Multiple representations and GeoGebra-based learning environments

The dynamic mathematics software GeoGebra offers the possibility of generating interactive applets for use in learning environments. Its graphics, algebra, computer algebra and spreadsheet views combine multiple mathematical representations with each other in an interactive and connected way. On the one hand, the software facilitates the visualization of mathematical concepts and facts. On the other hand, GeoGebra supports the interaction of different forms of representation of mathematical objects. In this paper, the use of GeoGebra applets is particularly addressed concerning tablet computers, which are becoming increasingly important and are distinguished by their intuitive operation with fingers. Abstract mathematics now becomes available at students’ fingertips allowing a very direct form of interaction with mathematical concepts and objects. One way to implement such learning environments are collections of interactive applets in so called “GeoGebraBooks” which are presented in this paper

Gaining momentum: GeoGebra inspires educators and students around the world

The use of technology is slowly becoming a substantial part of today’s education. Although due to the increased accessibility of affordable computing technologies in the 1980s and 90s it was predicted that computers would become rapidly integrated into mathematics teaching and learning (Kaput, 1992), technology uptake in schools has been considerably slow. The current expansion of technology use took a new unconventional direction: a bottom-up, community-based collaborative development, catalyzed by Internet-based communities and increasingly available community-developed software packages. During the past decades it has been demonstrated that a large number of enthusiasts can alter conventional thinking and models of development and innovation. The success of open source projects like Linux, Firefox, Moodle, and Wikipedia shows that collaboration and sharing can produce valuable resources in a variety of areas of life. While working on the open-source project GeoGebra we are witnessing the emergence of an enthusiastic international community around the software

Deciding geometric properties symbolically in GeoGebra

It is well known that Dynamic Geometry (DGS) software systems can be useful tools in the teaching/learning of reasoning and proof. GeoGebra 5.0 was recently extended by an Automated Theorem Prover (ATP) subsystem that is able to compute proofs of Euclidean geometry statements. Free availability and portability of GeoGebra has made it possible to harness these novel techniques on tablets, smartphones and computers. Then, we think it is urgently necessary to address the new challenges posed by the availability of geometric ATP?s to millions of students worldwide

Determinando propiedades geométricas simbólicamente con GeoGebra

Los programas de Geometría Dinámica (GD) constituyen unas herramientas tan útiles como provocadoras para la enseñanza/aprendizaje de los conceptos matemáticos de razonamiento y prueba. Así, estos programas de GD facilitan a los estudiantes la formulación de ciertos hechos geométricos (por ejemplo, como pasos intermedios para establecer la prueba de una proposición dada) dibujando diagramas auxiliares que permiten, luego, convencerse de la verdad/falsedad de la afirmación conjeturada al poder verificar su validez en muchos casos, tras arrastrar al azar algunos elementos de la figura y comprobar, en la figura arrastrada, la permanencia de determinadas propiedades

BSRLM geometry working group: establishing a professional development network to support teachers using dynamic mathematics software GeoGebra

The embedding of technology into mathematics teaching is known to be a complex process. GeoGebra, an open-source dynamic mathematics software that incorporates geometry and algebra into a single package, is proving popular with teachers - yet solely having access to such technology can be insufficient for the successful integration of technology into teaching. This paper reports on aspects of an NCETM-funded project that involved nine experienced teachers collaborating in developing ways of providing professional development and support for other teachers across England in the use of GeoGebra in teaching mathematics. The participating teachers tried various approaches to better integrate the use of GeoGebra into the mathematics curriculum (especially in geometry) and they designed and led professional development workshops for other teachers. As a result, the project initiated a core group which has started to be a source of support and professional development for other teachers of mathematics in the use of GeoGebra

Automated Theorem Proving in GeoGebra: Current Achievements

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

Integrating STEM-related Technologies into Mathematics Education at a Large Scale

This paper outlines the growing phenomenon and need to integrate technologies into mathematics and science teaching and learning. There are a number of successful projects for valuable integration of technologies around the world, however, these successes are often limited reaching a relatively small number of teachers and students. In this paper, we aim to offer examples of large-scale technology projects that could create a critical mass of users that could further drive innovation and sustainability for educational technology integration. We outline how GeoGebra became one of the most widely used dynamic mathematics software with a user base of more than 100 million; highlight directions of research for technology development and integration; and describe the Geomatech project that aimed to train 2500 teachers in 950 schools in Hungary. We hope that such examples, the developed technology, resources and pedagogies could contribute to further valuable integrations of technologies in mathematics and science education

Establishing a professional development network around dynamic mathematics software in England

In this paper, we outline some results of a project funded by NCETM (the National Centre for Excellence in the Teaching of Mathematics) that aimed to establish a professional development network in England around an open-source mathematical software - GeoGebra. During the past few years a large international user and developer community has formed around various GeoGebra-related activities. Most teachers who are currently using GeoGebra have not received professional training in the implementation of the software in their teaching practices, but have begun using it due to their own enthusiasm or through encouragement by their colleagues. However, research suggests that, for the majority of teachers, solely providing technology is insufficient for the successful integration of technology into their teaching. It has been suggested that adequate training and collegial support can boost teachers' willingness to integrate technology into their teaching and to develop successful technology-assisted teaching practices. Thus, in our project, involving nine experienced teachers in England, we developed suitable priorities for professional development, including designing a range of supporting materials for use by teachers more widel

GeoGebra 4.4 – from Desktops to Tablets

The open source software GeoGebra is rapidly gaining popularity in the teaching and learning of mathematics around the world. Currently, GeoGebra is translated to more than 50 languages, used in 190 countries, and downloaded half a million times each month. In this paper, we offer a brief introduction to the history of the software, introduce its worldwide community, outline new features of the latest version GeoGebra 4.2, and share future software development plans, in particular about the upcoming release of the first GeoGebra Apps for tablet computers

GeoGebra 3.2 - The new Spreadsheet View

The release 3.2 of GeoGebra will add another – third – view for mathematical objects: the Spreadsheet View. In this paper we will introduce the new view, present some examples and discuss the opportunities the new Spreadsheet View will offer for teaching and learning of mathematics