Visualizations for Mathematics Courses Based on a Computer Algebra System

This paper discusses the introduction of a computer-algebra system to perform visualizations in mathematics education. With theIllustratedMathematicsproject, we provide a comprehensive collection of graphics and animations for various topics in mathematics, which can directly be used for teaching. Because the programs (written inMathematica) we used for the creation of this collection are included, it is easy to design new examples by modifying parameters in existing examples. Therefore,IllustratedMathematicscan be used as a first step of the introduction of a computer-algebra system in mathematics education. In the second part, we report on the development of a workbench and learning environment, with which the students can discover the mathematical concepts by themselves. For that, the given examples have to be didactically enriched and processed. By creating their own visualizations of increasing complexity, the students improve their knowledge about the underlying computer-algebra system.