Revisiting the Effects and Affordances of Virtual Manipulatives for Mathematics Learning

Revisiting the Effects and Affordances of Virtual Manipulatives for Mathematics Learning

Patricia S. Moyer-Packenham (Utah State University, USA) and Arla Westenskow (Utah State University, USA)
DOI: 10.4018/978-1-4666-8847-6.ch009
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Abstract

In this paper, we revisit the research on virtual manipulatives by synthesizing the findings from 104 research reports, with 46 studies yielding 104 effect size scores reporting the effects of VMs on student achievement. The 104 reports also contributed to a conceptual synthesis analysis that produced categories of affordances that promote mathematical learning. The results of the effect size scores analysis yielded overall moderate effects for VMs compared with other instructional treatments, which was consistent with the first meta-analysis we conducted. There were large, moderate, and small effects when VMs were compared with physical manipulatives, textbooks, and examined by mathematical domains, grade levels, study duration, study quality, year of study publication, and study size. Revisiting the affordance categories confirmed our first analysis which produced five categories of features in the VMs that promoted students' mathematical learning (motivation, simultaneous linking, efficient precision, focused constraint, and creative variation).
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Theoretical Perspective

We use the definition of a virtual manipulative by Moyer, Bolyard and Spikell (2002): “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (p. 373). This definition applies to both virtual manipulatives driven by a computer mouse and those manipulated on touch-screen devices. A variety of websites feature large collections of virtual manipulatives, including the National Library of Virtual Manipulatives (NLVM) (http://shodor.com/curriculum/). The libraries contain interactive applets (or apps) designed to focus on a single mathematical concept. Many of the virtual manipulatives in the libraries are based on common physical manipulatives (e.g., algebra tiles or geoboards; see Figure 1). New libraries are also developing virtual manipulatives apps for the iPad also based on common physical objects (see Figure 2).

Figure 1.

In these examples from the National Library of Virtual Manipulatives, the app on the left is based on Algebra Tiles and the app on the right is based on the Geoboard.

Figure 2.

In these examples from the iPad app store, the app on the left is based on a Tens Frame and the app on the right is based on the Base-10 Blocks.

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