[email_address] http://mrlsmath.com www.tttpress.com “ Building mathematical skill on a foundation of understanding” Visua...
Overview <ul><li>Introduction to GeoGebra </li></ul><ul><li>User community </li></ul><ul><li>Using GeoGebra in the classro...
Why use Technology? “ Technology is essential in teaching and learning mathematics;  it influences the mathematics that is...
Technology or No Technology? “ What we have learned from all the media comparison research is that it’s  not the medium , ...
What is GeoGebra? <ul><li>Dynamic Mathematics Software </li></ul><ul><li>For Learning and Teaching in Schools </li></ul><u...
GeoGebra  = Geometry Algebra + Geometry & Graphics Window Algebra Window [email_address] http://mrlsmath.com www.tttpress....
<ul><li>Combination of elements of </li></ul><ul><ul><li>dynamic geometry software (Sketchpad, Cabri) </li></ul></ul><ul><...
2001-2006: Development <ul><li>Created by Markus Hohenwarter </li></ul><ul><li>Mar 2002: Master’s thesis in Computer Scien...
[email_address] http://mrlsmath.com www.tttpress.com
World Wide User Community <ul><li>40 languages </li></ul><ul><li>190 countries </li></ul><ul><li>400,000 visitors  per mon...
Visitors on www.geogebra.org [email_address] http://mrlsmath.com www.tttpress.com
GeoGebra as a Pedagogical Tool <ul><li>Presentation Tool dynamic visualizations </li></ul><ul><li>Modeling Tool dynamic co...
Educational Principles <ul><li>Student Activity </li></ul><ul><li>Modeling </li></ul><ul><li>Multiple Representations </li...
Examples of Using GeoGebra <ul><li>Visualizing students can “see” abstract concepts </li></ul><ul><li>Representations stud...
Creating Teaching Materials <ul><li>Static materials </li></ul><ul><ul><li>Static pictures </li></ul></ul><ul><ul><li>Cons...
Ways to use GeoGebra <ul><li>Tool for students for doing constructions from scratch </li></ul><ul><li>Tool for teachers </...
W h at does GeoGebra offer? <ul><ul><li>points, vectors, segments, polygons, lines, all conic sections and functions in x ...
Using Dynamic Worksheets <ul><li>Student opens  html file  with a web browser </li></ul><ul><li>Requirements on student‘s ...
Combined Representations <ul><li>There is no true understanding in mathematics for students who do not incorporate into th...
Age 6-10: Adding Integers [email_address] http://mrlsmath.com www.tttpress.com
Age 11-14: Multiplying Fractions [email_address] http://mrlsmath.com www.tttpress.com
Age 15-18: Geometry & Algebra [email_address] http://mrlsmath.com www.tttpress.com
Age 17 up: Functions & Calculus [email_address] http://mrlsmath.com www.tttpress.com
Visualizing Parameters [email_address] http://mrlsmath.com www.tttpress.com
Construction Protocol -  a built-in way to replay constructions [email_address] http://mrlsmath.com www.tttpress.com
GeoGebra as a Pedagogical Tool <ul><li>Using for Geometry </li></ul><ul><ul><li>Midpoints </li></ul></ul><ul><ul><li>Angle...
Geometry Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address] ...
GeoGebra as a Pedagogical Tool <ul><li>Using for Algebra 1 </li></ul><ul><ul><li>Graphing lines & parabolas </li></ul></ul...
Algebra 1 Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address]...
GeoGebra as a Pedagogical Tool <ul><li>Using for Algebra 2 </li></ul><ul><ul><li>Graphing complex functions </li></ul></ul...
Algebra 2 Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address]...
GeoGebra as a Pedagogical Tool <ul><li>Using for Trig & Calculus </li></ul><ul><ul><li>Graphing complex functions </li></u...
Trig/Calculus Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_addr...
GeoGebra’s Web Export <ul><li>Every  GeoGebra Construction can be exported as a Web Page (html) Dynamic Worksheet </li></u...
GeoGebra is Open Source <ul><li>Available in schools and at home </li></ul><ul><li>Online collaboration </li></ul><ul><ul>...
International User Community [email_address] http://mrlsmath.com www.tttpress.com
GeoGebra User Forum www.geogebra.org/forum   [email_address] http://mrlsmath.com www.tttpress.com
GeoGebraWiki – Free Materials www.geogebra.org/wiki   [email_address] http://mrlsmath.com www.tttpress.com
Status Quo  <ul><li>What’s there? </li></ul><ul><ul><li>Free software and material </li></ul></ul><ul><ul><li>Extensive us...
Future Plans <ul><li>Make it Easier, Easier, Easier! </li></ul><ul><li>Spreadsheet Window </li></ul><ul><li>Symbolic Algeb...
Additional GeoGebra Information <ul><li>Download these slides:    www.geogebra.org/workshop </li></ul><ul><li>GeoGebra Web...
Teaching: The hardest job you’ll ever love just got easier with GeoGebra! ! [email_address] http://mrlsmath.com www.tttpre...
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Geogebra by Mr. L

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Bill Lombard's presentation on using Geogebra.

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Geogebra by Mr. L

  1. 1. [email_address] 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
  2. 2. Overview <ul><li>Introduction to GeoGebra </li></ul><ul><li>User community </li></ul><ul><li>Using GeoGebra in the classroom </li></ul><ul><li>Hands-on Activities </li></ul><ul><li>GeoGebra’s Web Export </li></ul><ul><li>Open Source & GeoGebra Support </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  3. 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) [email_address] http://mrlsmath.com www.tttpress.com
  4. 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) [email_address] http://mrlsmath.com www.tttpress.com
  5. 5. What is GeoGebra? <ul><li>Dynamic Mathematics Software </li></ul><ul><li>For Learning and Teaching in Schools </li></ul><ul><li>Geo metry, Al gebra and Calculus </li></ul><ul><li>Freely available from www.geogebra.org </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  6. 6. GeoGebra = Geometry Algebra + Geometry & Graphics Window Algebra Window [email_address] http://mrlsmath.com www.tttpress.com
  7. 7. <ul><li>Combination of elements of </li></ul><ul><ul><li>dynamic geometry software (Sketchpad, Cabri) </li></ul></ul><ul><ul><li>computer algebra systems (Derive, Maple) </li></ul></ul><ul><li>High technical portability </li></ul><ul><ul><li>runs on Windows, Linux, Solaris, MacOS X </li></ul></ul><ul><ul><li>dynamic worksheets (html) </li></ul></ul>GeoGebra is Innovative [email_address] http://mrlsmath.com www.tttpress.com
  8. 8. 2001-2006: Development <ul><li>Created by Markus Hohenwarter </li></ul><ul><li>Mar 2002: Master’s thesis in Computer Science & Mathematics Education </li></ul><ul><li>Nov 2002: European Academic Software Award </li></ul><ul><li>Mai 2005: User Forum & GeoGebraWiki </li></ul><ul><li>Feb 2006: PhD project in Mathematics Education funded by Austrian Academy of Sciences </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  9. 9. [email_address] http://mrlsmath.com www.tttpress.com
  10. 10. World Wide User Community <ul><li>40 languages </li></ul><ul><li>190 countries </li></ul><ul><li>400,000 visitors per month </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  11. 11. Visitors on www.geogebra.org [email_address] http://mrlsmath.com www.tttpress.com
  12. 12. GeoGebra as a Pedagogical Tool <ul><li>Presentation Tool dynamic visualizations </li></ul><ul><li>Modeling Tool dynamic constructions </li></ul><ul><li>Authoring Tool interactive online material </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  13. 13. Educational Principles <ul><li>Student Activity </li></ul><ul><li>Modeling </li></ul><ul><li>Multiple Representations </li></ul><ul><li>Experimental and Guided Discovery Learning </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  14. 14. Examples of Using GeoGebra <ul><li>Visualizing students can “see” abstract concepts </li></ul><ul><li>Representations students can make connections </li></ul><ul><li>Experiments students can discover mathematics </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  15. 15. Creating Teaching Materials <ul><li>Static materials </li></ul><ul><ul><li>Static pictures </li></ul></ul><ul><ul><li>Construction protocol </li></ul></ul><ul><ul><ul><li>Allows you to reconstruct steps of a construction </li></ul></ul></ul><ul><li>Dynamic materials </li></ul><ul><ul><li>Construction files (ggb) </li></ul></ul><ul><ul><li>Dynamic worksheets (html) </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  16. 16. Ways to use GeoGebra <ul><li>Tool for students for doing constructions from scratch </li></ul><ul><li>Tool for teachers </li></ul><ul><ul><li>Visualisation dynamic demonstrations </li></ul></ul><ul><ul><li>Creating Teaching Materials that foster student activity </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  17. 17. W h at does GeoGebra offer? <ul><ul><li>points, vectors, segments, polygons, lines, all conic sections and functions in x </li></ul></ul><ul><ul><li>dynamic constructions (mouse) </li></ul></ul><ul><ul><li>coordinates, equations, vectors, numbers and commands (keyboard) </li></ul></ul><ul><ul><li>easy-to-use interface </li></ul></ul><ul><ul><li>multilingual menus, commands, help </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  18. 18. Using Dynamic Worksheets <ul><li>Student opens html file with a web browser </li></ul><ul><li>Requirements on student‘s computer: </li></ul><ul><ul><li>Web browser e.g. Internet Explorer, Firefox, Safari </li></ul></ul><ul><ul><li>Java 1.4.2 or later free download from www.java.com </li></ul></ul><ul><ul><li>Note: GeoGebra is NOT needed to use worksheet </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  19. 19. Combined Representations <ul><li>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. </li></ul><ul><li>( Raymond Duval 1999) </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  20. 20. Age 6-10: Adding Integers [email_address] http://mrlsmath.com www.tttpress.com
  21. 21. Age 11-14: Multiplying Fractions [email_address] http://mrlsmath.com www.tttpress.com
  22. 22. Age 15-18: Geometry & Algebra [email_address] http://mrlsmath.com www.tttpress.com
  23. 23. Age 17 up: Functions & Calculus [email_address] http://mrlsmath.com www.tttpress.com
  24. 24. Visualizing Parameters [email_address] http://mrlsmath.com www.tttpress.com
  25. 25. Construction Protocol - a built-in way to replay constructions [email_address] http://mrlsmath.com www.tttpress.com
  26. 26. GeoGebra as a Pedagogical Tool <ul><li>Using for Geometry </li></ul><ul><ul><li>Midpoints </li></ul></ul><ul><ul><li>Angle bisectors </li></ul></ul><ul><ul><li>Perpendicular bisectors </li></ul></ul><ul><ul><li>Transformations </li></ul></ul><ul><ul><li>Conjecture / proof </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  27. 27. Geometry Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  28. 28. GeoGebra as a Pedagogical Tool <ul><li>Using for Algebra 1 </li></ul><ul><ul><li>Graphing lines & parabolas </li></ul></ul><ul><ul><li>Modeling with parameters </li></ul></ul><ul><ul><li>Solutions of equations </li></ul></ul><ul><ul><li>Families of functions </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  29. 29. Algebra 1 Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  30. 30. GeoGebra as a Pedagogical Tool <ul><li>Using for Algebra 2 </li></ul><ul><ul><li>Graphing complex functions </li></ul></ul><ul><ul><li>Conic sections (non-functions) </li></ul></ul><ul><ul><li>Exponential curves and logarithms </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  31. 31. Algebra 2 Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  32. 32. GeoGebra as a Pedagogical Tool <ul><li>Using for Trig & Calculus </li></ul><ul><ul><li>Graphing complex functions </li></ul></ul><ul><ul><li>Derivatives (slope of functions) </li></ul></ul><ul><ul><li>Area under a curve (sum of rectangles </li></ul></ul><ul><ul><li>Integrals </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  33. 33. Trig/Calculus Examples <ul><li>Mr. L demos using GeoGebra </li></ul><ul><ul><li>at the workshop </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  34. 34. GeoGebra’s Web Export <ul><li>Every GeoGebra Construction can be exported as a Web Page (html) Dynamic Worksheet </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  35. 35. GeoGebra is Open Source <ul><li>Available in schools and at home </li></ul><ul><li>Online collaboration </li></ul><ul><ul><li>International community </li></ul></ul><ul><ul><li>User forum – users help users </li></ul></ul><ul><ul><li>GeoGebraWiki – pool of shared materials </li></ul></ul><ul><li>Expandable by using other open source libraries </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  36. 36. International User Community [email_address] http://mrlsmath.com www.tttpress.com
  37. 37. GeoGebra User Forum www.geogebra.org/forum [email_address] http://mrlsmath.com www.tttpress.com
  38. 38. GeoGebraWiki – Free Materials www.geogebra.org/wiki [email_address] http://mrlsmath.com www.tttpress.com
  39. 39. Status Quo <ul><li>What’s there? </li></ul><ul><ul><li>Free software and material </li></ul></ul><ul><ul><li>Extensive user community </li></ul></ul><ul><ul><li>Immense expertise developed by enthusiasts </li></ul></ul><ul><li>What’s missing? </li></ul><ul><ul><li>Not enough training </li></ul></ul><ul><ul><li>Not enough support for teachers new to technology </li></ul></ul><ul><ul><li>Limited research on the impact of GeoGebra </li></ul></ul>[email_address] http://mrlsmath.com www.tttpress.com
  40. 40. Future Plans <ul><li>Make it Easier, Easier, Easier! </li></ul><ul><li>Spreadsheet Window </li></ul><ul><li>Symbolic Algebra Window (CAS) </li></ul><ul><li>3D extension </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  41. 41. Additional GeoGebra Information <ul><li>Download these slides: www.geogebra.org/workshop </li></ul><ul><li>GeoGebra Webpage: www.geogebra.org </li></ul><ul><li>Introduction to GeoGebra (Book) </li></ul><ul><ul><li>Print: www.lulu.com/content/2650846 </li></ul></ul><ul><ul><li>Online: www.geogebra.org/book/intro-en/ </li></ul></ul><ul><li>Contact: [email_address] [email_address] </li></ul>[email_address] http://mrlsmath.com www.tttpress.com
  42. 42. Teaching: The hardest job you’ll ever love just got easier with GeoGebra! ! [email_address] http://mrlsmath.com www.tttpress.com

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