The document introduces GeoGebra, a free dynamic mathematics software for learning and teaching mathematics. It can be used as a presentation, modeling, and authoring tool. GeoGebra allows users to visualize abstract mathematical concepts through its connections between symbolic expressions, graphics, and multiple representations. It also enables experimental and guided discovery learning as students can explore mathematics through changing parameters and discovering relationships. The document provides examples of using GeoGebra for visualizing functions and concepts, representing ideas in different ways, and allowing students to experiment and make unexpected discoveries.

1. Dynamic mathematics
with Geogebra
Dr Christian Bokhove
@cb1601ej
C.Bokhove@soton.ac.uk
Southampton Education School

2.  Who am I?
– Christian Bokhove, Netherlands
– Teacher maths & computer science
secondary school „98-‟12
– ICT & maths projects and PhD
 Disclaimer
– We do not favor one software or the other …but
we have to choose one
– Be critical about all software and hardware
– www.geogebra.org

3. And now…
 Who knows geogebra already?
 Can you describe geogebra in your own words?
 Short introduction

4. What is GeoGebra?
 Dynamic Mathematics
Software
 For Learning and Teaching
in Schools
 Geometry, Algebra and
Calculus
 Freely available from
www.geogebra.org

5. GeoGebra = Geometry + Algebra
Algebra
Window
Geometry & Graphics
Window

6. GeoGebra as a Pedagogical Tool
 Presentation Tool
dynamic visualizations
 Modeling Tool
dynamic constructions
 Authoring Tool
interactive online material

7. Examples of Using GeoGebra
 Visualizing
students can “see” abstract concepts
 Representations
students can make connections
 Experiments
students can discover mathematics

8. Visualizing Parameters

9. Visualizing Movement

10. Examples of Using GeoGebra
 Visualizing
students can “see” abstract concepts
 Representations
students can make connections
 Experiments
students can discover mathematics

11. Multiple Representations
 GeoGebra: Bidirectional Connection
Symbolic ⇔ Graphics
 Examples
– Coordinates ⇔ Point in Coordinate System
– Circle„s Equation ⇔
Circle drawn in Coordinate System
– Function„s Equation ⇔ Graph of Function

12. Representations:
Sketch & Graph

13. Unexpected Discoveries

14. Examples of Using GeoGebra
 Visualizing
students can “see” abstract concepts
 Representations
students can make connections
 Experiments
students can discover mathematics

15. Experiments: What happens when..?

16. Experiments: Approximation

17. Educational Principles
 Student Activity
 Modeling
 Multiple Representations
 Experimental and
Guided Discovery Learning
– Great to show you everything but better off
discovering yourselves!

18. Hands-on activities
 Do several activities
 Choose from the worksheet(s), on
Blackboard (or paper)
– Work from 1 to 5
– Then choose what you like from 6 onwards
– Main goal: learn to use geogebra
 Want to learn more? (e.g. scripting, customizing toolbars)
see
http://wiki.geogebra.org/en/Tutorial:Main_Page and
http://www.geogebra.org/en/wiki/index.php/Workshop_materials