The maths online Collection

Franz Embacher and Petra Oberhuemer

The purpose of this note is to give a brief account of the learning material to be found at the maths online website,

Each external link in this note opens a new browser window -- to return to this text, either close the new window or click on this window.

The aim of the maths online project, which started in 1998, is to develop a coherent online program suitable for mathematics teaching and self-learning, covering a range of six years mathematics education. The material serves the needs of school teaching, adult education, and undergraduate university courses.

Our goal is to enable learners to understand the ideas behind formal mathematical concepts. Let us mention a few points about how we try to achieved this:

We establish links between abstract notions (such as the derivative) and geometric intuition (tangent to a curve), e.g. in terms of dynamical diagrams.

Many features that are difficult to explain when just a static blackboard is used -- e.g. because only one particular value of a variable may be drawn at a time -- are better suited for dynamical visualization, using a scroll bar.

Jigsaw puzzles -- besides their nice game properties -- enable the learner to handle several mathematical objects (e.g. functions) and their relations at a time.

The German version of maths online contains more material -- in particular, a text-based outline of the mathematical backbround and a glossary. Both versions are used in a number of high schools and adult education courses, and students consult them on their own when learning mathematics.

The ways in which the learning units can be used are quite variable. They range from a short glance at a dynamical diagram in support of introduction of a new concept to extensive group work. If maths online is used in class, the teacher should be familiar with the material. Some of the units are designed to be used as tools that are appropriate for various purposes -- for instance, enabling teachers to create their own problem sheets, refering to the existing resources.

The material is grouped into several categories:


A collection of multimedia learning units (interactive diagrams or jigsaw puzzles, designed as Java applets) on various topics, usually dealing with the introduction of crucial mathematical notions. Two examples:

  -   Introducing 3-vectors

  -   On the definition of the derivative

Interactive tests:

A number of interactive units suitable for testing the extent to which key mathematical concepts have been understood. Most of them are designed as multiple choice tests or jigsaw puzzles. Two examples:

  -   Intersection and union

  -   The big function graph puzzle

Maths links and tools:

A large collection of WWW links to mathematical topics and online tools. In particular the online tools are valuable in everyday mathematical procedures. Some of these tools have been developed by ourselves, e.g. the maths online function plotter (see the link at the left).

Further services:

The complete website may be downloaded as a ZIP archive, currently 3.4 MB. Other services include

  -  two tools for generating one's own puzzles,

  -  a tool assisting authors in creating mathematical symbols for web pages,

  -  suggestions for the classroom, and

  -  two online questionnaires for feedback.

This brief outline is, of course, no substitute for a visit to the maths online website. Any feedback and suggestions are highly welcomed by the authors.

The authors:

Franz Embacher

Petra Oberhuemer

Postal address:

Institute for Theoretical Physics, University of Vienna
Boltzmanngasse 5
A-1090 Vienna