Franz Embacher[1]
and Petra Oberhuemer[2]
Institute
for Theoretical Physics
University
of Vienna
Boltzmanngasse
5, A1090 Wien
Talk
given at the 5^{th} International Workshop on
Interactive
Computer Aided Learning (ICL)
Carinthia
Tech Institute
Villach/Austria,
September 25 – 27, 2002
The goal of the project ”New Media in Mathematics Training“ is to integrate elements of electronically supported learning into the mathematical training at universities and ”Fachhochschulen“. New forms of teaching will be applied to a number of selected courses in ”pure“ mathematics as well as in areas needing mathematics as ancillary science. By concentrating on wellestablished ”regular” courses and taking into account the different conditions and resources at the partner institutions, a sustainable effect on the mathematical training system is envisaged.
At present, the possibilities provided by modern
information and communication technologies are used rather scarcely in
mathematics training and universities and ”Fachhochschulen“. This applies for
areas in which mathematics plays a supporting role, as well as for the
education of future mathematicians and mathematics teachers. In the former case
this seems to be due to the fact that mathematical techniques are utilized for
a broad range of purposes, which in turn limits the amount of available electronic learning material.
Furthermore, only very few time is spent on mathematics training in most of
these areas. In the latter case of ”pure” mathematics, the existence of a
wellestablished set of analytical methods and paradigms provides a certain
barrier against the use of novel forms of visualization and interaction. In
addition, the institutions experience different basic conditions, and the
widespread spectrum of expertises of the lecturers implies a variety of
approaches and teaching methods.
On the other hand, students are confronted with severe
problems, in particular during their first semesters. Their knowledge brought
from school is diverse and often inadequate. A major problem in mathematics
courses for beginners is to establish a necessary common standard. Deficiencies
and shortcomings in their earlier mathematics education – or simply the
complexity of the mathematical content – implies lack of understanding and
frustration.
The project ”New Media in Mathematics Training“
strives to cope with this situation. Aiming at interaction and communication,
the technologies of the World Wide Web provide a variety of means to support the process of
understanding und the motivation. Beginning with a selected number of courses
held at different institutions, an attempt is made to integrate elements of
electronically supported teaching and learning into mathematics training. The
composition of the project team represents a broad spectrum of requirements,
basic conditions, experiences and resources.
The project was submitted within the framework of ”New Media in Universities and Fachhochschulen,
2^{nd} call“ („Neue Medien in der Lehre an Universitäten und
Fachhochschulen, 2. Ausschreibungsrunde“, see http://www.nml.at/)
and is just about to start, running over the next two years. It will be funded
by the Austrian Federal Ministry for Education, Science and Culture.
The project consortium consists of the following
institutions:

”mathe online” team, Faculty for
Natural Sciences and Mathematics, University of Vienna

Institute for Philosophy, University
of Vienna

Institute for Psychology, University
of Vienna

Institute for Sociology, University
of Vienna

Department of Engineering
Mathematics, Geometry and Computer Science, University of Innsbruck

Institute for Mathematics,
University of Vienna

Carinthia
Tech Institute

WIFI
Wien und Fachhochschulstudiengänge der Wiener Wirtschaft (FHW)

Paedagogical Academy in Vienna

Institute for Institute for
Communication Science, University of Vienna
In close cooperation, suitable web based materials are
developed and adapted. Thereby two goals have to be met:

A high degree of coherence of the material,
despite the broad spectrum of areas involved. This applies in particular to
mathematical background texts, visualizations of mathematical key notions and
exercises of general character. Material of this type should also be
appropriate the use in other areas – not represented in the project – in which
mathematics plays the role of an ancillary science.

Consideration of the specific characteristics of
the different courses, areas and existing curricula. This mainly applies to
specializations not relevant for all areas, but also to activities affected by
technical and organisational issues (e.g. the use of particular software in
technical areas).
The web platform used will be designed as an extension of the existing
mathematics portal ”mathe online“ (http://www.matheonline.at, whose
smaller English version ”maths online“ is
accessible from http://www.univie.ac.at/future.media/moe/).
Together with material already developed for the use in school math education,
this will give rise to a pool of mathematical learning units smoothly passing
over from school issues to university content, thus providing a helpful tool
for students.
In close cooperation, all partners will develop
scenarios for the selected courses. In order to achieve a sustainable effect on
the mathematical training system, the focus is on ”regular”, wellestablished
courses being part of existing curricula in the different areas. The new
concepts have to be integrated into these structures. Most courses are
”traditional” university lectures, supplemented by an exercises course.
The role of information technology is twofold:

Application of interactive learning
units (which, depending on the scenario, are processed by the students in a
computerequipped lecture hall or at home).

Additional asynchronous tools for
(asynchronous) communication among students and between students and lecturers.
This allows – at least to some extent – a continuous distance support.
The main motivations for this action are:

Modern web technologies provide new
possibilities to understand complex mathematical issues. This is in particular
relevant for the transition from school to university/”Fachhochschule”.

The problem of extremely large
student numbers in some areas.
Taking into account the different resources at the partner institutions, these actions will be applied during the next four semesters.
In addition to the web based material described above,
several short video clips dealing with mathematical key notions and methods
will be developed and produced. Their purpose is to take into account cognitive
types of learners, who learn and understand easier and faster by listening and
watching rather than reading. The chosen topics will be applicable for a broad
group of students and areas. The clips are generally accessible to the students
and may thus be viewed on demand. Whenever appropriate, they may be used during
the courses as well.
As a more experimental track, live events (synchronous
communication), supporting the community aspect of learning, will be organised.
Two scenarios are envisaged:

MOO/chat: The lecturer provides web
based material accessed by students using their web browser. The
synchronization is realized by the functionality of an educational MOO (=
Multiuser domain Object Oriented). Simultaneously, a chat provides the
possibility for discussion. This scenario is considered to be suitable for a
repetition or summary of a lecture.

MOO/audio: The voice of the lecturer
is transmitted to the students. Again the simultaneous presentation of web
based material is synchronization by a MOO. In some cases an additional chat
(or onewaychat for asking questions) may be reasonable. This scenario is
considered to be suitable for ”question time”likeevents or (panel)
discussions about general topics.
The events are
recorded and made accessible to the students for later use on demand. Both
scenarios will be tested with respect to acceptance by the students and
suitability of the technology for the communication about mathematical content.
The realization and evaluation of this project track will in particular need
the cooperation of dedicated students.
In order to cope with the technological evolution, it shall be tested
whether the XML based Mathematical Markup Language (MathML) and respective
tools are suitable for being used in everyday course issues.
At the end of the project (presumably in autumn 2004),
a final conference will be organised.
Afterwards ...
… the material and tools developed will generally be
accessible. A thorough project documentation shall help future initiatives to
profit from the experiences gained.