__Electronic Proceedings
of the 12 ^{th} 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

Keywords:

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.