We report two experiments concerned with a reconstructive processing model of reasoning/remembering dependencies in cognitive development. According to this model, such dependencies occur because problem-solving tasks often permit children to answer short-term memory probes by activating the same information-processing operations that they use to solve problems, not because reasoning and remembering compete for the same supply for scarce resources. This claim was examined in the context of mental arithmetic problems that were accompanied by memory probes for problem-relevant information. The data were generally consistent with the view that preschoolers and elementary schoolers can respond to memory probes by applying arithmetical processing to running gist from recently solved problems. The findings are discussed with reference to two competing interpretations of the development of working memory, fuzzy-trace theory and the generic-resources hypothesis.