There is a long tradition in linguistics implicating child language acquisition as a major driver of language change, the classic intuition being that innovations or "errors" which emerge during the acquisition process may occasionally propagate through through speech communities and accumulate as change over time. In order to better understand this relationship, I establish new methods for reasoning about language acquisition in the past. I demonstrate that certain aspects of child linguistic experience may be reasonably estimated from historical corpora and employ a quantitative model of productivity learning to investigate the role acquisition played as the driver of four well-documented instances of phonological, syntactic, and morphological change: transparent /aɪ/-raising in modern North American English, the innovation and lexical spread of the to-dative in Middle English, the analogy of the lengthened *ē-grade in Proto-Germanic strong verbs, and the forms of the past participles and "t-deverbals" in Classical and Late Latin. These case studies provide new insights into the implications of sparsity and variation on the first language acquisition process, the role that acquisition plays as the actuator of community-level change, and the complementary nature of acquisition and diachronic evidence for synchronic representation.