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Automated theorem proving in GeoGebra: current achievements
Botana F., Hohenwarter M., Janicic P., Kovács Z., Petrović I., Recio T., Weitzhofer S. Journal of Automated Reasoning55 (1):39-59,2015.Type:Article
Date Reviewed: Oct 6 2015

Mathematics has been for a long time, and is still today, a difficult subject for many students. Teachers continuously look for ways to help students understand mathematical theorems, rules, and the relation between algebra and geometry. Besides many tools, information technology (IT) has greatly helped the learning process, especially in mathematics classrooms. Today, there are many useful software tools, such as the Geometer’s Sketchpad, Cabri Geometry, Cinderella, Euklides, EucliDraw, Descartes, and others. All of them are useful in teaching dynamic geometry, but each one has a special environment and in some ways is closed with the hardware platform. However, GeoGebra is an open software multiplatform tool that is easy to install and use by ordinary students and teachers. It also has many advantages that make it a widely used tool: it actively connects algebra and geometry; it covers the content of many mathematics curricula; and it generates the dynamic image on the web as an ordinary applet. This is why there are many titles on GeoGebra use, especially in the context of dynamic learning research. So what is covered in this paper on GeoGebra?

The authors present a new method of dynamic geometry teaching based on the GeoGebra tool, with special attention on proving a geometry theorem in an automated way within GeoGebra. They present their activity on automated theorem-proving methods and the integration of automated theorem-proving features in GeoGebra. Thus, they describe in short the specialties of several dynamic geometry software options and their theorem-proving capabilities. Since GeoGebra is open-source software, the authors describes their goals in adding proving capabilities to GeoGebra accompanied with the new GeoGebra commands that have been designed. All of these obstacles are well documented with several examples, which are enriched with high-quality images so that readers can easily understand the main ideas. An additional contribution of this research is the presentation of the educational relevance of teaching proofs in a classroom. The authors briefly describe how proofs can support student understanding of mathematical concepts, and consequently focus on how automated theorem proving in geometry as well as dynamic geometry software could improve the educational process.

Although this research is still in progress, the paper is a valuable source for further research in automated theorem proving in geometry. It shows possible ways for solving problems of dynamic geometry understanding. Thus, it surely has the potential to be an outstanding contribution to the field of dynamic learning.

Reviewer:  F. J. Ruzic Review #: CR143823 (1602-0160)
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