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106 François Roosegaarde Bisschop is ICT coordinator and timetabler in the secondary cycle of the European School, Karlsruhe. Giacomello Vladimiro is a maths teacher in the Italian section in the secondary cycle of the European School, Karlsruhe. The introduction of dynamic geometry software has completely changed mathematics teaching. This article introduces a very powerful and easy-to-use piece of dynamic geometry freeware called GeoGebra, produced by the Austrian mathematician, Markus Hohenwarter. Die Einführung der dynamischen Software im Bereich der Geometrie veränderte die Art des Mathematikunterrichts. Dieser Artikel stellt die sehr gute, leicht anzuwendende und frei erhältliche dynamische Software "GeoGebra" vor. Produziert wurde sie von dem österreichischem Mathematiker Markus Hohenwarter. L'introduction des logiciels de géométrie dynamique a complètement révolutionné la façon dont les mathématiques sont enseignées. L'article présente GeoGebra (produit par le mathématicien autrichien Markus Hohenwarter), un logiciel particulièrment puissant et facile à utiliser. PANORAMA DYNAMIC GEOMETRY SOFTWARE IN MATHS TEACHING BY FRANÇOIS ROOSEGAARDE & GIACOMELLO VLADIMIRO
In the late 1980s, the introduction of two dynamic geometry applications, Cabri Geometry and Geometer's Sketchpad, produced a revolution in maths teaching. The idea of creating, manipulating and dynamically changing geometric shapes brought a breath of fresh air to maths lessons of every grade. Today the market offers several very good products: the above-mentioned Cabri and Geometer’s Sketchpad, Euklid DynaGeo and C.a.R. and Cinderella, among others. A particularly powerful and easy to use piece of software is GeoGebra. It is a Javabased application developed by the Austrian mathematician Markus Hohenwater. It is freeware and can be downloaded from www.geogebra.org. It is also possible to run the software directly from the internet, without downloading it. The website provides versions for Windows, Mac, Linux or other Java platforms, online and PDF guides, links to a users forum and to GeoGebraWiki, an entire section of Wikipedia which provides a huge amount of material in several languages. The present version, 3.2 has been translated into 42 languages. The GeoGebra user interface consists of a geometry pad, a spreadsheet, an algebra window, a menu bar, a toolboxes bar, an input bar and a command bar. With the Toolbox buttons it is possible to draw points, find points of intersection and midpoints, draw lines, segments and vectors, perpendicular lines, parallel lines, angle bisectors, tangents, polar lines, best fit lines and loci. You can also draw polygons, circles, semicircles, arcs and circular sections, conic sections and angles. In addition, length, area and slope can be found, and reflections, rotations, translations and enlargements built. You can introduce sliders, check boxes, text and images. Finally, the drawing pad can be moved to zoom and to show or hide objects. I would like to present a simple example of how GeoGebra can be used during maths lessons in the lower classes of the seconday school. Plot the points A=(-3,4), B=(-1,4), C=(-1,1) and D=(-3,1). Translate the rectangle ABCD 5 lines to the right. Write the new coordinates of each vertex. Click on View-Grid. Insert the points in the Input Bar. A=(-3,4) B=(-1,4) C=(-1,1) D=(-3,1) Create a new polygon using the toolbox polygon and clicking on the points ABCD. Create a vector 5 units towards right using the toolbox vectors. Click on Translate Object by Vector. Click first on the polygon and then on the vector to create the translated rectangle. The coordinates of the vertices of the translated rectangle can be read on the Algebra Window. Click on Move and then move point F to change vector and, consequently, the translated rectangle. This is just one example, but the software offers many possibilities. The software can be used from year 5 in primary, to the last year of secondary. Links: www.geogebra.org http://www.geogebra.org/en/wiki/index. php/Main_Page http://www.slu.edu/classes/maymk/ GeoGebra/ http://math247.pbworks.com/GeoGebra François Roosegaarde, Giacomello Vladimiro PANORAMA 107
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