Full list of participants and email addresses
Presenter: Roger Brown, The International Baccalaureate Organization, UK
[DOWNLOAD BROWN'S PAPER]
Reactors: David Leigh-Lancaster, Victorian Curriculum and Assessment Authority
Melbourne, Australia; Lynda Ball and Peter Flynn, University of Melbourne, Australia
[DOWNLOAD LEIGH-LANCASTER'S PAPER]
[DOWNLOAD BALL'S PAPER]
[DOWNLOAD FLYNN'S PAPER]
Most, but not all, Mathematics curricula have fixed-time, individual, summative examinations. We are now in a state where some of these examinations allow or encourage students to do these with CAS-calculators. This is a very interesting development, which raises many issues and a number of problems. A related issue is the use of CAS in student portfolio work. The plenary addresses covered the following issues:
- Wider international perspectives on forms of assessment in Mathematics.
- The rationale, structure and key design elements of a particular CAS-encouraged curriculum and associated assessment.
- Issues concerned with students using different brands of CAS, on CAS-neutral and CAS-active questions and on new style of questions.
SUMMARY OF THE THEME 1 GROUP DISCUSSION [DOWNLOAD]
Presenter: Luc Trouche, Laboratoires ERES et LIRMM IREM, Université
Montpellier II, France [DOWNLOAD
TROUCHE'S PAPER]
Reactor: Celia Hoyles, Institute of Education, London, UK [DOWNLOAD
HOYLES' PAPER]
Revised versions of these papers are scheduled for publication in the International Journal of Computers for Mathematical Learning in 2004.
The learning of mathematics is often presented as a primarily mental activity that involves the construction of mathematical objects and relations. Likewise conceptual understanding is often presented as different from the application of skills in the performance of routine procedures. Further to this it has been claimed that technology such as computer algebra systems can perform these procedures leaving the learner free to concentrate on the building of mathematical concepts.
This vision has proved to be inadequate: evidence shows that using a computer algebra device requires insight into procedures as well as into the concepts involved. Also, the way computer algebra deals with the procedures - for example, its demands concerning notation, syntax and representation - affects students’ mathematical conceptions. Machine technique and mental conception interact while working in the technological environment.
The central issue in this strand was to consider mind - machine relations in more detail, to survey important aspects that play a role in this relation and, in particular, to investigate how the use of the computer algebra machine may evoke productive mental activities by the students.
SUMMARY OF THE THEME 2 GROUP DISCUSSION [DOWNLOAD]
Presenters: Al Cuoco and Paul Goldenberg, Education Development Center,
Massachusetts, USA
[DOWNLOAD CUOCO & GOLDENBERG'S PAPER]
Reactor: Colette Laborde, Université Joseph Fourier, Grenoble, France
[DOWNLOAD LABORDE'S PAPER]
It is clear that computer algebra systems bring serious changes in the goals, content, methods and forms of social interaction in mathematics teaching. As more mathematics educators became familiar with CAS a new area has surfaced, the design of CAS-based curricular materials. As more CAS-related studies are conducted, more questions are asked. What CAS-tasks engage students in conceptual aspects of mathematics? How do we assess the quality of these tasks? What is the role of CAS in emerging curricula? Should the use of CAS simply be allowed or should it be encouraged?
Participants in the group [DOWNLOAD].
During the group discussion, short presentations were made by: Ivan Cnop [DOWNLOAD], Thierry Dana-Picard and Joseph Steiner [DOWNLOAD], J. Orlando Freitas and J. Sousa Ramos [DOWNLOAD], and Baerbel Barzel [DOWNLOAD].
SUMMARY OF THE THEME 3 GROUP DISCUSSION [DOWNLOAD]