ABSTRACT
From infancy, children are sensitive to quantitative relations in the world around them. Already in the first months of life, they discriminate between different auditory or visual stimuli on the basis of their quantitative properties, and by early in the second year, they distinguish between sequential presentations of two quantities in which both quantities are equal to each other, the second is less than the first, or the second is greater than the first (cf. chap. 2). With the assignment of numerical values to quantities, however, a form of quantitative thinking emerges that differs profoundly from these preverbal quantitative discriminations. In order to arrive at a numerical representation of a quantity—regardless of whether it is a verbal or a nonverbal one—it is necessary to apply some kind of unit to that quantity, and that introduces the possibility of using a smaller or a larger unit and with it the need to recognize that the numerical value that is obtained is a function of the chosen unit as well as of the quantity being represented. The many kinds of numerical knowledge that develop across early and middle childhood—from counting to adding and subtracting, then multiplying and dividing and knowledge about rational numbers and fractions—are profoundly interconnected because of their common dependence on the concept of unit.
