‘Concrete’ Manipulatives, Concrete Ideas

The notion of ‘concrete,’ from concrete manipulatives to pedagogical sequences such as ‘concrete to abstract,’ is embedded in educational theories, research, and practice, especially in mathematics education. In this article, the author considers research on the use of manipulatives and offers a critique of common perspectives on the notions of concrete manipulatives and concrete ideas. He offers a reformulation of the definition of ‘concrete’ as used in psychology and education and provides illustrations of how, accepting that reformulation, computer manipulatives may be pedagogically efficacious.

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