Post on 02-Jan-2016
GeoGebraDynamic Geometry, Algebra and CalculusMarkus Hohenwarter, 2005www.geogebra.at
GeoGebra
What is GeoGebra?
dynamic mathematicssoftware
for students and teachers
dynamic geometry, algebra and calculus
open source (free of charge)
GeoGebra
GeoGebra = Geometry Algebra+
GeoGebra
DGS and CAS Dynamic Geometry Software
drag mode (dynamic) graphical representation
Cabri, Cinderella, Euklid Dynageo, Geometer‘s Sketchpad, Geonext, Ruler and Compass, …
Computer Algebra Systems algebraic and numerical computations symbolic representationDerive, Mathematica, Maple, MuPad, MathCAD, …
GeoGebra
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)
GeoGebra
Bidirectional Combination Bidirectional change of representation
symbolic ⇔ iconic (visual)
Examplescoordinates ⇔ point in coordinate system function‘s equation ⇔ graph of functioncircle‘s equation ⇔
circle drawn in coordinate system
GeoGebra
New Possibilities
3: GeoGebra
equation of the circle ⇔ dynamic plot of the circle (drag the circle with the
mouse)
1: DGS Construct a circle ⇒ equation is shown
2: CASEnter the equation of a circle ⇒circle is plotted
GeoGebra
Didactic Principlesusing Wittmann (1981)
Student activity orientation principle
Interaction of representations principle(iconic and symbolic representations)
Genetic principle(experimental learning of mathemtics)
GeoGebra
Activity based learning
Iconic and Symbolic representations (Bruner)
GeoGebra
What does GeoGebra offer?points, vectors, segments, polygons, lines,
all conic sections and functions in xdynamic constructions (mouse)coordinates, equations, vectors, numbers
and commands (keyboard) intuitive notation c: (x - 3)² + (y + 2)² = 25easy-to-use interfacemultilingual menus, commands, help
GeoGebra
GeoGebra is Innovative
Bidirectional combination of elements ofdynamic geometry softwarecomputer algebra
High technical portabilityruns on Windows, Linux,
Solaris, MacOS Xdynamic worksheets (html)
GeoGebra
Dynamic Geometry and Algebra
ruler and compass geometry
analytic geometry
vectors
GeoGebra
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Dynamic Calculus
functions in x
derivatives
integrals
GeoGebra
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GeoGebra
Dynamic Mathematics for School
GeoGebra – the dynamic mathematics softwarewww.geogebra.at
GeoGebraWiki – the interactive pool of materialswww.geogebra.at/wiki
GeoGebra User Forumwww.geogebra.at/forum
GeoGebra
GeoGebra Markus Hohenwarter © 2001-2005