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Virtual Manipulatives & Online Collaboration with the free math software GeoGebra
Markus Hohenwarter Florida Atlantic University
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Virtual Manipulatives
NSF MSP FAU-Broward
NSF Math & Science PartnershipFlorida Atlantic University & Broward County Schools (2004 - 2009)PIs: Heinz-Otto Peitgen, Richard Voss
Master’s program for Middle School Mathematics Teachers at FAU
Focus on Math Content Knowledge & Technology Integration into Teaching
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Virtual Manipulatives
Outline Virtual Manipulatives
What are Virtual Manipulatives?What we KnowWhat‘s Missing
Online Collaboration with GeoGebraGeoGebra – free dynamic math softwareGeoGebraWiki – reusable & changeable VMs International GeoGebra Institute
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Virtual Manipulatives
What areVirtual Manipulatives?
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Virtual Manipulatives
What are Manipulatives? Physical objects used to promote learning
e.g. tangram, base ten blocks
Well-established as being valuable education tools for mathematics(Sowell 1989)
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Virtual Manipulatives
What are Virtual Manipulatives? “… an interactive, web-based visual representation
of a dynamic object that presents opportunities for constructing mathematical knowledge”
(Moyer, Bolyard, & Spikell 2002)
Web-based Manipulable
Synonyms: Math Applets, Mathlets, Widgets, Gizmos
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Virtual Manipulatives
Student Activity
“Mathematics is not, as has been said, a spectator sport. Too much of current instruction fails to actively involve students.”
(National Library of Virtual Manipulatives)
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Virtual Manipulatives
Example: Multiplying Fractions Animation (Cyberlearning.org)
Web-basedNOT manipulable
Virtual Manipulative (GeoGebra)
Web-basedManipulable
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Virtual Manipulatives
Examples: Virtual Manipulatives
Slope-Intercept Form Angles in a Clock
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Collections of K-12 VMs
National Library of Virtual Manipulatives NCTM Illuminations MERLOT Mathematics Portal Project Interactive MathTools GeoGebraWiki
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Virtual Manipulatives
Virtual LearningWhat we Know
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Virtual Manipulatives
Which medium is best?
“What we have learned from all the media comparison research is that it’s not the medium, but rather the instructional methods that cause learning. When the instructional methods remain essentially the same, so does the learning, no matter how the instruction is delivered.”(Clark & Mayer 2007: e-Learning and the Science of Instruction)
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Web-Based Virtual Learning
“Student achievement in courses using email and web-based virtual learning is slightly better than in courses using traditional instruction.”
(Meriti 2006: Technology in Schools: What research says)
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Virtual Manipulatives
Technology in Schools
“Overall, across all uses in all content areas technology does provide a small, but significant, increase in learning when implemented with fidelity.”
(Meriti 2006: Technology in Schools: What research says)
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Virtual Manipulatives
Virtual ManipulativesWhat we Know
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Virtual Manipulatives
Logistic Benefits of VMs
Easily accessible and manageable Low technological learning curve Available out-of-school Many people can develop them Can do things that are not possible with
physical manipulatives or pencil and paper(Young 2006)
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Virtual Manipulatives
Example: Reflection at Line
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Virtual Manipulatives
Teaching Benefits of VMs Instantaneous, corrective feedback Various representations at the same time Help students to understand abstract concepts Lead to more complex, richer understanding Promote problem solving and the ability
to test hypotheses Helpful for students with disabilities Increase attention and motivation
(also in teachers) (Young 2006, CITEd 2007)
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Virtual Manipulatives
Teachers are important
“The mere use of manipulatives does not guarantee that students understand concepts and procedures and be able to connect these concepts to abstract symbols without teachers making these connections explicit.”
(Reimer & Moyer 2005)
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Virtual ManipulativesWhat‘s Missing?
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Virtual Manipulatives
What’s missing for VM?
Professional Development: Support for teachers on how to find and use them
Reusable and Changeable VMs:Teachers should be able to adapt VMs to their specific needs
Research: More classroom studies, especially in high schools
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Virtual Manipulatives
Outline
Virtual ManipulativesWhat are Virtual Manipulatives?What we KnowWhat‘s Missing
Online CollaborationGeoGebra – free dynamic math softwareGeoGebraWiki – collaborative VMs International GeoGebra Institute
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Virtual Manipulatives
Online Collaborationwith the free math software GeoGebra
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Virtual Manipulatives
What is GeoGebra?
Dynamic MathematicsSoftware
For Learning and Teachingin Schools
Geometry, Algebra and Calculus
Open Sourcewww.geogebra.org
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GeoGebra = Geometry Algebra+
Geometry & Graphics Window
Algebra Window
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Educational Principles
Student Activity Multiple Representations Experimental and
Guided Discovery Learning
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Virtual Manipulatives
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Virtual Manipulatives
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Virtual Manipulatives
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Virtual Manipulatives
GeoGebra Virtual Manipulatives
Every GeoGebra figure can be exported as a web-page (html)
So calledDynamic Worksheet
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Virtual Manipulatives
Open Source & Online Collaboration
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Virtual Manipulatives
Why Open Source? Available free of charge
in Schools and at Home Online Collaboration
International CommunityUser Forum – Users help UsersGeoGebraWiki – Pool of Shared Materials
Expandableby using other Open Source Libraries
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Virtual Manipulatives
World Wide User Community
35 languages 190 countries 300,000 visitors
per month
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Virtual Manipulatives
GeoGebra User Forum
www.geogebra.org/forum
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GeoGebraWiki – Free Materials
www.geogebra.org/wiki
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International GeoGebra Institute (IGI)
IGI Activities Offers free GeoGebra training for teachers Issues GeoGebra certification Nurtures a community of researchers
IGI supports you to Establish an IGI site at your university Join projects and collaborate with researchers Write grant proposals Participate in IGI conferences
www.geogebra.org/IGI
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What’s missing for VMs?
Reusable and Changeable Virtual Manipulatives
→ Dynamic GeoGebra Worksheets, GeoGebraWiki
Professional Development
→ MSP projects, IGI workshops
Research
→ MSP collaboration, IGI
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References 1/2
CITEd Research Center (2007). Learning Mathematics with Virtual Manipulatives. Retrieved Dec 2007 from http://www.cited.org/index.aspx?page_id=151
Clark, R. C., & Mayer, R. E. (2007). E-learning and the science of instruction (2nd ed). San Francisco: Jossey-Bass.
Hohenwarter, M., & Preiner, J. (2007). Dynamic mathematics with GeoGebra. Journal of Online Mathematics and its Applications. ID 1448, vol. 7, March 2007
Hohenwarter, M., & Preiner, J. (2007). Creating mathlets with open source tools. Journal of Online Mathematics and its Applications. ID 1574, vol. 7, August 2007
Hohenwarter, M., & Lavicza, Z. (2007). Mathematics teacher development with ICT: towards an International GeoGebra Institute. Proceedings of the British Society for Research into Learning Mathematics. 27(3):49-54. University of Northampton, UK
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References 2/2
Metiri Group (2006): Technology in Schools: What research says. Retrieved Dec 2007 from http://www.cisco.com/web/strategy/docs/education/TechnologyinSchoolsReport.pdf
Moyer, P.S., Bolyard, J.J. & Spikell, M.A. (2002). What Are Virtual Manipulatives? Teaching Children Mathematics. 8(6), 372-377.
Reimer, K., & Moyer, P.S. (2005). Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study. Journal of Computers in Mathematics and Science Teaching. 42(1), 5-25.
Sowell, E. J. (1989). Effects of Manipulative Materials in Mathematics Education. Journal for Research in Mathematics Education. 20(5) pp. 498-505.
Young, D. (2006). Virtual Manipulatives in Math Education. Retrieved Dec 2007 from http://plaza.ufl.edu/youngdj/talks/vms.htm
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The instructional practices and assessments discussed or shown in thesepresentations are not intended as an endorsement by the U.S. Department of Education.