GeoGebra 1 “ 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 and /

GeoGebra 2 Overview Introduction to GeoGebra User community Using GeoGebra in the classroom Hands-on Activities GeoGebra’s Web Export Open Source & GeoGebra Support

GeoGebra 3 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 4 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)

GeoGebra 5 What is GeoGebra? Dynamic Mathematics Software For Learning and Teaching in Schools Geometry, Algebra and Calculus Freely available from

GeoGebra 6 GeoGebra =GeometryAlgebra+ Geometry & Graphics Window Algebra Window

GeoGebra 7 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) GeoGebra is Innovative

GeoGebra : 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

GeoGebra 9

GeoGebra 10 World Wide User Community 40 languages 190 countries 400,000 visitors per month

GeoGebra 11 Visitors on

GeoGebra 12 GeoGebra as a Pedagogical Tool Presentation Tool dynamic visualizations Modeling Tool dynamic constructions Authoring Tool interactive online material

GeoGebra 13 Educational Principles Student Activity Modeling Multiple Representations Experimental and Guided Discovery Learning

GeoGebra 14 Examples of Using GeoGebra Visualizing students can “see” abstract concepts Visualizing Representations students can make connections Representations Experiments students can discover mathematics Experiments

GeoGebra 15 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)

GeoGebra 16 Ways to use GeoGebra Tool for students for doing constructions from scratch Tool for teachers  Visualisation dynamic demonstrations  Creating Teaching Materials that foster student activity

GeoGebra 17 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

GeoGebra 18 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 or later free download from  Note: GeoGebra is NOT needed to use worksheet

GeoGebra 19 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)

GeoGebra 20 Age 6-10: Adding Integers

GeoGebra 21 Age 11-14: Multiplying Fractions

GeoGebra 22 Age 15-18: Geometry & Algebra

GeoGebra 23 Age 17 up: Functions & Calculus

GeoGebra 24 Visualizing Parameters

GeoGebra 25 Construction Protocol - a built-in way to replay constructions

GeoGebra 26 GeoGebra as a Pedagogical Tool Using for Geometry  Midpoints  Angle bisectors  Perpendicular bisectors  Transformations  Conjecture / proof

GeoGebra 27 Geometry Examples Mr. L demos using GeoGebra at the workshop

GeoGebra 28 GeoGebra as a Pedagogical Tool Using for Algebra 1  Graphing lines & parabolas  Modeling with parameters  Solutions of equations  Families of functions

GeoGebra 29 Algebra 1 Examples Mr. L demos using GeoGebra at the workshop

GeoGebra 30 GeoGebra as a Pedagogical Tool Using for Algebra 2  Graphing complex functions  Conic sections (non-functions)  Exponential curves and logarithms

GeoGebra 31 Algebra 2 Examples Mr. L demos using GeoGebra at the workshop

GeoGebra 32 GeoGebra as a Pedagogical Tool Using for Trig & Calculus  Graphing complex functions  Derivatives (slope of functions)  Area under a curve (sum of rectangles  Integrals

GeoGebra 33 Trig/Calculus Examples Mr. L demos using GeoGebra at the workshop

GeoGebra 34 GeoGebra’s Web Export Every GeoGebra Construction can be exported as a Web Page (html) Dynamic Worksheet

GeoGebra 35 GeoGebra is Open Source Available in schools and at home Online collaboration  International community  User forum – users help users User forum  GeoGebraWiki – pool of shared materials GeoGebraWiki Expandable by using other open source libraries

GeoGebra 36 International User Community

GeoGebra 37 GeoGebra User Forum um

GeoGebra 38 GeoGebraWiki – Free Materials wiki

GeoGebra 39 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

GeoGebra 40 Future Plans Make it Easier, Easier, Easier! Spreadsheet Window Symbolic Algebra Window (CAS) 3D extension

GeoGebra 41 Additional GeoGebra Information Download these slides: GeoGebra Webpage: Introduction to GeoGebra (Book)  Print:  Online: Contact:

GeoGebra 42 Teaching: The hardest job you ’ ll ever love just got easier with GeoGebra! !