Computer algebra systems are finding their way into the mathematics classroom more and more, in hand-held as well as in desk-top format. Although good teaching examples and experiences exist, it is clear that the efficient and successful use of an ICT tool such as computer algebra is not self-evident. Recent research has focused on the relation between techniques and conceptual understanding, on the role of the teacher, and on the affordances of technology in realising specific pedagogical approaches. The CAME 2001 symposium examined this research in both plenary and discussion sessions, grouped into four themes as described below.

Plenary speakers

• Michèle Artigue (University of Paris, France)
• Neil Challis (Sheffield Hallam University, UK)
• Koeno Gravemeijer (Freudenthal Institute, Utrecht, The Netherlands)
• Kathleen Heid (Pennsylvania State University, USA)
• Kenneth Ruthven (University of Cambridge, UK)
• Kaye Stacey (University of Melbourne, Australia)
• Michal Yerushalmy (Haifa University, Israel)
• Rose Mary Zbiek (University of Iowa, USA)

Symposium organising committee

• Paul Drijvers (Freudenthal Institute, Utrecht University, The Netherlands)
• Joel Hillel (Concordia University, Canada)
• Phillip Kent (Institute of Education, London, UK)
• Giora Mann (Levinski College of Education, Israel)
• John Monaghan (University of Leeds, UK)
• Nurit Zehavi (Weizmann Institute, Israel)

Sponsors

We thank the following for financial support of this event:

• The Program Board for Educational Research of the Netherlands National Research Council (NWO/PROO) [www.nwo.nl]
• Texas Instruments [www.ti.com]

Proceedings of the Symposium (arranged by theme)

Most of the papers presented at the Symposium have been published in the International Journal of Computers for Mathematical Learning or the International Journal of Computer Algebra in Mathematics Education - see the individual theme pages for details.

1. CAS and techniques

The relationship between paper-and-pencil techniques, CAS techniques and conceptual understanding is a subtle one. The nature of paper-and-pencil techniques is different from that of CAS techniques. How do these different kinds of techniques interact with concept development and understanding? What is the nature of the "instrumentation" process, during which a tool gradually develops into an instrument, for learning to do mathematics using a computer algebra system? ... more

2. CAS and teachers

The teacher, of course, plays an important role in the students’ learning of how to integrate computer algebra into mathematical work. It appears that teachers may be very influential in privileging certain ways of using (or not using) a computer algebra device. How do teachers do that? What professional development is needed for teachers in order to be able to integrate the use of the technology in an effective way in their teaching? ... more

3. The role of theoretical frameworks on current CAS research into students' learning

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? ... more

4. The explicitness and expressiveness of a CAS environment

In using a CAS, a particular explicit symbolism is forced: each input requires a particular forced way of viewing things and expressing relationships and the output needs to be interpreted similarly. A CAS is expressive in the sense that one can express ideas (mental objects) in concrete form (visible, public objects). For an observer (teacher, educational researcher), the concrete, syntactically-precise expression of thought in actions (writing and rewriting of computer code, gestures and spoken remarks with respect to code and graphical and numerical displays) offers an unprecedented "window" onto students’ mathematical thinking. In this theme, we examined the nature and practical implications of a CAS as an "expressive medium". ... more

The future of CAME

The final session of the Symposium featured some discussion as to the future activities of CAME. Nurit Zehavi described the origins of the CAME Symposium as an attempt to make connections between CAS researchers and mainstream mathematics education research by organising the event just after the annual Psychology of Mathematics Education (PME) conference, and encouraging people from one event to attend the other. Up to now, the link with PME has provided very useful ideas for shaping the theoretical/research aspects of CAME. It is a link that we want to continue, but we should also be trying to develop links with other conferences and communities.

There are no definite plans yet for the next CAME meeting/symposium. The organisers would like to maintain it as a bi-annual event, but Nurit noted that the next International Congress in Mathematics Education (ICME-10) is going to be happening in Denmark in 2004, and CAME ought to have a significant presence there. The following suggestions were made as to arranging the next CAME symposium; the organisers welcome your feedback on these:

• in tandem with ICME-10 in 2004
• in tandem with PME in the UK in July 2002
• in tandem with PME in Hawaii in July 2003
• as an independent event in the summer of 2003, possibly in France
• linking up in some way with next ICTMT (Intl. Conference on Technology in the Teaching of Mathematics) conference in 2003 -- this is a bi-annual event held in a different European venue each time (the last was in Austria in August 2001)

To keep in touch with developments about CAME, please join the e-mailing list: simply send your email address (and, for reference, postal address) to Nurit Zehavi [Nurit.Zehavi@weizmann.ac.il].