Formalizing developmental phenomena as continuous-time systems: Relations between mathematics and language development

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.