Attaching meaning to the number words: contributions of the object tracking and approximate number systems. Issue 1 (15th December 2016) - vanMarle, Kristy; Chu, Felicia W.; Mou, Yi; Seok, Jin H.; Rouder, Jeffrey; Geary, David C.
Abstract: Children's understanding of the quantities represented by number words (i.e., cardinality) is a surprisingly protracted but foundational step in their learning of formal mathematics. The development of cardinal knowledge is related to one or two core, inherent systems – the approximate number system (ANS) and the object tracking system (OTS) – but whether these systems act alone, in concert, or antagonistically is debated. Longitudinal assessments of 198 preschool children on OTS, ANS, and cardinality tasks enabled testing of two single‐mechanism (ANS‐only and OTS‐only) and two dual‐mechanism models, controlling for intelligence, executive functions, preliteracy skills, and demographic factors. Measures of both OTS and ANS predicted cardinal knowledge in concert early in the school year, inconsistent with single‐mechanism models. The ANS but not the OTS predicted cardinal knowledge later in the school year as well the acquisition of the cardinal principle, a critical shift in cardinal understanding. The results support a Merge model, whereby both systems initially contribute to children's early mapping of number words to cardinal value, but the role of the OTS diminishes over time while that of the ANS continues to support cardinal knowledge as children come to understand the counting principles. Abstract : Learning the meanings of the number words and how to apply them in the counting procedure mark children's first step into the world of formal, symbolic mathematics. We provide evidence that two core mechanisms ‐‐ the analog number system (ANS, in blue) and the object tracking system (OTS, in yellow) ‐‐ contribute to the initial stages of this process, but that only the ANS continues to influence children's learning as they acquire the cardinal principle and come to master the counting routine.