## 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.