Interoperable Interactive Geometry for Europe: an introduction

Abstract

Interactive or dynamic geometry is one of the three major software pillars of technology-based mathematics education, next to computer algebra systems (CAS) and spreadsheets. We can trace back the roots of this great tool for visualization and interactive manipulation to the work of Sutherland (1963), a system called Sketchpad which laid ground in computer science and human computer interaction. Since the introduction of Cabri-Geometre (Baulac, Bellemain and Laborde, 1988) and Geometers’ Sketchpad (Jackiw 1991), we could see several generations of such tools applied in mathematics education. During the last 20 years, interactive geometry software could establish a settled position in the mathematics education community, and for many researchers it is no longer a question whether to use these tools or not, but how to use them. However, what has convinced many in the academic field of mathematics education has still not become a standard in mathematics teaching in the classrooms (Intergeo Consortium 2008). While the lack of availability of computers in some schools or the cost of licensing might be reasons for the apparent underrepresentation, this cannot be the only reason. In particular, in Europe, most schools can offer access to networked computers, and there are several interactive geometry packages available free of cost. Also, there are thousands of web pages containing sketches, examples, activities and exercises—subsumed as ‘‘resources’’—using dynamic geometry. An initiative of Christian Mercat back in 2006 started what became the Intergeo project (Kortenkamp et al. 2009), funded through the eContentplus program of the European Union between October 2007 and 2010. This project intended to bring together teachers at all school levels from K-12 to university teaching and the wealth of resources available on the internet. By assembling the consortium and associate partners of the project from several major interactive geometry software producers from Europe (among them Cabri, Cinderella, GeoGebra, GEONExT, Geoplan-Geospace, TracenPoche, WIRIS and Z.u.L/C.a.R.), it was possible to include not only more than 3,000 resources contributing to the project, but the project could also strive for a common exchange format, a lingua franca for interactive geometry. A necessary condition for a true re-use of a resource lies in the possibility of using the resource in the environment familiar to the user regardless of the particular system used to create the resource. In addition, it was not clear how teachers can find exactly the content needed for his or her particular classroom situation. Helping people in this search for a specific content usually means adding to the resource itself metadata providing information about the resource. Then search engines can identify material based on keyword searches. The task is not trivial for mathematics and in particular geometry, as information cannot be extracted from a formula or graphical representation as easily as from a text. U. Kortenkamp (&) CERMAT, University of Education Karlsruhe, Postfach 11 10 62, 76060 Karlsruhe, Germany e-mail: kortenkamp@ph-karlsruhe.de; kortenkamp@cinderella.de