1. 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) Restart Show Read More: Outline: I.A & I.B Samples: “More VMs” Page

2. 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 http://plaza.ufl.edu/youngdj/ graphing_tool.html Read More: Outline: I.A & I.B Samples: “My VMs” Page Restart Show

3. 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 http://www.mste.uiuc.edu/murphy /MovingMan/MovingMan.html Read More: Outline: I.A & I.B Samples: “More VMs” Page Restart Show

4. Why Use Virtual Manipulatives?  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 Logistic Benefits: Read More: Outline: II.A.1 Restart Show

5. Why Use Virtual Manipulatives?  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) Teaching Benefits: Read More: Outline: II.A.2 Restart Show

6. Existing Research  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 Of seven articles describing actual research projects: Read More: Outline: II.C.1 Restart Show

7. Existing 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 Two alternative arguments exist to support the use of VM’s with research: Read More: Outline: II.C.2 Restart Show

8. Existing 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 Read More: Outline: II.C.2 Restart Show Two alternative arguments exist to support the use of VM’s with research:

9. Existing Collections  Mathlets - Journal of Online Math and Its Applications Mathlets  Illuminations - National Council of Teachers of MathematicsIlluminations  NLVM - National Library of Virtual Manipulatives NLVM  Project Interactivate - Shodor Education Foundation Project Interactivate  Thousands more in pay sites and private collections Read More: Outline: II.B Samples: “More VMs” Page Restart Show

10. 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 Read More: Outline: II.D & III.A Restart Show

11. 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. Read More: Outline: I.A & I.B Samples: “More VMs” Page Restart Show

12. Suggestions for Development Future Development of VMs Should:  Be based on current Human Computer Interface research  Avoid Redundancy  Promote Reusability Read More: Outline: II.D.1 Restart Show

13. 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? Read More: Outline: II.D.3 &III.C Restart Show

14. 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. Read More: Outline: References Restart Show Samples: My/More VMs Page

15. Conclusion For References: Please see outline on table Please Explore My Virtual Manipulatives and Others on the Adjacent Computer Read More: Outline: References Samples: My/More VMs Page Restart Show