Origins of number sense: The development of numerical cognition in infants and preschoolers

Experiments investigated the development of numerical cognition in infants and preschool children. First, infants' sensitivity to numerosity in auditory sequences was examined. When all continuous variables such as amount of sound and duration are controlled, infants successfully discriminate sound sequences of large numbers, with discrimination following Weber's Law. Six-month-old infants discriminate large number sound sequences in a 2.0 ratio (4 vs. 8 and 8 vs. 16), but not in a 1.5 ratio (4 vs. 6 and 8 vs. 12). Furthermore, nine-month-old infants discriminate large number sound sequences in a 1.5 ratio (4 vs. 6 and 8 vs. 12), but not in a 1.25 ratio (4 vs. 5 and 8 vs. 10). Infants' large number discrimination is subject to the same ratio limit signature of adults' numerosity discrimination, suggesting common mechanisms over development. Additional experiments found infants fail to discriminate 2 vs. 4 or 2 vs. 3 sounds, findings that accord with studies using visual-spatial arrays, suggest separate systems underlie representation of small and large numerosities.; The next experiments examined whether children use their nonverbal representations of number when learning number words. Five-year-old children were categorized as skilled or unskilled counters by a counting pretest. Children were then assessed with several tasks including verbal estimation and number word comprehension using numbers 20--120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities, whereas unskilled counters showed this only for smaller numbers. These findings suggest that large, approximate numerosity representations become linked to number words when children learn to count to those words. The fact that unskilled counters are not yet able to map large number words to nonsymbolic representations does not mean they know nothing about these words. The final studies examined what unskilled counters understand about the logic of the number system for large number words. These studies show that before children can count to large number words, they understand that these words refer to specific, unique cardinal values. Collectively, the experiments presented in this thesis suggest that number representations are available beginning in infancy, and that they are engaged as children learn to count. These findings show continuity in the developmental of numerical cognition and have important implications for mathematics education.