Limitations of the retrieval strategy dimension of Siegler's (1982, 1984) distributions-of-associations model of young children's estimation of sums are delineated, an alternative model is described, and findings of two studies designed to test key assumptions of the models are reported. In Study 1, kindergarten children with normal IQ and no formal arithmetic training were screened on prearithmetic skills, pretested 20 times over the course of 8 weeks on a set of problems to estimate their distributions of associations, given intensive arithmetic training for 8 weeks, and posttested. Transfer of learning was also assessed. Results provided little evidence of learning over the 20 repetitions of pretest problems. Pretest distributions of associations did not provide a good indication of how the children responded on the posttest. In Study 2, 30 moderately or mildly retarded subjects between the approximate ages of 6 and 20 were screened and tested to estimate their distributions of associations with a set of 16 basic addition combinations administered 20 times in seven or eight sessions over a period of 1 month. Results were similar to those from the kindergarten children, but mentally handicapped children tended more than kindergarten children to use one or two strategies that accounted for a large proportion of their responses. It was concluded that children's earliest estimates are not drawn randomly from all known numbers and that computing experience is insufficient to account for the type of estimation errors occurring before mastery of basic number combinations. (RH)