Abstract The use of “concrete manipulatives” in mathematics education is supported by research and often accepted as a sine qua non of “reform” approaches. This article reviews the research on the use of manipulatives and critiques common notions regarding concrete manipulatives. It presents a reformulation of the definition of concrete as used in educational psychology and educational research and provides a rationale of how, based on that reformulation, computer manipulatives may be pedagogically efficacious. The article presents 7 hypothesized, interrelated affordances of manipulatives and briefly reviews evidence for their empirical validity.
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