1. GeoGebra 1 bill.lombard@gmail.comhttp://mrlsmath.comwww.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

2. GeoGebra 2 Overview Introduction to GeoGebra User community Using GeoGebra in the classroom Hands-on Activities GeoGebra’s Web Export Open Source & GeoGebra Support bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

3. 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) bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

4. 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) bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

5. GeoGebra 5 What is GeoGebra? Dynamic Mathematics Software For Learning and Teaching in Schools Geometry, Algebra and Calculus Freely available from www.geogebra.org www.geogebra.org bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

6. GeoGebra 6 GeoGebra =GeometryAlgebra+ Geometry & Graphics Window Algebra Window bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

7. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

8. GeoGebra 8 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

9. GeoGebra 9 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

10. GeoGebra 10 World Wide User Community 40 languages 190 countries 400,000 visitors per month bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

11. GeoGebra 11 Visitors on www.geogebra.org bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

12. GeoGebra 12 GeoGebra as a Pedagogical Tool Presentation Tool dynamic visualizations Modeling Tool dynamic constructions Authoring Tool interactive online material bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

13. GeoGebra 13 Educational Principles Student Activity Modeling Multiple Representations Experimental and Guided Discovery Learning bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

14. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

15. 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) bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

16. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

17. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

18. 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 1.4.2 or later free download from www.java.comwww.java.com  Note: GeoGebra is NOT needed to use worksheet bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

19. 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) bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

20. GeoGebra 20 Age 6-10: Adding Integers bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

21. GeoGebra 21 Age 11-14: Multiplying Fractions bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

22. GeoGebra 22 Age 15-18: Geometry & Algebra bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

23. GeoGebra 23 Age 17 up: Functions & Calculus bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

24. GeoGebra 24 Visualizing Parameters bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

25. GeoGebra 25 Construction Protocol - a built-in way to replay constructions bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

26. GeoGebra 26 GeoGebra as a Pedagogical Tool Using for Geometry  Midpoints  Angle bisectors  Perpendicular bisectors  Transformations  Conjecture / proof bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

27. GeoGebra 27 Geometry Examples Mr. L demos using GeoGebra at the workshop bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

28. GeoGebra 28 GeoGebra as a Pedagogical Tool Using for Algebra 1  Graphing lines & parabolas  Modeling with parameters  Solutions of equations  Families of functions bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

29. GeoGebra 29 Algebra 1 Examples Mr. L demos using GeoGebra at the workshop bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

30. GeoGebra 30 GeoGebra as a Pedagogical Tool Using for Algebra 2  Graphing complex functions  Conic sections (non-functions)  Exponential curves and logarithms bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

31. GeoGebra 31 Algebra 2 Examples Mr. L demos using GeoGebra at the workshop bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

32. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

33. GeoGebra 33 Trig/Calculus Examples Mr. L demos using GeoGebra at the workshop bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

34. GeoGebra 34 GeoGebra’s Web Export Every GeoGebra Construction can be exported as a Web Page (html) Dynamic Worksheet bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

35. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

36. GeoGebra 36 International User Community bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

37. GeoGebra 37 GeoGebra User Forum www.geogebra.org/for um bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

38. GeoGebra 38 GeoGebraWiki – Free Materials www.geogebra.org/ wiki bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

39. 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 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

40. GeoGebra 40 Future Plans Make it Easier, Easier, Easier! Spreadsheet Window Symbolic Algebra Window (CAS) 3D extension bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

41. GeoGebra 41 Additional GeoGebra Information Download these slides: www.geogebra.org/workshop www.geogebra.org/workshop GeoGebra Webpage: www.geogebra.org www.geogebra.org Introduction to GeoGebra (Book)  Print: www.lulu.com/content/2650846www.lulu.com/content/2650846  Online: www.geogebra.org/book/intro-en/www.geogebra.org/book/intro-en/ Contact: judith@geogebra.org markus@geogebra.org judith@geogebra.org markus@geogebra.org bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com

42. GeoGebra 42 bill.lombard@gmail.comhttp://mrlsmath.comwww.tttpress.com Teaching: The hardest job you ’ ll ever love just got easier with GeoGebra! !