Proceedings of the Annual Meeting of the Cognitive Science Society

The successor function a recursive function S which states that for every natural number n, S(n) = n+1 underlies ourunderstanding of the natural numbers as an infinite class. Recent work has found that acquisition of this logical propertyis surprisingly protracted, completed several years after children master the counting procedure. While such work linkssuccessor knowledge with counting mastery, the exact processes underlying this developmental transition remain unclear.Here, we examined two possible mechanisms: (1) recursive counting knowledge, and (2) formal training with the +1 rulein arithmetic. We find that while both recursive counting and arithmetic mastery predict successor knowledge, arithmeticperformance is significantly lower than measures of recursive counting for all children. This dissociation suggests childrendo not generalize the successor function from trained mathematics; rather, we find evidence consistent with the hypothesisthat successor knowledge is supported by the extraction of recursive counting rules.