Development of Quantitative Thinking
For understanding development of quantitative thinking, the distinction between nonsymbolic and symbolic thinking is fundamental. Nonsymbolic quantitative thinking is present in early infancy, culturally universal, and similar across species. These similarities include the ability to represent and compare numerosities, the representations being noisy and increasing logarithmically with actual quantity, and the neural correlates of number representation being distributed in homologous regions of frontoparietal cortex. Symbolic quantitative thinking, in contrast, emerged recently in human history, differs dramatically across cultural groups, and develops over many years. As young children gain experience with symbols in a given numeric range and associate them with nonverbal quantities in that range, they initially map them to a logarithmically-compressed mental number line and later to a linear form. This logarithmic-to-linear shift expands children's quantitative skills profoundly, including their ability to estimate positions of numbers on number lines, to estimate measurements of continuous and discrete quantities, to categorize numbers by size, to remember numbers, and to estimate and learn answers to arithmetic problems. Thus, while nonsymbolic quantitative thinking is important and foundational for symbolic numerical capabilities, the capacity to represent symbolic quantities offers crucial cognitive advantages.