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A study of virtual manipulatives for elementary mathematics

, State University of New York at Buffalo, United States

State University of New York at Buffalo . Awarded


In this study, I explored and documented the use of virtual manipulatives, particularly those from the National Library of Virtual Manipulatives, compared to physical manipulatives, as a tool for learning mathematics. This research has two purposes: (1) to evaluate features of virtual manipulatives that facilitate learning or fail to do so, with an eye toward aiding future design, and (2) to contribute to a model of learning with virtual manipulatives.

The study was a teaching experiment involving weekly individual meetings with three students. I designed activities that allowed me to compare the use of virtual manipulatives with corresponding physical manipulatives. I scaffolded the students' learning as they worked on these activities, deriving my instructional methods from implications of sociocultural constructivism. As the researcher, I videotaped these sessions and analyzed them using analytic induction and constant comparison methods.

Findings supported the use of both physical and virtual manipulatives. The two types offered alternative representations within which students could reconstruct concepts.

Physical manipulatives were usually more concrete than the virtual manipulatives used in this study, allowing children access to concepts. Physical manipulatives, and virtual manipulatives could be used together in concretizing abstract concepts. Some virtual manipulatives and tutorials were not concrete and led to rote understandings. This study supports the use of situated contexts in virtual environments.

Some beneficial supports of virtual manipulatives used in this study included speed, extensibility, and cleanness. Other features were limiting because of their inconsistencies, potential to distract, or difficulty for the user to control. Linked representation was not used to its potential by the programs. Constraints were used successfully by programs to help students work within mathematical systems.

The teacher's presence is critical. There are types of scaffolding that the manipulatives do not offer such as offering technical support, finding tasks within the student's zones of proximal development, and encouraging justification and explanation.


Izydorczak, A.E. A study of virtual manipulatives for elementary mathematics. Ph.D. thesis, State University of New York at Buffalo. Retrieved January 18, 2020 from .

This record was imported from ProQuest on October 23, 2013. [Original Record]

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