The development of electronic communication media opens the possibilities for new ways of learning and understanding, in particular with respect to abstract structures. Traditional class teaching as well as various sectors of self and distant learning are affected thereby.

maths online tries to take into account this situation when realizing modern didactic concepts by interactive multimedia techniques. The goal is to contribute to the development of adequate standards for up to date maths education in school, highschool, college, university, and adults' qualification.

Learning mathematics ...

... is easy for some and difficult for others. In each case it requires efforts which may not be reduced to zero by whatever media. After all, mathematical fields, structures and insights, argumentation techniques and computation methods have been developed in a long historical process.

Nevertheless, suitable forms of teaching and learning may help one finding an approach to this formal and abstract world. It is a prominent goal of modern didactics to make clear on which issues the efforts should be concentrated. maths online does not want to teach some kind of "new mathematics", but rather the traditional goals of this subject, supported by modern methods.

Dynamical diagrams

The applets contained in the Gallery are dynamical diagrams, i.e. interactive units reacting immediately upon the user's activities like moving a scroll bar or typing some numerical input. In contrast to many other units, which at first glance seem to be quite similar to ours, maths online intends to lead the way towards the necessary efforts, not off from these. Most units contain problems to solve, thus pre-assuming a certain state of knowledge and aiming at a well-defined goal of understanding.

For example, sometimes a geometrically evident situation is coupled to the symbolic mathematical language. In order to solve the problems guven in such an applet, it will be necessary to "think together" both the geometric-intiutive and the abstract-symbolic description of the same object (see e.g. Coordinate system). Some of these applets are suitable for getting acquainted with mathematical notions long before the technical computational side is addressed (for example the basic notions of differential calculus in the applet On the definition of the derivative).

Additionally, the moving parts of a dynamical diagram may attract the user's attention in a very specific way. It is thus easier - as compared to the traditional print media - to distinguish between important and less important elements in a graphics.

A further example illustrating the new possibilities of adequately designed maths learning tool is provided by the group of jig-saw puzzles. In every day life, it is familiar to keep many things in one's head and to operate with these mentally. (So, if several persons are discussing about which movie they would watch tonight: everyone has to keep track of various cinemas, addresses, movie titles, reviews and clock times, in order to be able to play the "Pros and Cons" game). In maths teaching this is not necessarily the case: If the drawing of a simple function's graph is tied to a number of technical actions and takes (at best) several minutes, the number of expressions and graphs one may handle simultaneously is strongly limited. An example like Recognize functions 1 shows how multimedia support may make a new type of problems accessible to the learning.

Self-made puzzles

On frequent demand we have opened the Puzzle workshop, in which you may design your own puzzles, save it to your computer or publish it on the web. Puzzles generated in this way may serve various educational purposes and are not even restricted to mathematics.

Interactive tests ...

(in the form of multiple choice and puzzles) may help to check and improve one's knowledge and abilities (table of contents).

Maths links

Various people and institutions offer learning material and information about mathematical issues in the web. The interactive tools mostly consist of single of series of few units. Although material for the more advanced subjects is represented rather sparsely in the web, it altogether covers far more methods and contents than a single project like maths online could present.

The page Maths links und online tools collects various possibilities to include such material into the process of teaching and learning. On the one hand, offers ordered by topic shall facilitate the search for appropriate stuff. (All this material does not require the local installation of additional software). On the other hand, an extensive list of collections may serve as a starting points for the user's own discoveries.

Among the maths links, you find

Online tools

such as calculators, programs for plotting 2D and 3D function graphs, differentiating and integrating. (Some of them rely on the computer algebra system Mathematica). They are started in their own browser windows, so that they may be used simultaneously with other pages of maths online (online tools).

Suggestions for the classroom ...

... are provided in the form of project type worksheets, suitable for work in small groups (table of contents) and shall facititate the teachers' approach to this new way of learning. We welcome any suggestion or worksheet sent to us by the users of maths online. Most of the worksheets may be designed as web pages. In order to support the users with elementery HTML knowledge in inserting mathematical symbols, we offer a maths online HTML formula tool.

The construction of maths online ...

... proceeds since March 1998. New material is added continuously.


In order to become independent of web data procession speed, or in case of missing access to the internet, it may be reasonable to download maths online. We offer this possibility for Windows 95/98/NT/2000 and MacIntosh.

Feedback from the users

In order to optimize contents and presentation of maths online, we would like to encourage all (teaching and learning) users to give us some feedback about their experience. If convenient, please use the questionnaire. Feedback notes are published in the Forum.


Since January 1999 maths online has a mirror site at the Universita degli Studi di Messina,,

and since June 2000 it is available from the server of the Inter-University Institute of Macau,


Technical remarks

The units of maths online are Java applets. Hence, no download of additional software is necessary. The necessary computer abilities are thus reduced to a minimum. Moreover, most of the applets are designed such that they do not need further data after being initialized. Hence, the connection to the web may be disrupted once the respective web page has been opened in the browser.

As a consequence, the applets work only in a Java-enabled browser. (The page Optimal preferences for computer, browser and screen contains a test you can perform). The screen resolution should be at least 800 x 600 pixels (otherwise some applet windows will be "too large"). For an optimal appearance, the color depth of your screen should be adjusted to be greater than 256 colors.

Are you behind a fire-wall or a severe proxy server which keeps Java applets out of your local net? Consult this page!

The functionality of Java applets should be the same for all platforms, at least in theory. In reality, the continuous development of both Java and the browser technology sometimes cause inconveniences. Should this happen, please tell us.

Most parts of maths online developed before May 2000 are suitable for Netscape Navigator 3 and Microsoft Internet Explorer 4. Some applications, however (in particular the puzzles of the interactive tests), as well as the applets developed after May 2000 do not run in Netscape Navigator 3. If you use it, is hightly recommended to switch over to a newer version (4.0 or higher).

Contact us ...

... by E-mail or web page form, snail-mail, fax, or give us a call (see Authors).

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Bundesministerium für Unterricht und kulturelle Angelegenheiten
Verband Wiener Volksbildung
Magistrat der Stadt Wien, MA13
Oesterreichische Nationalbank