Inference and Association in Children’s Early Numerical Estimation

How do children map number words to the numerical magnitudes they represent? Recent work in adults has shown that two distinct mechanisms—structure mapping and associative mapping—connect number words to nonlinguistic numerical representations (Sullivan & Barner, 2012). This study investigated the development of number word mappings, and the roles of inference and association in children’s estimation. Fifty-eight 5- to 7-year-olds participated, and results showed that at both ages, children possess strong item-based associative mappings for numbers up to around six, but rely primarily on structure mapping—an inferential process—for larger quantities. These findings suggest that children rely primarily on an inferential mechanism to construct and deploy mappings between number words and large approximate magnitudes. How do number words like seven and thirty-five get linked to sets of things in the world? When children make these mappings, do they form item-by-item associations between numerals and quantities? Or do they use inferential processes based on their knowledge of how numbers are related to one another? Although philosophical discussions of mathematical knowledge provide strong reasons to doubt that perception alone could supply the logi-cal meanings encoded by number words (e.g., Frege, 1884/1953; Kant, 1781/1929), experimental psychologists have established that once children acquire such meanings, number words do eventu-ally get mapped to perceptual representations o