Dynamic mathematics
with Geogebra
What is GeoGebra? Dynamic Mathematics
Software
For Learning and Teachingin Schools
Geometry, Algebra and Calculus
Freely available fromwww.geogebra.org
GeoGebra =
Geometry
Algebra+
Geometry & Graphics Window
Algebra Window
GeoGebra as a Pedagogical Tool
Presentation Tooldynamic visualizations
Modeling Tooldynamic constructions
Authoring Toolinteractive online material
Examples of Using GeoGebra
Visualizingstudents can “see” abstract concepts
Representationsstudents can make connections
Experimentsstudents can discover mathematics
Visualizing Parameters
Visualizing Movement
Examples of Using GeoGebra
Visualizingstudents can “see” abstract concepts
Representationsstudents can make connections
Experimentsstudents can discover mathematics
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
Representations: Sketch & Graph
Unexpected Discoveries
Examples of Using GeoGebra
Visualizingstudents can “see” abstract concepts
Representationsstudents can make connections
Experimentsstudents can discover mathematics
Experiments: What happens when..?
Experiments: Approximation
Educational Principles
Student Activity
Modeling
Multiple Representations
Experimental and Guided Discovery Learning– Great to show you everything but better off
discovering yourselves!
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.