GeoGebra

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Visualize Algebra Geometry Concepts with the
Greatest of Ease A tool to help meet
the California Mathematics Standards presentatio
n by Bill Lombardsome graphics from
http//en.wikipedia.org and /http//commons.wiki
media.org
bill.lombard_at_gmail.com http//mrlsmath.com www.ttt
press.com Building mathematical skill on a
foundation of understanding
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Overview

• Introduction to GeoGebra
• User community
• Using GeoGebra in the classroom
• Hands-on Activities
• GeoGebras Web Export
• Open Source GeoGebra Support

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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)
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Technology or No Technology?
What we have learned from all the media
comparison research is that its 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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What is GeoGebra?

• Dynamic MathematicsSoftware
• For Learning and Teachingin Schools
• Geometry, Algebra and Calculus
• Freely available fromwww.geogebra.org

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GeoGebra
Geometry
Algebra

Algebra Window
Geometry Graphics Window
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GeoGebra is Innovative

• Combination of elements of
• dynamic geometry software (Sketchpad, Cabri)
• computer algebra systems (Derive, Maple)
• High technical portability
• runs on Windows, Linux, Solaris, MacOS X
• dynamic worksheets (html)

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2001-2006 Development

• Created by Markus Hohenwarter
• Mar 2002 Masters 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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World Wide User Community

• 40 languages
• 190 countries
• 400,000 visitors per month

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Visitors on www.geogebra.org
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GeoGebra as a Pedagogical Tool

• Presentation Tooldynamic visualizations
• Modeling Tooldynamic constructions
• Authoring Toolinteractive online material

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Educational Principles

• Student Activity
• Modeling
• Multiple Representations
• Experimental and Guided Discovery Learning

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Examples of Using GeoGebra

• Visualizingstudents can see abstract concepts
• Representationsstudents can make connections
• Experimentsstudents can discover mathematics

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Creating Teaching Materials

• Static materials
• Static pictures
• Construction protocol
• Allows you to reconstruct steps of a construction
• Dynamic materials
• Construction files (ggb)
• Dynamic worksheets (html)

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Ways to use GeoGebra

• Tool for studentsfor doing constructions from
  scratch
• Tool for teachers
• Visualisationdynamic demonstrations
• Creating Teaching Materialsthat foster student
  activity

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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 interface
• multilingual menus, commands, help

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Using Dynamic Worksheets

• Student opens html file with a web browser
• Requirements on students 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

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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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Age 6-10 Adding Integers
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Age 11-14 Multiplying Fractions
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Age 15-18 Geometry Algebra
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Age 17 up Functions Calculus
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Visualizing Parameters
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Construction Protocol - a built-in way to replay
constructions
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GeoGebra as a Pedagogical Tool

• Using for Geometry
• Midpoints
• Angle bisectors
• Perpendicular bisectors
• Transformations
• Conjecture / proof

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Geometry Examples

• Mr. L demos using GeoGebra
• at the workshop

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GeoGebra as a Pedagogical Tool

• Using for Algebra 1
• Graphing lines parabolas
• Modeling with parameters
• Solutions of equations
• Families of functions

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Algebra 1 Examples

• Mr. L demos using GeoGebra
• at the workshop

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GeoGebra as a Pedagogical Tool

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

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Algebra 2 Examples

• Mr. L demos using GeoGebra
• at the workshop

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GeoGebra as a Pedagogical Tool

• Using for Trig Calculus
• Graphing complex functions
• Derivatives (slope of functions)
• Area under a curve (sum of rectangles
• Integrals

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Trig/Calculus Examples

• Mr. L demos using GeoGebra
• at the workshop

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GeoGebras Web Export

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

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GeoGebra is Open Source

• Available in schools and at home
• Online collaboration
• International community
• User forum users help users
• GeoGebraWiki pool of shared materials
• Expandable by using other open source libraries

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InternationalUser Community
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GeoGebra User Forum
www.geogebra.org/forum
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GeoGebraWiki Free Materials
www.geogebra.org/wiki
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Status Quo

• Whats there?
• Free software and material
• Extensive user community
• Immense expertise developed by enthusiasts
• Whats missing?
• Not enough training
• Not enough support for teachers new to technology
• Limited research on the impact of GeoGebra

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Future Plans

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

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Additional GeoGebra Information

• Download these slides www.geogebra.org/wor
  kshop
• GeoGebra Webpage www.geogebra.org
• Introduction to GeoGebra (Book)
• Print www.lulu.com/content/2650846
• Online www.geogebra.org/book/intro-en/
• Contact judith_at_geogebra.org
  markus_at_geogebra.org

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Teaching The hardest job youll ever
love just got easier with GeoGebra! !