Transcript Virtual Manipulatives & Online Collaboration

Virtual Manipulatives
& Online Collaboration
with the free math software GeoGebra
Markus Hohenwarter
Florida Atlantic University
[email protected]
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Virtual Manipulatives
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
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Virtual Manipulatives
Outline
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Virtual Manipulatives
 What
are Virtual Manipulatives?
 What we Know
 What‘s Missing
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Online Collaboration with GeoGebra
– free dynamic math software
 GeoGebraWiki – reusable & changeable VMs
 International GeoGebra Institute
 GeoGebra
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What are
Virtual Manipulatives?
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What are Manipulatives?
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Physical objects used to promote learning
e.g. tangram,
base ten blocks
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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
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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
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Animation (Cyberlearning.org)
 Web-based
 NOT
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manipulable
Virtual Manipulative (GeoGebra)
 Web-based
 Manipulable
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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 Learning
What we Know
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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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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
What we Know
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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
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(Young 2006)
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Example: Reflection at Line
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Teaching Benefits of VMs
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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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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 Manipulatives
What‘s Missing?
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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 Manipulatives
 What
are Virtual Manipulatives?
 What we Know
 What‘s Missing

Online Collaboration
– free dynamic math software
 GeoGebraWiki – collaborative VMs
 International GeoGebra Institute
 GeoGebra
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Online Collaboration
with the free math software GeoGebra
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What is GeoGebra?
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Dynamic Mathematics
Software
For Learning and Teaching
in Schools
Geometry, Algebra and
Calculus
Open Source
www.geogebra.org
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GeoGebra = Geometry + Algebra
Algebra Window
Geometry & Graphics Window
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Educational Principles
 Student
Activity
 Multiple Representations
 Experimental and
Guided Discovery Learning
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GeoGebra Virtual Manipulatives
Every GeoGebra
figure can be
exported as a
web-page (html)
 So called
Dynamic
Worksheet
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Open Source &
Online Collaboration
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Why Open Source?
Available free of charge
in Schools and at Home
 Online Collaboration
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 International
Community
 User Forum – Users help Users
 GeoGebraWiki – Pool of Shared Materials
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Expandable
by 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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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)
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IGI Activities
 Offers free GeoGebra training for teachers
 Issues GeoGebra certification
 Nurtures a community of researchers
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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
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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
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Metiri Group (2006): Technology in Schools: What research says.
Retrieved Dec 2007 from
http://www.cisco.com/web/strategy/docs/education/TechnologyinSch
oolsReport.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 these
presentations are not intended as an endorsement by the U.S. Department
of Education.
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