Geo Gebra Dynamic Geometry Algebra and Calculus Markus
Geo. Gebra Dynamic Geometry, Algebra and Calculus Markus Hohenwarter, 2005 www. geogebra. at
Geo. Gebra What is Geo. Gebra? ¨ dynamic mathematics software ¨ for students and teachers ¨ dynamic geometry, algebra and calculus ¨ open source (free of charge)
Geo. Gebra = Geometry + Algebra
Geo. Gebra DGS and CAS n Dynamic Geometry Software ¨ drag mode (dynamic) ¨ graphical representation Cabri, Cinderella, Euklid Dynageo, Geometer‘s Sketchpad, Geonext, Ruler and Compass, … n Computer Algebra Systems ¨ algebraic and numerical computations ¨ symbolic representation Derive, Mathematica, Maple, Mu. Pad, Math. CAD, …
Geo. Gebra Combined Representations „There is no true understanding in mathematics for students who do not incorporate into their cognitive architecture the various registers of semiotic representations used to do mathematics. “ (Duval 1999)
Geo. Gebra Bidirectional Combination n Bidirectional change of representation symbolic ⇔ iconic (visual) n Examples ¨ coordinates ⇔ point in coordinate system ¨ function‘s equation ⇔ graph of function ¨ circle‘s equation ⇔ circle drawn in coordinate system
Geo. Gebra New Possibilities n n 1: DGS Construct a circle ⇒ equation is shown n 2: CAS Enter the equation of a circle ⇒ circle is plotted 3: Geo. Gebra equation of the circle ⇔ dynamic plot of the circle (drag the circle with the mouse)
Geo. Gebra Didactic Principles using Wittmann (1981) n Student activity orientation principle n Interaction of representations principle (iconic and symbolic representations) n Genetic principle (experimental learning of mathemtics)
Geo. Gebra Activity based learning Iconic and Symbolic representations (Bruner)
Geo. Gebra What does Geo. Gebra offer? ¨ points, vectors, segments, polygons, lines, all conic sections and functions in x ¨ dynamic constructions (mouse) ¨ coordinates, equations, vectors, numbers and commands (keyboard) ¨ intuitive notation c: (x - 3)² + (y + 2)² = 25 ¨ easy-to-use interface ¨ multilingual menus, commands, help
Geo. Gebra is Innovative Bidirectional combination of elements of ¨ dynamic geometry software ¨ computer algebra High technical portability ¨ runs on Windows, Linux, Solaris, Mac. OS X ¨ dynamic worksheets (html)
Geo. Gebra Dynamic Geometry and Algebra n ruler and compass geometry n analytic n vectors geometry
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Geo. Gebra Dynamic Calculus n functions in x n derivatives n integrals
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Geo. Gebra Dynamic Mathematics for School n Geo. Gebra – the dynamic mathematics software www. geogebra. at n Geo. Gebra. Wiki – the interactive pool of materials www. geogebra. at/wiki n Geo. Gebra User Forum www. geogebra. at/forum
Geo. Gebra Markus Hohenwarter © 2001 -2005
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