The algorithmic origins of counting

Symbolic metaprogram search improves learning efficiency and explains rule learning in humans

Throughout their lives, humans seem to learn a variety of rules for things like applying category labels, following procedures, and explaining causal relationships. These rules are often algorithmically rich but are nonetheless acquired with minimal data and computation. Symbolic models based on program learning successfully explain rule-learning in many domains, but performance degrades quickly as program complexity increases. It remains unclear how to scale symbolic rule-learning methods to model human performance in challenging domains. Here we show that symbolic search over the space of metaprograms-programs that revise programs-dramatically improves learning efficiency. On a behavioral benchmark of 100 algorithmically rich rules, this approach fits human learning more accurately than alternative models while also using orders of magnitude less search. The computation required to match median human performance is consistent with conservative estimates of human thinking time. Our results suggest that metaprogram-like representations may help human learners to efficiently acquire rules.

Formalizing theories of child development: Introduction to the special section

Here we introduce a Special Section of Child Development entitled "Formalizing Theories of Child Development." This Special Section features five papers that use mathematical models to advance our understanding of central questions in the study of child development. This landmark collection is timely: it signifies growing awareness that rigorous empirical bricks are not enough; we need solid theory to build the house. By stating theory in mathematical terms, formal models make concepts, assumptions, and reasoning more explicit than verbal theory does. This increases falsifiability, promotes cumulative science, and enables integration with mathematical theory in allied disciplines. The Special Section contributions cover a range of topics: the developmental origins of counting, interactions between mathematics and language development, visual exploration and word learning in infancy, referent identification by toddlers, and the emergence of typical and atypical development. All are written in an accessible manner and for a broad audience.