Revisiting the Definition of a Virtual Manipulative

  • Patricia S. Moyer-PackenhamEmail author
  • Johnna J. Bolyard
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 7)


In 2002, Moyer, Bolyard and Spikell defined a virtual manipulative as an “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (p. 373). The purpose of this chapter is to revisit, clarify and update the definition of a virtual manipulative. After clarifying what a virtual manipulative is and what it is not, we propose an updated definition for virtual manipulative: an interactive, technology-enabled visual representation of a dynamic mathematical object, including all of the programmable features that allow it to be manipulated, that presents opportunities for constructing mathematical knowledge. The chapter describes the characteristics of five of the most common virtual manipulative environments in use in education: single-representation, multi-representation, tutorial, gaming and simulation.


Mathematical Knowledge Number Line Mathematical Object Programmable Feature Multiple Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Patricia S. Moyer-Packenham
    • 1
    Email author
  • Johnna J. Bolyard
    • 2
  1. 1.Utah State UniversityLoganUSA
  2. 2.West Virginia UniversityMorgantownUSA

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