Abstract
Over 9 months, structured clinical interviews with 17 kindergartners were used to study (a) the learning of a concrete counting strategy for addition, (b) the transition from concrete to mental counting strategies, and (c) the role of the commutativity principle in developing more economical counting strategies. Kindergartners appear to differ in their readiness to use a concrete strategy. Many children persisted in counting all with objects. The most common sequence of mental counting strategies was counting all starting with the first addend, counting all starting with the larger addend, and then counting on from the larger addend. A knowledge of commutativity does not appear to be necessary to invent counting strategies that disregard addend order.
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