Geogebra intro

1. Dynamic mathematics
with Geogebra

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

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

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

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

6. Visualizing Parameters

7. Visualizing Movement

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

9. 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

10. Representations:
Sketch & Graph

11. Unexpected Discoveries

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

13. Experiments: What happens when..?

14. Experiments: Approximation

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

16. Hands-on activities
 ... of this module you should:
Know more about Geogebra.
 Have constructed a worksheet and succeeded in
posting it online, adding it to your journal in
BLACKBOARD.
Didactics will follow in January.
Concretely, your journal, should have:
 An uploaded geogebra worksheet.
 A 300 word evaluation of the strengths and
weaknesses of Geogebra for teaching mathematics.