Geogebra by Mr. L

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GeoGebra

[email protected] http://mrlsmath.com www.tttpress.com

“Building mathematical skill on a foundation of understanding”

Visualize Algebra & Geometry Concepts with the Greatest of Ease

A tool to help meet the California Mathematics Standards

presentation by Bill Lombard

some graphics from http://en.wikipedia.org and /http://commons.wikimedia.org

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GeoGebra

Overview

Introduction to GeoGebra User community Using GeoGebra in the classroom Hands-on Activities GeoGebra’s Web Export Open Source & GeoGebra Support


GeoGebra

Why use Technology?

“Technology is essential in teaching and learning mathematics;

it influences the mathematics that is taught and enhances students’ learning.”

(NCTM Principles and Standards, 2000)


GeoGebra

Technology or No Technology?“What we have learned from all the media

comparison research is that it’s not the medium, but rather the instructional methods that cause learning. When the instructional methods remain essentially the same, so does the learning, no matter how the instruction is delivered.”

(Clark & Mayer, e-Learning and the Science of Instruction, 2002)


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GeoGebra

What is GeoGebra?

Dynamic MathematicsSoftware

For Learning and Teachingin Schools

Geometry, Algebra and Calculus

Freely available fromwww.geogebra.org


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GeoGebra

GeoGebra = Geometry Algebra+

Geometry & Graphics Window

Algebra Window


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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


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GeoGebra

2001-2006: Development

Created by Markus Hohenwarter Mar 2002: Master’s thesis in Computer Science

& Mathematics Education Nov 2002: European Academic Software Award Mai 2005: User Forum & GeoGebraWiki Feb 2006: PhD project in Mathematics

Education funded by Austrian Academy of Sciences


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GeoGebra


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GeoGebra

World Wide User Community

40 languages 190 countries 400,000 visitors

per month


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GeoGebra

Visitors on www.geogebra.org


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GeoGebra

GeoGebra as a Pedagogical Tool

Presentation Tooldynamic visualizations

Modeling Tooldynamic constructions

Authoring Toolinteractive online material


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GeoGebra

Educational Principles

Student Activity Modeling Multiple Representations Experimental and

Guided Discovery Learning


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GeoGebra

Examples of Using GeoGebra

Visualizingstudents can “see” abstract concepts

Representationsstudents can make connections

Experimentsstudents can discover mathematics


GeoGebra

Creating Teaching Materials Static materials

Static picturesConstruction protocol

Allows you to reconstruct steps of a construction

Dynamic materialsConstruction files (ggb)Dynamic worksheets (html)


GeoGebra

Ways to use GeoGebra

Tool for studentsfor doing constructions from scratch

Tool for teachersVisualisation

dynamic demonstrations

Creating Teaching Materialsthat foster student activity


GeoGebra

What does GeoGebra offer?

points, vectors, segments, polygons, lines, all conic sections and functions in x

dynamic constructions (mouse)coordinates, equations, vectors, numbers

and commands (keyboard)easy-to-use interfacemultilingual menus, commands, help


GeoGebra

Using Dynamic Worksheets Student opens html file with a web browser

Requirements on student‘s computer: Web browser

e.g. Internet Explorer, Firefox, Safari

Java 1.4.2 or later free download from www.java.com

Note: GeoGebra is NOT needed to use worksheet


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. (Raymond Duval 1999)


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GeoGebra

Age 6-10: Adding Integers


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GeoGebra

Age 11-14: Multiplying Fractions


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GeoGebra

Age 15-18: Geometry & Algebra


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GeoGebra

Age 17 up: Functions & Calculus


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GeoGebra

Visualizing Parameters


GeoGebra

Construction Protocol - a built-in way to replay constructions


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GeoGebra


Using for GeometryMidpointsAngle bisectorsPerpendicular bisectorsTransformationsConjecture / proof


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GeoGebra

Geometry Examples

Mr. L demos using GeoGebraat the workshop


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GeoGebra


Using for Algebra 1Graphing lines & parabolasModeling with parametersSolutions of equationsFamilies of functions


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GeoGebra

Algebra 1 Examples



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GeoGebra


Using for Algebra 2Graphing complex functionsConic sections (non-functions)Exponential curves and logarithms


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GeoGebra

Algebra 2 Examples



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GeoGebra


Using for Trig & CalculusGraphing complex functionsDerivatives (slope of functions)Area under a curve (sum of

rectanglesIntegrals


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GeoGebra

Trig/Calculus Examples



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GeoGebra

GeoGebra’s Web Export

Every GeoGebra Construction can be

exported as a Web Page (html)

Dynamic Worksheet


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GeoGebra

GeoGebra is Open Source Available

in schools and at home Online collaboration

International communityUser forum – users help usersGeoGebraWiki – pool of shared materials

Expandableby using other open source libraries


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GeoGebra

InternationalUser Community


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GeoGebra

GeoGebra User Forum

www.geogebra.org/forum


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GeoGebra

GeoGebraWiki – Free Materials

www.geogebra.org/wiki


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GeoGebra

Status Quo What’s there?

Free software and material Extensive user community Immense expertise developed by enthusiasts

What’s missing? Not enough training Not enough support for teachers new to technology Limited research on the impact of GeoGebra


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GeoGebra

Future Plans

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


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GeoGebra

Additional GeoGebra Information Download these slides:

www.geogebra.org/workshop

GeoGebra Webpage: www.geogebra.org

Introduction to GeoGebra (Book) Print: www.lulu.com/content/2650846 Online: www.geogebra.org/book/intro-en/

Contact: [email protected] [email protected]


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GeoGebra


Teaching:

The hardest job you’ll ever love

just got easier with GeoGebra! !