There are many theories on the learning and the instruction of mathematics. These theories existed before the development of CAS and it is interesting to investigate how they can be applied to or be related to the teaching of mathematics using computer algebra. The questions are: What do specific theories on the learning and teaching of mathematics predict concerning the role of CAS? What are the results of research studies that take a particular theoretical framework as a starting point?
(Revised version of Heid's paper published in IJCAME vol 9, no 2, 2002: How Theories About the Learning and Knowing of Mathematics can Inform the Use of CAS in School Mathematics: One Perspective)
In the discussion that followed the presentation and reaction, Michele Artigue
commented that the relation between theory and practice is twofold:
---- Theory can be a lens through which one explicitly looks at
practise to understand what happens.
---- Theory can be used to justify
an educational approach or an experimental design.
Members of the group: P. Drijvers (chair), A.-B. Fuglestad, K. Gravemeijer, A. Hayes, K. Heid, W. Hoekstra, M. Kendall, W. Peschek, E. Schneider, E. Torrence, L. Trouche.
There were four parts to the discussion, followed by the writing-up of a summary poster that was delivered to the final plenary session of the Symposium.
The group session started with reactions to the plenary papers. Participants took the occasion to discuss the idea of macro- and micro-procedures in more detail. In relation to this, also the topic of 'encapsulation'. There was a manifest need to speak about the meaning of the different words we use: if it is not clear what we mean when we use a specific expression, we cannot understand each other.
Luc Trouche presented the ideas of his French colleague Pierre Rabardel. Again, there was a need for explaining the exact meaning of concepts such as instrumentation, mediation, artefact.
[Powerpoint slides of the Trouche presentation] (354 KBytes - LARGE!!)
(Revised version of this paper published in IJCAME vol 9, no 3, 2002: Computer algebra systems (cas) and mathematical communication)
Werner Peschek and Edith Schneider presented their ideas on the role of CAS in education. Central to their talk was the idea that CAS is an "expert" that can be used for the outsourcing of work.
[PDF file of the Peschek and Schneider presentation] (27 KBytes)
Note: They also published an article on this topic in The International Journal of Computer Algebra in Mathematics Education, Vol 8, No. 1, pp. 7 - 22.
Drijvers distinguishes between local CAS theories and general theories on mathematics education. He presented an interview with a student and explained how he has tried to relate theory to these observations.
[Powerpoint slides of the Drijvers presentation] (73 KBytes)
The achievements of the group were presented to the final session of the Symposium in the form of a poster.
[Word file of the Poster] (38 KBytes)