What Are Virtual Manipulatives?
Moyer, Patricia S., Bolyard, Johnna J., Spikell, Mark A., Teaching Children Mathematics
As a result of innovations in technology, the prevalence of the Internet, and the increasing availability of computers in classrooms and homes, an enhanced approach for teaching and learning mathematics using manipulatives and computers is emerging. This new approach essentially creates a new class of manipulatives, called virtual manipulatives, as well as new capabilities, or toolkits, for computer programs that use visual representations. These new virtual manipulatives have all the useful properties of existing computer manipulatives while overcoming many of their disadvantages, yet very little is known or written about them. The purpose of this article is to establish a working definition of virtual manipulatives, highlight examples of virtual manipulatives on the Internet, and discuss their current and potential classroom use.
Defining Virtual Manipulatives
Two types of representations on the World Wide Web are being called virtual manipulatives--these are static and dynamic visual representations of concrete manipulatives (Spicer 2000). Consequently, two types of virtual manipulatives are available as teaching and learning tools. Because one of these types is far more powerful and has much greater utility and potential for teaching, drawing the distinction between the two is important. Establishing a name and definition that uniquely describe these dynamic images is equally important to avoid confusion.
Static visual representations are essentially pictures. They are the sorts of visual images ordinarily associated with pictures in books, drawings on an overhead projector, sketches on a chalkboard, and so on. Although such representations resemble concrete manipulatives, they cannot be used in the same ways that concrete manipulatives can. That is, a student can actually slide, flip, and turn concrete manipulatives but cannot perform the same actions with a static picture of the concrete manipulative. These static visual representations are not true virtual manipulatives.
In contrast, dynamic visual representations of concrete manipulatives are essentially "objects." They are visual images on the computer that are just like pictures in books, drawings on an overhead projector, sketches on a chalkboard, and so on. In addition, these dynamic visual representations can be manipulated in the same ways that a concrete manipulative can. Just as a student can slide, flip, and turn a concrete manipulative by hand, he or she can use a computer mouse to actually slide, flip, and turn the dynamic visual representation as if it were a three-dimensional object. This kind of visual representation is truly a virtual manipulative.
Although many people currently use the term virtual manipulative to refer to any computer-generated image that appears on a monitor and is intended to represent concrete manipulatives, this meaning is much too simplistic to be descriptive or useful. The ability to manipulate the visual representation, or object, on the computer connects the user with the real teaching and learning power of virtual manipulatives, that is, the opportunity to make meaning and see relationships as a result of one's own actions. This kind of user engagement distinguishes virtual manipulative sites from those sites where the act of pointing and clicking results in the computer's providing an answer in visual or symbolic form. We think that the term virtual manipulative should be restricted to describing this interactive capability.
In our view, a virtual manipulative is best defined as an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge. Currently, virtual manipulatives are modeled on the concrete manipulatives commonly used in schools, such as pattern blocks, tangrams, fraction bars, geoboards, and geometric solids. When such objects are available through the Web, they may be …
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Publication information: Article title: What Are Virtual Manipulatives?. Contributors: Moyer, Patricia S. - Author, Bolyard, Johnna J. - Author, Spikell, Mark A. - Author. Magazine title: Teaching Children Mathematics. Volume: 8. Issue: 6 Publication date: February 2002. Page number: 372+. © 1999 National Council of Teachers of Mathematics, Inc. COPYRIGHT 2002 Gale Group.
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