Dynamic Geometry Software Supplemented with a Computer Algebra System as a Proving Tool

The topic of this contribution is aimed at lower and upper secondary school mathematics teaching as well as at university training of teachers of mathematics. Joint use of computer algebra (CAS) and dynamic geometry software (DGS) or even an incorporation of CAS into DGS brings new possibilities to the teaching of mathematics, such as experimentation, the modelling of real-world situations or the deriving and proving of conjectures. We will deal with all these issues and how they can be realized with the free dynamic mathematics software GeoGebra, mainly in terms of the use of its tools of automated theorem proving. Particular examples of possible ways of utilizing the methods and tools of automated theorem proving will be presented with the aim of illustrating that dynamic geometry enriched with algebraic features can contribute to the effective fulfilment of the requirements for educational proof, from a decision on the correctness of a geometric property to the modelling of real-world phenomena.