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Dynamic mathematics
with GeogebraDr Christian Bokhove@cb1601ej
Southampton Education School
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
And now…
Who knows geogebra already?
Can you describe geogebra in your own words?
Short introduction
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 activitiesDo 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) seehttp://wiki.geogebra.org/en/Tutorial:Main_Page and http://www.geogebra.org/en/wiki/index.php/Workshop_materials
