While high-performing language models are typically trained on hundreds of billions of words, human children become fluent language users with a much smaller amount of data. What are the features of the data they receive, and how do these features support language modeling objectives? To investigate this question, we train GPT-2 models on 29M words of English-language child-directed speech and a new matched, synthetic dataset (TinyDialogues), comparing to a heterogeneous blend of datasets from the BabyLM challenge. We evaluate both the syntactic and semantic knowledge of these models using developmentally-inspired evaluations. Through pretraining experiments, we test whether the global developmental ordering or the local discourse ordering of children's training data support high performance relative to other datasets. The local properties of the data affect model results, but somewhat surprisingly, global properties do not. Further, child language input is not uniquely valuable for training language models. These findings support the hypothesis that, rather than proceeding from better data, children's learning is instead substantially more efficient than current language modeling techniques.