Two Plus Three Is Five: Discovering Efficient Addition Strategies without Metacognition

Steven Stenberg HansenStanford University
Cameron Ross Lloyd McKenzieStanford University
James L. McClellandStanford University

Abstract

When learning addition, children appear to perform a remarkable feat: as they practice counting out sums on their fingers, they discover more efficient strategies while avoiding conceptually flawed procedures. Existing models that seek to explain how children discover good strategies while avoiding bad ones postulate metacognitive filters that reject faulty strategies. However, this leaves unexplained how the domain-specific knowledge required to evaluate a strategy might be acquired prior to addition being mastered. We introduce a biased exploration model, which demonstrates that new addition strategies can be discovered without invoking metacognitive filtering. This model provides a fit to data comparable to previous models, with the considerable advantage of avoiding an appeal to knowledge whose source is not itself explained. Specifically, we fit the pattern of changes in strategy use over time as children learn addition, as well as the overall error rate and error types reported empirically. The model suggests that the critical element allowing strategy discovery may be prior learning, rather than metacognitive strategy evaluation. We close by offering several empirical predictions and propose that what others have called strategies might often be decomposable into elements that can be assembled on the fly as problem solving unfolds in real time.

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Two Plus Three Is Five: Discovering Efficient Addition Strategies without Metacognition (379 KB)



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