A Model of Knower-Level Behavior in Number-Concept Development.

We develop and evaluate a model of behavior on the Give-N task, a commonly-used measure of young children's number knowledge. Our model uses the knower-level theory of how children represent numbers. To produce behavior on the Give-N task, the model assumes children start out with a base-rate that make some answers more likely a priori than others, but is updated on each experimental trial in a way that depends on the interaction between the experimenter's request and the child's knower-level. We formalize this process as a generative graphical model, so that the parameters-including the base-rate distribution and each child's knower-level-can be inferred from data using Bayesian methods. Using this approach, we evaluate the model on previously published data from 82 children spanning the whole developmental range. The model provides an excellent fit to these data, and the inferences about the base-rate and knower-levels are interpretable and insightful. We discuss how our modeling approach can be extended to other developmental tasks, and can be used to help evaluate alternative theories of number representation against the knower-level theory.