Do children learn a new word by tracking co-occurrences between words and referents across multiple instances ("cross-situational learning" models), or is word-learning a "one-track" process, where learners maintain a single hypothesis about the possible referent, which may be verified or falsified in future occurrences ("propose-but-verify" models)? Using a novel word-learning task, we ask which learning procedure is utilized by preschool-aged children. We report on findings from three studies comparing the word-learning strategies across different populations of child learners: monolingual English learners, Spanish-English dual language learners, and learners at risk for language-delay. In all three studies, we ask what, if anything, is retained from prior exposures and whether the amount of information retained changes as children get older. The ability to make a good initial hypothesis was a function of various factors, including language ability and experience, but across-the-board, children were no better than chance after a wrong initial hypothesis. This suggests that children do not retain multiple meaning hypotheses across learning instances, lending support to the propose-but-verify models.