1 Virtual Manipulatives & Online Collaboration with the free math software GeoGebra Markus Hohenwarter Florida Atlantic University

Virtual Manipulatives 2 NSF MSP FAU-Broward NSF Math & Science Partnership Florida Atlantic University & Broward County Schools ( ) 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

Virtual Manipulatives 3 Outline Virtual Manipulatives  What are Virtual Manipulatives?  What we Know  What‘s Missing Online Collaboration with GeoGebra  GeoGebra – free dynamic math software  GeoGebraWiki – reusable & changeable VMs  International GeoGebra Institute

Virtual Manipulatives 4 What are Virtual Manipulatives?

Virtual Manipulatives 5 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)

Virtual Manipulatives 6 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

Virtual Manipulatives 7 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)

Virtual Manipulatives 8 Example: Multiplying Fractions Animation (C yberlearning.org) Animation  Web-based  NOT manipulable Virtual Manipulative ( GeoGebra) Virtual Manipulative  Web-based  Manipulable

Virtual Manipulatives 9 Examples: Virtual Manipulatives Slope-Intercept FormAngles in a Clock

Virtual Manipulatives 10 Collections of K-12 VMs National Library of Virtual Manipulatives NCTM Illuminations MERLOT Mathematics Portal Project Interactive MathTools GeoGebraWiki

Virtual Manipulatives 11 Virtual Learning What we Know

Virtual Manipulatives 12 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)

Virtual Manipulatives 13 Web-Based Virtual Learning “Student achievement in courses using and web-based virtual learning is slightly better than in courses using traditional instruction.” (Meriti 2006: Technology in Schools: What research says)

Virtual Manipulatives 14 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)

Virtual Manipulatives 15 Virtual Manipulatives What we Know

Virtual Manipulatives 16 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)

Virtual Manipulatives 17 Example: Reflection at Line

Virtual Manipulatives 18 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)

Virtual Manipulatives 19 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)

Virtual Manipulatives 20 Virtual Manipulatives What‘s Missing?

Virtual Manipulatives 21 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

Virtual Manipulatives 22 Outline Virtual Manipulatives  What are Virtual Manipulatives?  What we Know  What‘s Missing Online Collaboration  GeoGebra – free dynamic math software  GeoGebraWiki – collaborative VMs  International GeoGebra Institute

Virtual Manipulatives 23 Online Collaboration with the free math software GeoGebra

Virtual Manipulatives 24 What is GeoGebra? Dynamic Mathematics Software For Learning and Teaching in Schools Geometry, Algebra and Calculus Open Source

Virtual Manipulatives 25 GeoGebra =GeometryAlgebra+ Geometry & Graphics Window Algebra Window

Virtual Manipulatives 26 Educational Principles Student Activity Multiple Representations Experimental and Guided Discovery Learning

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Virtual Manipulatives 30 GeoGebra Virtual Manipulatives Every GeoGebra figure can be exported as a web-page (html) So called Dynamic Worksheet Dynamic Worksheet

Virtual Manipulatives 31 Open Source & Online Collaboration

Virtual Manipulatives 32 Why Open Source? Available free of charge in Schools and at Home Online Collaboration  International Community  User Forum – Users help Users User Forum  GeoGebraWiki – Pool of Shared Materials GeoGebraWiki Expandable by using other Open Source Libraries

Virtual Manipulatives 33 World Wide User Community 35 languages 190 countries 300,000 visitors per month

Virtual Manipulatives 34 GeoGebra User Forum

Virtual Manipulatives 35 GeoGebraWiki – Free Materials

Virtual Manipulatives 36 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

Virtual Manipulatives 37 What’s missing for VMs? Reusable and Changeable Virtual Manipulatives → Dynamic GeoGebra Worksheets, GeoGebraWiki Professional Development → MSP projects, IGI workshops Research → MSP collaboration, IGI

Virtual Manipulatives 38 References 1/2 CITEd Research Center (2007). Learning Mathematics with Virtual Manipulatives. Retrieved Dec 2007 from 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): University of Northampton, UK

Virtual Manipulatives 39 References 2/2 Metiri Group (2006): Technology in Schools: What research says. Retrieved Dec 2007 from oolsReport.pdf oolsReport.pdf Moyer, P.S., Bolyard, J.J. & Spikell, M.A. (2002). What Are Virtual Manipulatives? Teaching Children Mathematics. 8(6), 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), Sowell, E. J. (1989). Effects of Manipulative Materials in Mathematics Education. Journal for Research in Mathematics Education. 20(5) pp Young, D. (2006). Virtual Manipulatives in Math Education. Retrieved Dec 2007 from

Virtual Manipulatives 40 The instructional practices and assessments discussed or shown in these presentations are not intended as an endorsement by the U.S. Department of Education.