Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt strategy. The use of overt strategies most often on the hardest problems was adaptive and efficient. How children knew when to use overt strategies, though, remained unclear. Addressing this problem, Siegler and Shrager (1984) proposed a distribution of associations model to explain how children arrive at their addition strategies. Their model involves representation and process. In brief, children represent correct and incorrect answers that vary in "strength of association" between problem and answer. Then they retrieve an answer. If the answer is sufficiently strongly associated with the problem, the child advances the retrieved answer. If not, the child elaborates through overt strategies the representation of the problem. Elaboration of representation is followed by retrieval. This alternation between elaboration of representation and retrieval may progress through three phases. The model has implications for explaining parallels between children's and adults' problem-solving behavior. In addition, it suggests that ordering children not to use overt strategies such as counting on their fingers is worse than useless. (RH)