GeoGebra

Please INSTALL GeoGebra

WITH INTERNET Go to www.geogebra.org Click WebStart

third item in the left menu Click button WebStart

GeoGebra is installed automaticallyWITHOUT INTERNET Ask us for USB flash drive with

GeoGebra

GeoGebraFree Dynamic Mathematics Software

Markus & Judith Hohenwarter www.geogebra.org

GeoGebra

Overview

What is GeoGebra? Using GeoGebra for Teaching &

Learning GeoGebra’s Web Export Open Source & GeoGebra Support Hands-on Activities

GeoGebra

What is GeoGebra?

Dynamic MathematicsSoftware

For Learning and Teachingin Schools

Geometry, Algebra and Calculus

Freely available fromwww.geogebra.org

GeoGebra

GeoGebra = Geometry Algebra+

Geometry & Graphics Window

Algebra Window

GeoGebra

Combination of elements ofdynamic geometry software (Sketchpad, Cabri)computer algebra systems (Derive, Maple)

High technical portabilityruns on Windows, Linux,

Solaris, MacOS Xdynamic worksheets (html)

GeoGebra is Innovative

GeoGebra

GeoGebra

Using GeoGebra forTeaching & Learning

GeoGebra

GeoGebra as a Pedagogical Tool

Presentation Tooldynamic visualizations

Modeling Tooldynamic constructions

Authoring Toolinteractive online material

GeoGebra

Examples of Using GeoGebra

Visualizingstudents can “see” abstract concepts

Representationsstudents can make connections

Experimentsstudents can discover mathematics

GeoGebra

Visualizing Adding Integers

GeoGebra

Visualizing Multiplying Fractions

GeoGebra

Visualizing Parameters

GeoGebra

Visualizing Parameters

GeoGebra

Visualizing Movement

GeoGebra

Visualizing Slope Functions

GeoGebra

Examples of Using GeoGebra

Visualizingstudents can “see” abstract concepts

Representationsstudents can make connections

Experimentsstudents can discover mathematics

GeoGebra

Multiple Representations GeoGebra: Bidirectional Connection

Symbolic ⇔ Graphics

ExamplesCoordinates ⇔ Point in Coordinate SystemCircle‘s Equation ⇔

Circle drawn in Coordinate SystemFunction‘s Equation ⇔ Graph of Function

GeoGebra

Representations: Sketch & Graph

GeoGebra

Unexpected Discoveries

GeoGebra

Representations: Geometry & Algebra

GeoGebra

Examples of Using GeoGebra

Visualizingstudents can “see” abstract concepts

Representationsstudents can make connections

Experimentsstudents can discover mathematics

GeoGebra

Experiments: Math & Real World

GeoGebra

Experiments: What happens when ... ?

GeoGebra

Experiments: Connections

GeoGebra

Experiments: Approximation

GeoGebra

Educational Principles

Student Activity Modeling Multiple Representations Experimental and

Guided Discovery Learning

GeoGebra

GeoGebra Communtiyand free software

GeoGebra

Why is it Free? Accessability

Available in Schools and at Home Online Collaboration

International Community User Forum – Users help Users GeoGebraWiki – Pool of Shared Materials Volunteers (Translators, Programmers)

Expandableby using other free software libraries

GeoGebra

World Wide User Community

40 languages 190 countries 400,000 visitors

per month

GeoGebra

GeoGebra User Forum

www.geogebra.org/forum

GeoGebra

GeoGebra’s Web Export

Every GeoGebra Construction can be exported as a Web Page (html)

Dynamic Worksheet

Examples:Theorem of ThalesCenter of a Round Table (ggb)

Solution worksheet

GeoGebra

GeoGebraWiki – Free Materials

www.geogebra.org/wiki

GeoGebra

Future Plans

Make it Easier, Easier, Easier! Spread Sheet Window Symbolic Algebra Window (CAS) 3D extension

GeoGebra

Hands-on ActivitiesSee handout