Virtual Manipulatives & Online Collaboration with the free math software GeoGebra Markus Hohenwarter Florida Atlantic University markus@geogebra.org Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

NSF MSP FAU-Broward NSF Math & Science Partnership Florida 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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Outline Virtual Manipulatives Online Collaboration with GeoGebra 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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

What are Virtual Manipulatives? Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Example: Multiplying Fractions Animation (Cyberlearning.org) Web-based NOT manipulable Virtual Manipulative (GeoGebra) Manipulable Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Examples: Virtual Manipulatives Slope-Intercept Form Angles in a Clock Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Collections of K-12 VMs National Library of Virtual Manipulatives NCTM Illuminations MERLOT Mathematics Portal Project Interactive MathTools GeoGebraWiki Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Virtual Learning What we Know Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

(Meriti 2006: Technology in Schools: What research says) “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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Virtual Manipulatives What we Know Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Example: Reflection at Line Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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) Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Virtual Manipulatives What‘s Missing? Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Outline Virtual Manipulatives Online Collaboration What are Virtual Manipulatives? What we Know What‘s Missing Online Collaboration GeoGebra – free dynamic math software GeoGebraWiki – collaborative VMs International GeoGebra Institute Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Online Collaboration with the free math software GeoGebra Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

What is GeoGebra? Dynamic Mathematics Software For Learning and Teaching in Schools Geometry, Algebra and Calculus Open Source www.geogebra.org Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

GeoGebra = Geometry + Algebra Algebra Window Geometry & Graphics Window Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Educational Principles Student Activity Multiple Representations Experimental and Guided Discovery Learning Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Markus Hohenwarter, FAUMarkus. Hohenwarter@sbg. ac. at, 2004 - www Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Markus Hohenwarter, FAUMarkus. Hohenwarter@sbg. ac. at, 2004 - www Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Markus Hohenwarter, FAUMarkus. Hohenwarter@sbg. ac. at, 2004 - www Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

GeoGebra Virtual Manipulatives Every GeoGebra figure can be exported as a web-page (html) So called Dynamic Worksheet Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Open Source & Online Collaboration Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

Why Open Source? Available free of charge in Schools and at Home Online Collaboration International Community User Forum – Users help Users GeoGebraWiki – Pool of Shared Materials Expandable by using other Open Source Libraries Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

World Wide User Community 35 languages 190 countries 300,000 visitors per month Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

GeoGebra User Forum www.geogebra.org/forum Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

GeoGebraWiki – Free Materials www.geogebra.org/wiki Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

What’s missing for VMs? Reusable and Changeable Virtual Manipulatives → Dynamic GeoGebra Worksheets, GeoGebraWiki Professional Development → MSP projects, IGI workshops Research → MSP collaboration, IGI Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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 Markus Hohenwarter, FAUMarkus.Hohenwarter@sbg.ac.at, 2004 - www.geogebra.at

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