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We argue that to test preschoolers' understanding of counting, one has to use tasks that relate counting to the goal of doing arithmetic, as counting and arithmetic principles are mutually constrained. A naturalistic study in the preschool classroom led to the development of an "arithmetic-counting" task, where counting was being related to the goal of doing arithmetic. In solving an arithmetic problem, the child viewed the addition or subtraction of X items from a set with a known number, predicted the answer, and then counted the items in the resultant array to check the prediction. Three experiments, one with 4-year-olds who had relevant in-class experience with the task (Experiment 1), and two others with 4-year-olds (Experiment 2) and 3-year-olds (Experiment 3) who were novices with regard to the task, are reported. All children, even the 3-year-olds, offered reasonable cardinal values during the prediction phase and used counting to check their predictions. Predictions were reliable, in the correct direction or correct, and checking counts were very accurate. Young children's ability to make reasonable predictions and coordinate these with counts "to check" indicated the implicit understanding of counting and arithmetic principles. The theoretical and practical implications of our findings are discussed.

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