Breaking Down GeoGebra: Two Dimensions of the GeoGebra Software Application

Abstract

GeoGebra is a professionally produced, freely available, interactive and dynamic open-source educational mathematics software designed for teaching and learning mathematics at all levels of education, from elementary school to universities. In many educational systems around the world, the GeoGebra program is integrated into textbooks and various projects. GeoGebra is designed to combine the properties of dynamic geometry software and a computer algebra system into a single, integrated and easy-to-use tool for teaching and learning mathematics. GeoGebra has the ability to bridge the gaps that exist between different mathematical disciplines, combining the content of the fields: geometry, algebra, statistics, analysis, and tabular and graphical displays in a simple, convenient package. GeoGebra is equally popular among students and among teachers. It attracts students with its dynamism and interactivity, but also because it provides visual and conceptual feedback. It has been found that it encourages students to learn mathematics, helps them analyze different problems and simulate physical phenomena through dynamic structures. It offers unlimited opportunities for experimentation to students, which leads to better mastering of the teaching content and to effective learning. GeoGebra can also be used beyond the classroom: students can use it at home, when doing homework, for practice, for repeating lessons already learned and for preparing for future lessons. The use of GeoGebra modernizes teaching and positively affects the creativity of students and their critical thinking, helps to facilitate the acquisition and improvement of 21st century skills, intensifies the application of active learning methods. Apart from being a computer tool, many authors consider GeoGebra as a conceptual (ideal), pedagogical, cognitive and transformational tool in teaching and learning mathematics. In practice, we distinguish two main dimensions regarding the application of GeoGebra. On one hand, GeoGebra can serve as a tool for demonstration and visualization of formal mathematical knowledge. GeoGebra actually represents a virtual experimental mathematical laboratory, a place where hypotheses can be set up and tested; to monitor and verify scientific facts; to illustrate tasks and problems, their variations and sets of solutions; to analyze the properties of different geometric objects; to discover geometric places of points that satisfy certain conditions, to find significant points of functions; to prove mathematical statements; to demonstrate various proofs of mathematical statements and the like. On the other hand, GeoGebra can serve as an authoring tool for creating interactive learning materials. With GeoGebra, multimedia contents such as animations, simulations and computer games can be created that will serve as didactic tools, in the function of getting to know, studying and visualizing terms, concepts, ideas, ties or phenomena, as well as complex processes that cannot be easily described and explained in word and text, especially those involving some degree of abstraction. In this paper concrete examples of practical demonstration of these two dimensions of using the GeoGebra software will be presented and explained in detail.