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

We demonstrate how developmental theories may be instantiated as statistical models, using hierarchical continuous-time dynamic systems. This approach offers a flexible specification and an often more direct link between theory and model parameters than common modeling frameworks. We address developmental theories of the relation between the academic competencies of mathematics and language, using data from the online learning system Mindsteps. We use ability estimates from 160,164 observation occasions, across N = 4623 3rd to 9th grade students and five ability domains. Model development is step-by-step from simple to complex, with ramifications for theory and modeling discussed at each step.