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‘Concrete’ Manipulatives, Concrete Ideas

Authors: Douglas H. Clements;

‘Concrete’ Manipulatives, Concrete Ideas

Abstract

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.

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    145
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
145
Top 1%
Top 1%
Average
bronze