This document discusses GeoGebra, a dynamic mathematics software, and TAO 2.0, an assessment platform. It provides an overview of GeoGebra's history from its origins in 2001 as a tool for analytic geometry to its current community of over 50 institutes and millions of users. GeoGebra can be used for teaching mathematics through visualization, representations, and experimentation. Current projects include GeoGebra 4.0 with new tools and GeoGebraMobile to make applets work on mobile devices. The document also describes a project using GeoGebra in primary schools and how TAO collects data on tool usage to analyze learning.

1. GeoGebra(Mobile)
and TAO 2.0
unleashing the power of assessment
in dynamic mathematics
Dr. Yves Kreis
University of Luxembourg
yves@geogebra.org
Raynald Jadoul
CRP Henri Tudor
raynald.jadoul@tudor.lu

2. GeoGebra(Mobile) and TAO 2.0
Overview
 GeoGebra(Mobile)
 History
 Community
 Teaching
 Current and Future
Projects
 GeoGebra and TAO

3. GeoGebra(Mobile) and TAO 2.0
GeoGebra‘s
History

4. GeoGebra(Mobile) and TAO 2.0
Interactive Geometry Software

5. GeoGebra(Mobile) and TAO 2.0
Computer Algebra Systems
Derive Mathematica

6. GeoGebra(Mobile) and TAO 2.0
GeoGebra = Geometry & Algebra
 2001/02
Master’s Project
Univ. Salzburg
 April 2002
Version 1.0
Tool for Analytic Geometry:
points, vectors, lines, conic sections
 November 2002
European Academic Software Award

7. GeoGebra(Mobile) and TAO 2.0
Dynamic Worksheets
 January 2004
Version 2.1
 Interactive
web pages

8. GeoGebra(Mobile) and TAO 2.0
GeoGebra‘s
Community

9. GeoGebra(Mobile) and TAO 2.0
Visitors on www.geogebra.org
5
Millions
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
2004 2005 2006 2007 2008 2009
 Visitors: 23.500/day or 705.000/month
 Downloads: 12.500/day or 375.000/month
from 196 Countries & Territories

10. GeoGebra(Mobile) and TAO 2.0
GeoGebra in Numbers
 14 Developers
 50 Institutes
 56 Languages
 171 Translators
 18.500 Online
Learning Objects
 Millions of Users in 196 Countries/Territories

11. GeoGebra(Mobile) and TAO 2.0
Teaching with
GeoGebra

12. GeoGebra(Mobile) and TAO 2.0
Teaching with GeoGebra
 Presentation Tool
 Teacher centered
 Tool for Mathematical
Experiments
 Student centered
 Authoring Tool
 Static images
 Dynamic worksheets

13. GeoGebra(Mobile) and TAO 2.0
Technology can Enhance Learning
 Visualising
students can “see” abstract concepts
 Representations
students can make connections
 Experiments
students can discover mathematics

14. GeoGebra(Mobile) and TAO 2.0
Composition of Functions

15. GeoGebra(Mobile) and TAO 2.0
Newton’s Method

16. GeoGebra(Mobile) and TAO 2.0
Theo Jansen’s Beach Beast

17. GeoGebra(Mobile) and TAO 2.0
Fake-3D with GeoGebra 3.2

18. GeoGebra(Mobile) and TAO 2.0
GeoGebra‘s
Current & Future Projects

19. GeoGebra(Mobile) and TAO 2.0
GeoGebra 4.0.0.0
 Release Date: 31th August 2011
 Selected Features:
 2nd graphics window
 CAS window
 New Tools/Commands
 Implicit curves and multivariate functions
 Spreadsheet improvements
 Scripting

20. GeoGebra(Mobile) and TAO 2.0
GeoGebra 5.0.0.0
 Release Date: ???
Andre Eriksson, Sweden & Mathieu Blossier, France

21. GeoGebra(Mobile) and TAO 2.0
GeoGebraMobile
GeoGebra Applets
should work on
mobile (multitouch)
devices like
iPhone, iPad,
Android ...
Gabor Ancin, Hungary & Zoltan Kovacs, Hungary

22. GeoGebra(Mobile) and TAO 2.0
GeoGebra
inside TAO

23. GeoGebra(Mobile) and TAO 2.0
The Project GeoGebraPrim
 uni.lu founded
 Main focus:
 Usage of GeoGebra(Prim) in primary school
 Goals:
 Improvement of the children’s understanding
of the basic geometric concepts
 Deeper insight in the bond of geometry and
algebra

24. GeoGebra(Mobile) and TAO 2.0
Pre-Test Post-Test #1
#Comp
#2
 Results (max. 50)  Results (max. 17)
31)
 t[57]= –0,44  t[57]= 3,16
3,01
 p = 0,66  p = 0,002
0,003
 d = –0,12  d = 0,84
0,81

25. GeoGebra(Mobile) and TAO 2.0
Collected data
 Snapshot of the stimulus
 Usage of virtual tool
 Usage of a GeoGebra tool
 Usage of dynamics
 History with all recorded events
 Generation of a movie of the actions

26. GeoGebra(Mobile) and TAO 2.0
Thank you!
Slides of this talk
http://www.geogebra.org/talks
Dr. Yves Kreis
yves.kreis@uni.lu
Raynald Jadoul
raynald.jadoul@tudor.lu