From Magnitudes to Math: Developmental Precursors of Quantitative Reasoning

The uniquely human mathematical mind sets us apart from all other animals. Although humans typically think about number symbolically, we also possess nonverbal representations of quantity that are present at birth and shared with many other animal species. These primitive numerical representations are thought to arise from an evolutionarily ancient system termed the Approximate Number System (ANS). The present dissertation aims to determine how these preverbal representations of quantity may serve as the foundation for more complex quantitative reasoning abilities. To this end, the five studies contained herein investigate the relations between representations of number, representations of other magnitude dimensions, and symbolic math proficiency in infants, children, and adults. The first empirical study, described in Chapter 2, investigated whether infants engage the ANS to represent the full range of natural numbers. The study presented in Chapter 3 compared infants' acuity for detecting changes in contour length to their acuity for detecting changes in number to assess whether representations of continuous quantities are primary to representations of number in infancy. The study presented in Chapter 4 compared individual differences in acuity for number, line length, and brightness in children and adults to determine how the relations between these magnitudes may change over development. Chapter 5 contains a longitudinal study investigating the relation between preverbal number sense in infancy and symbolic math abilities in preschool-aged children. Finally, the study presented in Chapter 6 investigated the mechanisms underlying the maturation of the number sense and determined which features of the number sense are predictive of symbolic math skill. Taken together, these findings confirm that number is a salient feature of the environment for infants and young children and suggest that approximate number representations are fundamental for the acquisition of symbolic math.