Abstracts of Research Papers:

Learning Algebra in a Computer Algebra Environment
Paul Drijvers
Freudenthal Institute, Utrecht University, the Netherlands
p.drijvers@fi.uu.nl

This article summarises a doctoral thesis entitled ‘Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter’ (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of the concept of parameter while working with computer algebra. The findings indicate that an increased understanding in some of the roles of parameter was observed, but that the instrumentation of computer algebra was a difficult process, which provided obstacles. The thesis can be accessed online at www.fi.uu.nl/~pauld/dissertation.

Emptying the Bowl: An Investigation of Probability and Mathematics using CAS as an Inquiry-Based Counting Tool
Michael T Edwards
Department of Mathematics and Computer Science, John Carroll University, University Heights, Ohio USA 44118
mtedwards@jcu.edu

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions involving experimental and theoretical probabilities. Throughout the investigation, CAS provides intermediate results rather than "final answers." The unforeseen complexities that underlie "Emptying the Bowl" encourage students (and their teachers) to reconsider connections between early grades and upper level mathematics.

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Technology as a Bypass for Theoretical Knowledge
Thierry Dana Picard
Department of Applied Mathematics, Jerusalem College of Technology, Havaad Haleumi Str. 21, POB 16031, Jerusalem 91160 - Israel
dana@mail.jct.ac.il

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students’ conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids the blockage due to this lack of theoretical background. We illustrate this with examples from calculus.