Geo gebra ws_1_intro

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Geo gebra ws_1_intro

  1. 1. Please INSTALL GeoGebra <ul><li>WITH INTERNET </li></ul><ul><li>Go to www.geogebra.org </li></ul><ul><li>Click WebStart third item in the left menu </li></ul><ul><li>Click button WebStart GeoGebra is installed automatically </li></ul><ul><li>WITHOUT INTERNET </li></ul><ul><li>Ask us for USB flash drive with GeoGebra </li></ul>
  2. 2. GeoGebra Free Dynamic Mathematics Software Markus & Judith Hohenwarter www.geogebra.org
  3. 3. Overview <ul><li>What is GeoGebra? </li></ul><ul><li>Using GeoGebra for Teaching & Learning </li></ul><ul><li>GeoGebra’s Web Export </li></ul><ul><li>Open Source & GeoGebra Support </li></ul><ul><li>Hands-on Activities </li></ul>
  4. 4. 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>
  5. 5. GeoGebra = Geometry Algebra + Geometry & Graphics Window Algebra Window
  6. 6. <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
  7. 8. Using GeoGebra for Teaching & Learning
  8. 9. 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>
  9. 10. 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>
  10. 11. Visualizing Adding Integers
  11. 12. Visualizing Multiplying Fractions
  12. 13. Visualizing Parameters
  13. 14. Visualizing Parameters
  14. 15. Visualizing Movement
  15. 16. Visualizing Slope Functions
  16. 17. 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>
  17. 18. Multiple Representations <ul><li>GeoGebra: Bidirectional Connection </li></ul><ul><li>Symbolic ⇔ Graphics </li></ul><ul><li>Examples </li></ul><ul><ul><li>Coordinates ⇔ Point in Coordinate System </li></ul></ul><ul><ul><li>Circle‘s Equation ⇔ Circle drawn in Coordinate System </li></ul></ul><ul><ul><li>Function‘s Equation ⇔ Graph of Function </li></ul></ul>
  18. 19. Representations: Sketch & Graph
  19. 20. Unexpected Discoveries
  20. 21. Representations: Geometry & Algebra
  21. 22. 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>
  22. 23. Experiments: Math & Real World
  23. 24. Experiments: What happens when ... ?
  24. 25. Experiments: Connections
  25. 26. Experiments: Approximation
  26. 27. 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>
  27. 28. GeoGebra Communtiy and free software
  28. 29. Why is it Free? <ul><li>Accessability </li></ul><ul><ul><li>Available in Schools and at Home </li></ul></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><ul><li>Volunteers (Translators, Programmers) </li></ul></ul><ul><li>Expandable by using other free software libraries </li></ul>
  29. 30. 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>
  30. 31. GeoGebra User Forum www.geogebra.org/forum
  31. 32. GeoGebra’s Web Export <ul><li>Every GeoGebra Construction can be exported as a Web Page (html) Dynamic Worksheet </li></ul><ul><li>Examples: </li></ul><ul><ul><li>Theorem of Thales </li></ul></ul><ul><ul><li>Center of a Round Table ( ggb ) Solution worksheet </li></ul></ul>
  32. 33. GeoGebraWiki – Free Materials www.geogebra.org/wiki
  33. 34. Future Plans <ul><li>Make it Easier, Easier, Easier! </li></ul><ul><li>Spread Sheet Window </li></ul><ul><li>Symbolic Algebra Window (CAS) </li></ul><ul><li>3D extension </li></ul>
  34. 35. Hands-on Activities See handout

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