Combining CAS and DGS - Towards Algorithmic Thinking

Ulrich Kortenkamp
Media and Computing Department
University of Education Schwäbisch Gmünd
73525 Schwäbisch Gmünd, Germany

Abstract. Both computer algebra systems and dynamic geometry software established their place in schools. It seems to be a natural decision to combine the strengths of both systems into one: students should be able to do symbolic calculation and interactive manipulation of parameters at the same time. Further investigation of the topic shows that it is not straightforward to achieve this interaction. The reason for this might be the fundamentally different approach of the two systems.

First, the chronology is different; computer algebra activities usually consist of (typing and evaluation) actions that give a result which then can be plotted, tabled, or investigated in some other way. The software does most of the work while the user is waiting. For dynamic geometry software, it is different. The main computations take place while the user is manipulating the construction.

Second, computer algebra systems favor an algorithmic approach, where transformations of (symbolic) expressions are done step-by-step, either with user interaction or automatically. In dynamic geometry, once a construction is set up, the interaction tries to mimic a functional approach - dependent elements should move as if they are determined by the free elements.

In my talk I want to compare both approaches and show how they can be combined. Furthermore, I will demonstrate how a system that can accomodate both worlds can be used in teaching discrete mathematics, already in secondary school.