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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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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”

overview
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

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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)

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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)

what is geogebra
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

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

GeoGebra =

Geometry

+

Algebra

Algebra Window

Geometry & Graphics Window

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)

GeoGebra is Innovative

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

2001 2006 development

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
world wide user community
World Wide User Community

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

40 languages

190 countries

400,000 visitors per month

visitors on www geogebra org
Visitors on www.geogebra.org

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

geogebra as a pedagogical tool
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

educational principles
Educational Principles

Student Activity

Modeling

Multiple Representations

Experimental and Guided Discovery Learning

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

examples of using geogebra
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

creating teaching materials

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)
ways to use geogebra

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
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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
using dynamic worksheets

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
combined representations

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)

age 6 10 adding integers
Age 6-10: Adding Integers

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

age 11 14 multiplying fractions
Age 11-14: Multiplying Fractions

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

age 15 18 geometry algebra
Age 15-18: Geometry & Algebra

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

age 17 up functions calculus
Age 17 up: Functions & Calculus

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

visualizing parameters
Visualizing Parameters

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

geogebra as a pedagogical tool1
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

geometry examples
Geometry Examples

Mr. L demos using GeoGebra

at the workshop

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

geogebra as a pedagogical tool2
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

algebra 1 examples
Algebra 1 Examples

Mr. L demos using GeoGebra

at the workshop

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

geogebra as a pedagogical tool3
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

algebra 2 examples
Algebra 2 Examples

Mr. L demos using GeoGebra

at the workshop

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

geogebra as a pedagogical tool4
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

trig calculus examples
Trig/Calculus Examples

Mr. L demos using GeoGebra

at the workshop

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

geogebra s web export
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

geogebra is open source
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

geogebra user forum
GeoGebra User Forum

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

www.geogebra.org/forum

geogebrawiki free materials
GeoGebraWiki – Free Materials

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

www.geogebra.org/wiki

status quo
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
future plans
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

additional geogebra information

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

Teaching:

The hardest job you’ll ever love

just got easier with GeoGebra! !