Development of Teaching Modules on the Internet

This note concerns the launch of a new type of publication which we hope will better exploit the interactive potential of the electronic media . The concept is based on a previous note from Keith Tognetti published in the Gazette, Vol. 22, no.1, pp4-6, March 95, titled " A Hierarchy for Electronic Publishing"

This new publication will initially be in the form of a Teaching Module; a hopefully lively self contained entry to some mathematical topic that excites the author, written in such a way that the reader is infected with this excitement.

The Module author challenges you to make mostly constructive comments to further reveal the beauty of the underlying structures and uncover interconnections with allied structures. It is hoped that it is this "becoming" aspect which will give the publication its unique character. We would further ask that during this early formative stage the community offers comments in a spirit of cooperation rather than competition .

Eventually the Module will be set up in two parts: the original article and the commentaries. The main part will store the original paper in the form of read only. The other part will be a record of commentaries on the paper and will be interactive. Initially however, the Module will be stored as a single read only document with commentaries sent by e-mail ( see below) .

Every so often a review of the commentaries will be carried out which might result in editing the original and incorporating some of the commentaries Alternatively it might even be decided that those commentaries, which offer new ways of looking at the topic, should be kept in the form of an addendum to the original. It is hoped that in this way the Module will then develop a life of its own and will continually evolve into something more exciting and dynamic. What is more, by incorporating links to other allied areas, it should become a very good starter for entering some area for the first time as well as being of use to those who are trying to refresh themselves in a long forgotten area.

It is proposed to include such Modules in the Contents. We will also publish a short abstract within the Gazette under the new heading "Teaching Modules" - this issue begins with the abstract for the Module "e the exponential - the Magic Number of Growth" by Keith Tognetti.

At this stage we will avoid any claims that the Module is the `best' lesson on a particular topic, because what is best for a talented student might be worst for an average student; so this foreshadows a ranking of the modules, at some future stage, in terms of difficulty level. So to begin with we would like the key word to be "better" rather than "best". However we would like contributions in the spirit of our first Module which attempts to:

a) Provide a simple and self contained and hopefully exciting entry to a concept stating the assumed prior knowledge and, if a specialist treatment, for whom is it written,
b) Incorporate some history and lively anecdotage,
c) Give an axiomatic development of proofs as well as selections based on beauty and elegance,
d) Include references and eventually links to associated areas.
Rather than be a vehicle to demonstrate how clever the author is, the Module should demonstrate to the reader that he/she is the clever one who can understand ALL of the important steps in the presentation. In particular if you are tempted to humiliate the reader by using "it is easily shown that . . ", then don't! Instead spell out the steps or give a reference where these steps are indeed spelt out.

No we will not insist that your Module has all the above features - well not to get it up initially .

We believe that the Modules should not be computer aided lessons, rather they should introduce the serious student to the beauty of the underlying mathematical structures. We would hope that eventually links to such lessons will be added but we are not fussed about this at present as these are of such variable quality.

We would welcome suggestions on the general form of this new publication to be sent, preferably by e-mail, to BOTH of the following:
Keith Tognetti at the University of Wollongong. e-mail:
Ian Doust at the University of NSW. e-mail:

Initially we ask that your commentaries be sent to BOTH of the above at the same addresses - again we ask that at this stage they be offered in a spirit of cooperation rather than competition . Eventually we would like to start tapping those wonderful lessons from dedicated teachers that previously have disappeared from our community with the teacher.

Refereeing: All we ask initially is that some member of your Department at the level of lecturer or above is prepared to endorse the draft. But be warned that most of the refereeing will be done through the commentaries What better way to select the final referee than noting a commentator who has demonstrated an informed and spirited interest through the commentaries?

Finally we would ask that if you are interested in this new publication and would be prepared help us to reconcile the commentaries with the paper then could you please let Keith and Ian know. Even if you become interested in just the one paper that would be most helpful.

Keith Tognetti, Dept. of Mathematics, University of Woolongong, NSW, 2522
Ian Doust, Dept. of Pure Mathematics, University of New South Wales, NSW, 2052

Updated: 21 Mar 2008