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Two hundred and fifteen children aged between 5 and 9 years were asked to estimate the answers to addition sums. Their competence at addition was first assessed, and they were accordingly divided into five groups. Children of each level were given a set of estimation problems involving sums a little too difficult for them to calculate (termed their “base correspondence”). Of the 215 children, 108 were then given sets of estimation problems corresponding to levels higher than their own. In the base correspondence, children of higher levels tended to produce more reasonable estimates than did children of lower levels. As difficulty increased beyond the base correspondence, the reasonableness of the estimates declined. The existence and nature of a zone of partial knowledge and understanding are discussed.


Journal article


Mathematical Cognition

Publication Date





140 - 153


Ann Dowker, Oxford University, Dept of Experimental Psychology, South Parks Road, Oxford, OX1 3UD, England


Young children, Cognitive development, Estimation, Number concepts, Partial knowledge, Mathematical development, Arithmetic