Content uploaded by Zoltán Kovács
Author content
All content in this area was uploaded by Zoltán Kovács on Nov 09, 2016
Content may be subject to copyright.
GeoGebra Tools with Proof Capabilities
Abstract
presentation slides
... A number of authors have discussed GeoGebra as a tool for automated proving and justification of numerous results-from the Pythagorean Theorem, Ceva's Theorem, Thale's Theorem (Kovács et al., 2016), angle bisector theorem, side bisectors of triangles to showing properties of geometric figures like triangles and circles (Chan, 2013;Laigo et al., 2016). Moreover, others have explored Geo-Gebra's effectiveness as a tool for helping students solve linear optimization word problems (Molnár, 2016), in understanding plane geometry (Pereira et al., 2017), and visualizing concepts of eigenvalues and eigenvectors in linear algebra (José et al., 2017). ...
In this review, the authors provide a survey of research of the dynamic mathematics software, Geo-Gebra, in the teaching and learning of school mathematics and related fields-including statistics, physics, chemistry and geography. The authors explore the role of GeoGebra as a tool to foster student achievement and teacher efficacy.
... A number of authors have discussed GeoGebra as a tool for automated proving and justification of numerous results-from the Pythagorean Theorem, Ceva's Theorem, Thale's Theorem (Kovács et al., 2016), angle bisector theorem, side bisectors of triangles to showing properties of geometric figures like triangles and circles (Chan, 2013;Laigo et al., 2016). Moreover, others have explored Geo-Gebra's effectiveness as a tool for helping students solve linear optimization word problems (Molnár, 2016), in understanding plane geometry (Pereira et al., 2017), and visualizing concepts of eigenvalues and eigenvectors in linear algebra (José et al., 2017). ...
In the modern era where technology usage is a tradition of the generation, integrating the teaching and learning with mediums that could catch up and satisfy pupils' interest is noteworthy. In line with this, the contributions of GeoGebra in the teaching-learning of mathematics: as a tool to foster students' interest and achievement, and as an environment to flourish different learning styles are explored in this study. Besides, the cautions to consider before implementing a GeoGebra integrated lesson with the challenges, limitations and areas of future development are indicated. Among these: the belief and technology fluency of users and the student class ratio are found to be among the challenges for effective integration of GeoGebra in mathematics lessons. The difficulty of some commands in the input bar especially for students and teachers with no prior programming experience are considered among the limitations of GeoGebra.
... Reference [15] is given in list but not cited in text. Please cite in text or delete from list. ...
We present two approaches to symbolically obtain isoptic curves in the dynamic geometry software GeoGebra in an automated, interactive process. Both methods are based on computing implicit locus equations, by using algebraization of the geometric setup and elimination of the intermediate variables. These methods can be considered as automatic discovery.
GeoGebra is open source mathematics education software being used in thousands of schools worldwide. It already supports equation system solving, locus equation computation and automatic geometry theorem proving by using an embedded or outsourced CAS. GeoGebra recently changed its embedded CAS from Reduce to Giac because it fits better into the educational use. Also careful benchmarking of open source Gröbner basis implementations showed that Giac is fast in algebraic computations, too, therefore it allows heavy Gröbner basis calculations even in a web browser via Javascript.
Gröbner basis on ℚ for revlex ordering implementation in Giac is a modular algorithm (E. Arnold). Each ℤ/pℤ computation is done via the Buchberger algorithm using F4 linear algebra technics and “remake” speedups, they might be run in parallel for large examples. The output can be probabilistic or certified (which is much slower). Experimentation shows that the probabilistic version is faster than other open-source implementations, and about 3 times slower than the Magma implementation on one processor, it also requires less memory for big examples like Cyclic9.
GeoGebra is an open-source educational mathematics software tool, with millions of users worldwide. It has a number of features (integration of computer algebra, dynamic geometry, spreadsheet, etc.), primarily focused on facilitating student experiments, and not on formal reasoning. Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather mature stage, we embarked on a project of incorporating and testing a number of different automated provers for geometry in GeoGebra. In this paper, we present the current achievements and status of this project, and discuss various relevant challenges that this project raises in the educational, mathematical and software contexts. We will describe, first, the recent and forthcoming changes demanded by our project, regarding the implementation and the user interface of GeoGebra. Then we present our vision of the educational scenarios that could be supported by automated reasoning features, and how teachers and students could benefit from the present work. In fact, current performance of GeoGebra, extended with automated deduction tools, is already very promising—many complex theorems can be proved in less than 1 second. Thus, we believe that many new and exciting ways of using GeoGebra in the classroom are on their way.
The introduction of smartphones with broadband Internet access allows students to access educational materials from almost everywhere. While the open source software GeoGebra is widely used on desktop and laptop computers, it is currently not available for the majority of mobile touchscreen devices like Apple’s iPhone/iPad or Google’s Android devices. In a former paper we described the project GeoGebraMobile which aimed to overcome this limitation by making GeoGebra applets accessible to students on a wide range of mobile devices. In our present paper we outline several enhancements of this former work leading to the new GeoGebraWeb project, report on its current status, and describe future plans.
- C Delobelle
- J Denizet
- Á Éliás
- L Fekete
Delobelle, C. Denizet, J. Éliás, Á. Fekete, L. Gál, Z. Kone£ný, Z. Kovács,
S. Lizelfelner, B. Parisse & G. Sturr (2014). GeoGebra 5.
The Relation Tool in GeoGebra 5
- Z Kovács
Z. Kovács (2015). The Relation Tool in GeoGebra 5. In Post-conference
Proceedings of the 10th International Workshop on Automated Deduction
in Geometry (ADG 2014), 9-11 July 2014, Lecture Notes in Computer
Science. Springer.