number (e.g., addition and subtraction). The notion of 1-to-1 correspondences connects the counting numbers to the cardinal value of sets. Another important aspect of number is the way one writes and says them using the base 10 system (see Chapters 2 and 5 for further discussion). Knowledge of number is foundational to children’s mathematical development and gradually develops over time, so not all aspects of the number are present during the earliest years.
Several studies (e.g., Starkey, Spelke, and Gelman, 1990; Strauss and Curtis, 1984) examined whether infants understand that small sets that share their numerosity but contain different kinds of entities form a category (e.g., two dogs, two chicks, two jumps, two drumbeats). Starkey and colleagues (1990) examined this question by habituating infants to sets of two or three aerial photographs of different household objects. At test, infants were shown novel photographs that alternated between sets of two and sets of three. Infants dishabituated to the novel set size, suggesting that they considered different sets of two (or three) as similar. Whereas these studies might be regarded as suggesting that infants form numerical equivalence classes over visual sets containing disparate objects, these studies may have tapped infants’ sensitivity to continuous amount rather than number, as described above (Clearfield and Mix, 1999, 2001). That is, unless careful controls are put in place, sets with two elements will on average be smaller in amount than sets of three elements (e.g., Clearfield and Mix, 1999, 2001; Mix et al., 2002).
Findings showing that infants consider two objects and two sounds to form a category would not be subject to this criticism and thus could be considered as strong evidence for abstract number categories. In an important study, Starkey, Spelke, and Gelman (1983) tested whether infants have such categories. While the results seemed to indicate that 7-month-olds regarded sets of two (or three) objects and drumbeats as similar, several attempts to replicate these important findings have called them into question (Mix, Levine, and Huttenlocher, 1997; Moore et al., 1987). Thus, whether infants have an abstract concept of number that allows them to group diverse sets that share set size remains an open question. The findings, reviewed below, showing that 3-year-olds have difficulty matching visual and auditory sets on the basis of number, and that this skill is related to knowledge of conventional number words, suggest that the ability to form equivalence classes over sets that contain different kinds of elements may depend on the acquisition of conventional number skills. Kobayashi, Hiraki, Mugitani, and Hasegawa (2004) suggest that the methods used may be too abstract to tap this intermodal knowledge and that when the sounds made are connected to objects, for example, the sound of an object landing on a surface, evidence of abstract number categories may be revealed at younger ages, perhaps even in infants.