held October 19-20, 2005 in Roanoke, Virginia USA
in conjunction with the PME-NA-27 conference [www.pmena.org]
The rationale and goals for the CAME Symposia are to serve as a bridge between two communities, the CAS research community and the main mathematics education community. Thus, the 4th CAME Symposium was held directly before the Psychology of Mathematics Education - North America conference.
Each of the themes was addressed in plenary lectures and in topic groups, where the issues were worked on in more detail, based on the experiences of the participants. The topic groups produced a synthesis of the discussions in the plenary and topic group sessions.
Further short presentations were made in the group discussions, and papers for some of these are included here.
Coordinator : Kathleen Heid, Pennsylvania State University, USA
Presenter : John Monaghan, University of Leeds, UK
Reactor: Glen Blume, Pennsylvania State University, USA
[DOWNLOAD MONAGHAN'S PAPER (pdf)] [DOWNLOAD BLUME'S PAPER (pdf)]
With regard to computer algebra in mathematics education, "instrumentation and the anthropological approach" refers predominantly to the work of French mathematics educators who have developed a combination of ergonomic and socio-cultural interpretations of using computer algebra systems in mathematics classrooms. This work has generated a new depth of discussion in CAS work. The plenary session will address three themes: (i) An overview of this work from an Anglo-American perspective. (ii) An examination of some tensions in the situating of instrumentation through both an ergonomic and an anthropological lens. (iii) How these ideas have influenced possible directions for future mathematics education research and practice with regard to both computer algebra and other forms of technology.
Coordinator : Robert Mayes, West Virginia University, USA
Presenter : Werner Peschek, University of Klagenfurt, Austria
Reactor: Carolyn Kieran, University of Quebec at Montreal , Canada
[DOWNLOAD PESCHEK'S PAPER (pdf)] [DOWNLOAD KIERAN'S PAPER (pdf)]
Short papers from the topic group discussion: [Mann, Dana-Pickard and Zehavi (pdf)] [Sarvari (pdf)]
There is no doubt, that (creative) symbolic operating is a basic and central mathematical activity. But Computer Algebra Systems first of all have been developed to enable us for outsourcing symbolic operations to computers. (It is really astonishing that this central aspect of CAS is often hidden or covered up modestly in education discussions.)
What does this mean for our understanding of mathematical education now? Have operative knowledge and skills become obsolete as important parts of mathematical education (what someone can buy for a few dollars could hardly be an essential part of education)? Can we do mathematics lessons without skills? Or is the cognitive availability of operative knowledge and skills essential for mathematics education in spite of CAS? Or have operative knowledge and skills changed their meanings and do they now mean an adequate handling with CAS? Does the mathematics lesson have other tasks now (which ones?) Or do CAS help us to realize other important educational aims? Which ones?
Coordinator : Rose Mary Zbiek, Pennsylvania State University, USA
Presenter : Baerbel Barzel, Universität Duisburg-Essen, Germany
Reactor: Jean-Baptiste Lagrange, I.U.F.M., Reims, France
[DOWNLOAD BARZEL'S PAPER (pdf)] [DOWNLOAD LAGRANGE'S PAPER (pdf)]
Short paper from the topic group discussion: [Lavicza (pdf)]
[DOWNLOAD SUMMARY OF TOPIC GROUP DISCUSSION (pdf)]
Teacher learning while teaching with CAS has many dimensions, including learning about the technology, about mathematics, and about pedagogy. A crucial aspect of teacher learning unites these areas as teachers learn how to link multiple goals and manage multiple constraints. The plenary presentation involves teachers learning about how to blend computer algebra use and student-centered learning within the confines of curriculum requirements and time demands. Specific examples of how to develop content and process competence will initiate the conversation in classroom reality. Qualitative and quantitative results of a research project at the University of Duisburg-Essen, Germany, will lend an empirical eye. Reaction and discussion will further consideration of supporting and studying teacher learning while teaching with CAS.
M. Kathleen Heid, Pennsylvania State University, USA
Jean-Baptiste Lagrange, I.U.F.M., Reims, France
John Monaghan, University of Leeds, UK
Werner Peschek, University of Klagenfurt, Austria
Antonio Quesada, Akron University, Ohio, USA
Skip Wilson, Virginia Tech, USA
Rose Mary Zbiek, Pennsylvania State University, USA
Nurit Zehavi, Weizmann Institute, Israel
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(this page updated 13 March 2006)