What is a Virtual Manipulative?
"... an interactive, Web-based visual
representation of a dynamic object that
presents opportunities for constructing
mathematical knowledge."
(Moyer, Bolyard, & Spikell 2002, p.373)
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Outline: I.A & I.B
Samples:
“More VMs” Page
What is a Virtual Manipulative?
Example 1: Graphing Linear Equations
Young, D. (2006). Linear
Equations. Retrieved April
23, 2006 from:
http://plaza.ufl.edu/youngdj/
graphing_tool.html
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Outline: I.A & I.B
Samples:
“My VMs” Page
What is a Virtual Manipulative?
Example 2: The Moving Man Project
Murphy, L. D. (2000). The
Moving Man Project. Retrieved
April 23, 2006 from:
http://www.mste.uiuc.edu/murphy
/MovingMan/MovingMan.html
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Outline: I.A & I.B
Samples:
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Why Use Virtual Manipulatives?
Logistic Benefits:
Easily accessible and manageable
Low technological learning curve
Available out-of-school
Many people can develop them
Can do things not possible with Physical
Manipulatives, pencil and paper, or other tools
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Outline: II.A.1
Why Use Virtual Manipulatives?
Teaching Benefits:
Instantaneous feedback
Multiple representations of concepts
Link symbolic concepts with concrete representations
Promotes problem solving and hypothesis testing
Helpful for students with disabilities
Increases attention and motivation (even in teachers)
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Outline: II.A.2
Existing Research
Of seven articles describing actual research projects:
 Three were classroom studies, in which two found
some benefits and one found no difference.
 Three were studies of teacher use and attitudes,
which showed mixed feelings and little experience.
 One purported to show that Java-Applets could do
things that graphing calculators could not 4
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Outline: II.C.1
Existing Research
Two alternative arguments exist to support the use of
VM’s with research:
1) Cholmsky (2003) and Reimer & Moyer (2005) used
Marzano’s (1998) meta-analysis of instructional methods
that work to justify use of VMs:
Graphical representations
Physical Manipulatives
Hypothesis Testing
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Outline: II.C.2
Existing Research
Two alternative arguments exist to support the use of
VM’s with research:
2) Clements and McMillen (1996) used Piaget and Holt
to argue that computer manipulatives are no less
concrete than physical.
Both physical and virtual manipulatives are simply
symbolic representations
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Outline: II.C.2
Existing Collections
Mathlets - Journal of Online Math and Its
Applications
 Illuminations - National Council of Teachers of
Mathematics
NLVM - National Library of Virtual Manipulatives
Project Interactivate - Shodor Education Foundation
Thousands more in pay sites and private collections
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Outline: II.B
Samples:
“More VMs” Page
What’s Missing?
Online Schools have not been included in the
discussion of VMs, and should be:
The online nature of VMs make them suitable
for virtual schools
Face-to-face and online teaching methods
often differ
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Outline: II.D & III.A
What’s Missing?
Secondary Education
Most existing applets are focused on
elementary, middle-school and undergraduate
topics.
Virtually all of the existing research deals with
elementary and middle school age students
and topics.
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Outline: I.A & I.B
Samples:
“More VMs” Page
Suggestions for Development
Future Development of VMs Should:
 Be based on current Human Computer Interface
research
 Avoid Redundancy
Promote Reusability
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Outline: II.D.1
Suggestions for Research
 What aspects of some VMs make them more
effective than others?
 How can teachers be better educated on how and
when to use VMs?
 What topics may be most beneficial to be taught
with VMs?
Does the research base supporting physical
manipulatives transfer to virtual manipulatives?
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Outline: II.D.3 &III.C
Conclusion
•Virtual Manipulatives are a very promising tool for
mathematics education.
•As use, development, and research on VMs increases
they will become more effective teaching/learning tools.
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Outline: References
Samples:
My/More VMs Page
Conclusion
For References: Please see outline on table
Please Explore My Virtual Manipulatives and Others
on the Adjacent Computer
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Outline: References
Samples:
My/More VMs Page