Introduction: Issue and Context
Physical manipulatives have been in use in primary classrooms for many decades. Representing abstract mathematical concepts in the form of physical objects that can be touched, moved and joined with others, they allow students to “experience abstract notions directly before learning to describe them symbolically” (Mix, 2009). Popular examples include pop-sticks, counters, base-10 blocks, tangrams, pattern-blocks, shapes and solids.
Over the last two decades, virtual versions of these physical manipulatives have become available. Often referred to as applets or interactives and accessed via the web or downloaded on to tablets or other devices, their use is on the rise, with many perceiving them as powerful alternatives to their physical counterparts. Some are offered free of charge, others can be downloaded as individual apps for the cost of a few dollars, while others can be purchased as part of learning packages from educational publishers.
As with many technological developments, some teachers have embraced these new developments, others have resisted them, while still more take a laissez-faire approach, letting students play with interactives merely as an adjunct to formal teaching programs.
Considering their rising popularity, the mixed reaction they are receiving from teachers and the increasing curricular expectations that digital technologies will be incorporated into Mathematics programs, it is timely to examine the potential virtual manipulatives may offer in developing mathematical conceptual understanding in primary aged students.
What is a virtual manipulative?
Moyer, Bolyard & Spikell define a virtual manipulative as “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (2002, p. 379). Students manipulate the representation either directly (by acting upon the object on screen) or indirectly (by operating on symbols that alter the object) and receive immediate visual, verbal or symbolic feedback on their actions. They can be open-ended and exploratory, game-based, or focussed on solving specific problems (Moyer-Packenham, Salkind & Bolyard, 2008).