GeoGebra Dynamic Geometry, Algebra and Calculus Markus Hohenwarter, 2005 .

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

GeoGebra

Dynamic Calculus

functions in x

derivatives

integrals

GeoGebra

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 Dynamic Geometry, Algebra and Calculus Markus Hohenwarter, 2005 .

Documents

Transcript of GeoGebra Dynamic Geometry, Algebra and Calculus Markus Hohenwarter, 2005 .