Teaching and Learning Calculus with Free Dynamic Ma- thematics Software GeoGebra

Research suggests that despite the numerous benefits of using technology in mathematics education, the process of embedding technology in classrooms is slow and complex (Cuban, Kirkpatrick, & Peck, 2001). GeoGebra is open-source software for mathematics teaching and learning that offers geometry, algebra and calculus features in a fully connected and easy-to-use software environment. It is available free of charge and used by thousands of students and teachers around the world in classrooms and at home. In this presentation we will both present applications of GeoGebra for calculus teaching at the high school and college level, as well as raise some of the implications of free and easy-to-use software such as GeoGebra for technology integration into the teaching and learning of calculus. GeoGebra and Open Source Computer algebra systems (such as Derive, Mathematica, Maple or MuPAD) and dynamic geometry software (such as Geometer’s Sketchpad or Cabri Geometry) are powerful technological tools for teaching mathematics. Numerous research results suggest that these software packages can be used to encourage discovery and experimentation in classrooms and their visualization features can be effectively employed in teaching to generate conjectures (Lavicza 2006, Kreis 2004). However, different packages support teaching at a variety of curriculum levels and they require different amounts of classroom time for students to become proficient with the software. While computer algebra systems involve a considerable time commitment and their sophistication enables its use in upper level education, dynamic geometry software can be used as early as in elementary schools due to its mouse-driven user interface. The multi-platform, open-source dynamic mathematics software GeoGebra (Hohenwarter & Preiner 2007) tries to combine the ease-of-use of dynamic geometry software with the versatile possibilities of computer algebra systems. The basic idea of the software is to join geometry, algebra, and calculus, which other packages treat separately, into a single easy-to-use package for learning and teaching mathematics from elementary through university level. GeoGebra is available free of charge on the Internet, has been translated to 36 languages by volunteers, and gathers a rapidly growing worldwide user community. Currently, the website www.geogebra.org attracts about 300,000 visitors per month from 192 countries, and it can be estimated that more than 100,000 educators use the software for their teaching around the world. The open-source nature of the project has important implications both for educators and students. Unlike with commercial products, students are certainly not constrained to use the software only