virtual manipulatives & online collaboration

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Virtual Manipulatives & Online Collaboration with the free math software GeoGebra

Markus Hohenwarter Florida Atlantic University

markus@geogebra.org

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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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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 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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Virtual Manipulatives

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

GeoGebra Virtual Manipulatives

Every GeoGebra figure can be exported as a web-page (html)

So calledDynamic Worksheet

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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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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.