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GeoGebra

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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 ... – PowerPoint PPT presentation

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Title: GeoGebra


1
Visualize Algebra Geometry Concepts with the
Greatest of Ease A tool to help meet
the California Mathematics Standards presentatio
n by Bill Lombardsome graphics from
http//en.wikipedia.org and /http//commons.wiki
media.org
bill.lombard_at_gmail.com http//mrlsmath.com www.ttt
press.com Building mathematical skill on a
foundation of understanding
2
Overview
  • Introduction to GeoGebra
  • User community
  • Using GeoGebra in the classroom
  • Hands-on Activities
  • GeoGebras Web Export
  • Open Source GeoGebra Support

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)
4
Technology or No Technology?
What we have learned from all the media
comparison research is that its 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

6
GeoGebra
Geometry
Algebra

Algebra Window
Geometry Graphics Window
7
GeoGebra is Innovative
  • 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)

8
2001-2006 Development
  • Created by Markus Hohenwarter
  • Mar 2002 Masters 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
(No Transcript)
10
World Wide User Community
  • 40 languages
  • 190 countries
  • 400,000 visitors per month

11
Visitors on www.geogebra.org
12
GeoGebra as a Pedagogical Tool
  • Presentation Tooldynamic visualizations
  • Modeling Tooldynamic constructions
  • Authoring Toolinteractive online material

13
Educational Principles
  • Student Activity
  • Modeling
  • Multiple Representations
  • Experimental and Guided Discovery Learning

14
Examples of Using GeoGebra
  • Visualizingstudents can see abstract concepts
  • Representationsstudents can make connections
  • Experimentsstudents can discover mathematics

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)

16
Ways to use GeoGebra
  • Tool for studentsfor doing constructions from
    scratch
  • Tool for teachers
  • Visualisationdynamic demonstrations
  • Creating Teaching Materialsthat foster student
    activity

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

18
Using Dynamic Worksheets
  • Student opens html file with a web browser
  • Requirements on students 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
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)
20
Age 6-10 Adding Integers
21
Age 11-14 Multiplying Fractions
22
Age 15-18 Geometry Algebra
23
Age 17 up Functions Calculus
24
Visualizing Parameters
25
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

27
Geometry Examples
  • Mr. L demos using GeoGebra
  • at the workshop

28
GeoGebra as a Pedagogical Tool
  • Using for Algebra 1
  • Graphing lines parabolas
  • Modeling with parameters
  • Solutions of equations
  • Families of functions

29
Algebra 1 Examples
  • Mr. L demos using GeoGebra
  • at the workshop

30
GeoGebra as a Pedagogical Tool
  • Using for Algebra 2
  • Graphing complex functions
  • Conic sections (non-functions)
  • Exponential curves and logarithms

31
Algebra 2 Examples
  • Mr. L demos using GeoGebra
  • at the workshop

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

33
Trig/Calculus Examples
  • Mr. L demos using GeoGebra
  • at the workshop

34
GeoGebras Web Export
  • Every GeoGebra Construction can be exported as a
    Web Page (html) Dynamic Worksheet

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

36
InternationalUser Community
37
GeoGebra User Forum
www.geogebra.org/forum
38
GeoGebraWiki Free Materials
www.geogebra.org/wiki
39
Status Quo
  • Whats there?
  • Free software and material
  • Extensive user community
  • Immense expertise developed by enthusiasts
  • Whats 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

41
Additional GeoGebra Information
  • Download these slides www.geogebra.org/wor
    kshop
  • GeoGebra Webpage www.geogebra.org
  • Introduction to GeoGebra (Book)
  • Print www.lulu.com/content/2650846
  • Online www.geogebra.org/book/intro-en/
  • Contact judith_at_geogebra.org
    markus_at_geogebra.org

42
Teaching The hardest job youll ever
love just got easier with GeoGebra! !
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