Cognitive Play and Mathematical Learning in Computer Microworlds
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Based on the constructivist principle of active learning, we focus on children’s transformation of their cognitive play activity into what we regard as independent mathematical activity. We analyze how, in the process of this transformation, children modify their cognitive play activities. For such a modification to occur, we argue that the cognitive play activity has to involve operations of intelligence which yield situations of mathematical schemes.
We present two distinctly different cases. If the first case, the medium of the cognitive play activity was a discrete computer microworld. We illustrate how two children transformed the playful activity of making pluralities into situations of their counting schemes. In the second case, the medium was a continuous microworld. We illustrate two children’s transformation of the playful activity of making line segments (“sticks”) into situations of their counting schemes. We explain one child’s transformation as a generalizing assimilation because it was immediate and powerful. The transformation made by the other child was more protracted, and social interaction played a prominent role. We specify several types of accommodations induced by this social interaction, accommodations we see as critical for understanding active mathematics learning. Finally, we illustrate how a playful orientation of independent mathematical activity can be inherited from cognitive play.
KeywordsNumber Sequence Teaching Session Mathematical Activity Counting Scheme Segmented Number
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