Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics
Christopher J. Sangwin (1) 1 and Laura Naismith (2)

1 Mathematics, Statistics and OR Network, School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
2 McGill University, Montreal, Canada

C.J.Sangwin@bham.ac.uk

 laura.naismith@mcgill.ca

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education.  The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.  Randomised question parameters and immediate, tailored feedback support a pedagogy of practice.  We introduce a mathematical question type that encapsulates these features and describe its implementation within the CABLE online system.  In CABLE, the question authoring process is supported through options and by providing a programming-free interface for teachers.

Teaching with a Symbolic Calculator in 10th Grade – Evaluation of a One Year Project
Hans-Georg Weigand

Universität Würzburg, Didaktik der Mathematik, Würzburg, Germany

weigand@mathematik.uni-wuerzburg.de

A one year project was started in the school year 2003/04 to test the use of symbolic calculators (SC) – the TI-Voyage 200 – in six 10th grade classes of three grammar schools in Bavaria (Germany).  The project was repeated in school year 2004/05.  The evaluation of the project was intended give answers to the following questions: how basic mathematical skills (algebraic transformations, solving equations, working with tables and formulas) changed; how the questions posed in examinations changed if the students were allowed to use a symbolic calculator (with CAS); how the students evaluated the use of the new tool; and how teaching styles and methods changed in the mathematics lessons.  This article presents the results of this project.

Exciting Normal Distribution
Karl Josef Fuchs (1)  , Reinhard Simonovits (2)  and Bernd Thaller (3) 

1  University of Salzburg, Department of Mathematics and Informatics Education karl.fuchs@sbg.ac.at

2  Handelsakademie (HAK), Grazbachgasse, Graz reinhard.simonovits@uni-graz.at

3  University of Graz, Institute for Mathematics and Scientific Computing bernd.thaller@uni-graz.at

This paper describes a high school project where the mathematics teaching and learning software M@th Desktop (MD) based on the Computer Algebra System Mathematica was used for symbolical and numerical calculations and for visualisation.  The mathematics teaching and learning software M@th Desktop 2.0 (MD) contains the modules Basics including tools for teachers and students and fitting routines, Differentiation, Integration and MDTools.  The homepage of the project is www.deltasoft.at.  MD’s engine is Mathematica.  An evaluation copy of MD is downloadable.

After a short introduction delineating the initial situation, the aims of the project, and the methodological frame, we describe the teaching process and final outcomes.  First results indicate that computer-based teaching intensifies the students’ activities, their level of attention, and their contentment with mathematics.

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