. In the explanation, we need:

            1) physical phenomenon which is familiar to engineering students,

            and its mathematical model,

            2) graphic objects in the model, and

            3) vector operations and their graphical meanings.

            Our explanation and the implementation are described in this paper.