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bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com “ Building mathematical skill on a foundation of understandi

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. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

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bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com “ Building mathematical skill on a foundation of understandi

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  1. Visualize Algebra & Geometry Concepts with the Greatest of Ease A tool to help meet the California Mathematics Standards presentation by Bill Lombardsome graphics from http://en.wikipedia.org and /http://commons.wikimedia.org bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com “Building mathematical skill on a foundation of understanding”

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

  3. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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)

  4. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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)

  5. What is GeoGebra? Dynamic MathematicsSoftware For Learning and Teachingin Schools Geometry, Algebra and Calculus Freely available fromwww.geogebra.org bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  6. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com GeoGebra = Geometry + Algebra Algebra Window Geometry & Graphics Window

  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.com http://mrlsmath.com www.tttpress.com

  8. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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

  9. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

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

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

  12. GeoGebra as a Pedagogical Tool Presentation Tooldynamic visualizations Modeling Tooldynamic constructions Authoring Toolinteractive online material bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

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

  14. Examples of Using GeoGebra Visualizingstudents can “see” abstract concepts Representationsstudents can make connections Experimentsstudents can discover mathematics bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  15. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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)

  16. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com Ways to use GeoGebra • Tool for studentsfor doing constructions from scratch • Tool for teachers • Visualisationdynamic demonstrations • Creating Teaching Materialsthat foster student activity

  17. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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

  18. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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

  19. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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. (RaymondDuval 1999)

  20. Age 6-10: Adding Integers bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  21. Age 11-14: Multiplying Fractions bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  22. Age 15-18: Geometry & Algebra bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  23. Age 17 up: Functions & Calculus bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  24. Visualizing Parameters bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

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

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

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

  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.com http://mrlsmath.com www.tttpress.com

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

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

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

  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.com http://mrlsmath.com www.tttpress.com

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

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

  35. 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 bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com

  36. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com InternationalUser Community

  37. GeoGebra User Forum bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com www.geogebra.org/forum

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

  39. Status Quo bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com • 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

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

  41. bill.lombard@gmail.com http://mrlsmath.com www.tttpress.com 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: judith@geogebra.orgmarkus@geogebra.org

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

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