Editor’s note

An old dream has come true with the ViT-website produced by the project group at the University of Bergen.

ViT provides a visualization tool for linear algebra. Very often we see linear algebra courses that
focus mainly on algorithms like the Gaussian elimination and row reduction algorithms.
Therefore many of these courses appear quite algebraic.

On the other hand, many phenomena in linear algebra can best be seen geometrically. With a visual description many students will get an inroad to the concepts since they become more concrete: the
student can see what it is all about.

A geometrical intuition is crucial – not only because you can see the phenomena – but also because well-established geometrical concepts like a rotation or mirroring can be used to understand new
concepts like orthogonal transformations and determinants. Here, old and new knowledge is coupled together.

Another aspect of the ViT-website is that the phenomena from linear algebra not only are illustrated, but the learner may also change the elements in the situation interactively and the circumstances may be studied systematically. Thus the website becomes a useful toolbox which can be used to examine the subject. What does it mean that a transformation is degenerate? What does the image of a quadrilateral look like under these circumstances? What is it that collapses? Do all points necessarily merge into one single point?

The website is organized around seven different themes following some kind of natural progression in difficulty. Within each theme (where it is possible) the site is structured according to three
principals: Explain, Explore and Exercise. The Explain-parts give explanations and fit well in a classroom-situation, when new content is presented. The Explore-parts facilitate inquiry-based
activities, while the user may solve problems on the Exercise-parts.

A number of activities are presented as games. Here the user is invited to apply knowledge about the theme in a game situation. By these means the website wants to offer a supplement to other activities in usual linear algebra courses. Hopefully this will be an enrichment to the subject both with respect to teaching and to exploring linear algebra.

The production of the website is financed by Norgesuniversitetet and the Department of
Mathematics at the University of Bergen, Norway.

 

Norwegian version