Computer Based Conjectures and Proofs in Teaching Euclidean Geometry

The aim of this dissertation is to identify effective methods on extending teaching of conjectures and proofs of Euclidean geometry theorems in secondary schools by utilizing computers, and to develop corresponding technology and software tools by enhancing existing dynamic geometry systems. Based upon analysis of the possible aims of mathematics teaching and an overview of the existing software tools and the theory, • a general report highlights areas where computers can indeed help in the teaching process, and areas of typical dangers of abuse of computers are also presented, • an enhancement of the dynamic mathematics software GeoGebra is introduced to give more support for teachers and students concerning proofs, • an analysis of an effective mathematical method in theorem proving for the Euclidean geometry is introduced in an effort to help non-expert readers to learn the basics of the applied mathematical algorithms, • some typical classroom situations are shown by utilizing GeoGebra to support teaching of certain topics in Euclidean geometry. The results in this dissertation can be considered as a prototype, but they are elaborated enough to be integrated in classroom use already and also for developing it further to provide a wider range of use for teaching proofs.