A Tour of GeoGebra

Award Winning Free Software for Visualizing Math


Calgary City Teachers' Convention

February 15,  2013

Glen Reesor




Glen@GlenReesor.ca

GlenReesor.ca




A Tour of GeoGebra


  • Sight-seeing tour with a little bit of hands-on
  • GeoGebra features and constructions for typical high school math
  • We'll just be scratching the surface of GeoGebra's capabilities


  • Please ask questions during this presentation



What's This “GeoGebra” Thing?

Part 1

Classroom Example 1: Domain and Range


  • So straight forward, yet...
  • How about a graphical approach?










Classroom Example 2: Sine Law



  • Manipulate the equation
  • Understand the geometric implications







Classroom Example 3: Sine Law Ambiguous Case



  • Show students dynamically that it's a result of specifying two sides and a non-contained angle






What's This “GeoGebra” Thing?

Part 2

  • "GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package."
  • Created by Markus Hohenwarter as part of a Master's and then PhD in Math Education at University of Salzburg (2001), then continued at:
    • Florida Atlantic University (2006 - 2008)
    • Florida State University (2008 - 2009)
    • Johannes Kepler University (Austria) (2009 - Present)
  • Now developed by Hohenwarter and a team of open-source contributors around the world




  • Some supporting institutions:
    • Google Summer of Code  (2010 - 2012)
    • Austrian Ministry of Education
    • University of Luxembourg (2005 - 2010)
    • Department of Math Sciences, Florida Atlantic University (2006 - 2009)
    • Austrian Academy of Sciences
    • Department of Math, University of Salzburg
    • Free Software Foundation, Hungary



Today's Plan

What's This Geogebra Thing (Cont'd)

  • Hands On: Points, angles, functions, sliders, and more

10:45 - 11:15


Educational Scenarios

  • Demos, activities, animated solutions, mathematical justifications, multi-step constructions, picture creation, upload to website

11:15 - 11:30


Playtime!

  • Play with GeoGebra
  • Investigate others' constructions

11:30 - 11:50


GeoGebra is wonderful because...

11:50 - 12:00





Hands On


Inscribed Angles

  • Points
  • Line segments
  • Angles
  • Circles
  • Arcs









Investigating Cubic Functions

  • Functions
  • Sliders
  • Points
  • Color
  • Size






Educational Scenarios

  • Demonstrations
  • Activities
  • Animated problem solutions
  • Mathematical justifications
  • Multi-Step constructions
  • Picture creation
  • Upload to website / Learning Management System (Moodle, WebCT, etc)



Demonstrations: Parallel Lines and Transversals





Activities: Parameter Exploration





Animated Solutions: Vector Addition





Mathematical Justifications - Horizontal Translations





Mathematical Justifications - Horizontal Translations (Take 2)





Multi-step Constructions

  • GeoGebra isn't limited to the built-in commands.
  • How would you create a parabola given the vertex and one point?
  • Just do the math...










What a mess.  Does it work?






Picture Creation

  • Use GeoGebra to create beautiful, correct pictures in multiple formats (svg, png, emf, pdf, eps)
        




Upload to Website

  • Your constructions will be completely self-contained--no need for  students to download / install any software
  • Scenarios
    • Shared drive in computer lab
    • Learning Management System (Moodle, WebCT, Desire2Learn ...)
    • School / Personal website
    • www.geogebratube.org


Play Time!



GeoGebra is Wonderful Because...

  • It's a great tool for visualizing and exploring math concepts
  • It's absolutely free
  • You don't have to be a computer programmer to use it
  • There are many GeoGebra constructions on the Internet--either use them directly or modify to your liking (just File/Open the web address)
  • You can embed directly in webpages, thus students don't need to install any software
  • It understands lots of other math like parametric curves, conics, derivatives, integrals, taylor polynomials, geometric transformations, statistics
  • It has other powerful features such as a spreadsheet, CAS (computer algebra system), 3D (next version)
  • iPad and Android versions are in the works


Thank You!

Glen@GlenReesor.ca

GlenReesor.ca