Beginning in the 1960s and 1970s, researchers began to actively examine early numerical competencies, which led to a revised understanding of children’s numerical competence. This research identified a great deal of competence in preschool children, including counting and matching strategies that children use on Piaget’s conservation of number task (see the discussion in Chapter 5).

As we detail, infant and toddler studies have largely focused on the natural numbers (also called counting numbers). However, they have also examined representations of fractional amounts and proportional relations as well as geometric relationships, shape categories, and measurement. Moreover, although there is some disagreement in the field about the interpretation of the findings of infant and toddler studies as a whole, these findings are generally viewed as showing strong starting points for the learning of verbal and symbolic mathematical skills.

Infants’ Sensitivity to Small Set Size

Infant studies typically use habituation paradigms to examine whether infants can discriminate between small sets of objects, either static or moving (Antell and Keating, 1983; Starkey and Cooper, 1980; Strauss and Curtis, 1981; Van Loosbroek and Smitsman, 1990; Wynn, Bloom, and Chiang, 2002). In a typical habituation study, infants are repeatedly shown sets containing the same number of objects (e.g., 2) until they become bored and their looking time decreases to a specified criterion. The infant is then shown a different set size of objects or the same set size, and looking times are recorded. Longer looking times indicate that the infant recognizes that the new display is different from an earlier display. Results show that infants (ranging in age from 1 day old to several months old) can discriminate a set of two objects from a set of three objects, yet they are unable to discriminate four objects from six objects, even though the same 3:2 ratio is involved. These findings indicate that infants’ ability to discriminate small set sizes is limited by number rather than by ratio. Huttenlocher, Jordan, and Levine (1994) suggest that infants’ ability to discriminate small sets (2 versus 3) could be based on an approximate rather than on an exact sense of number.

Several studies suggest that the early quantitative sensitivity displayed by infants for small set sizes is actually based on their sensitivity to amount (surface area or contour length) which covaries with numerosity, rather than on number per se (Clearfield and Mix, 1999, 2001). That is, unless these variables are carefully controlled, the more items there are, the greater the amount of stuff there is. In studies that independently vary number and amount, Clearfield and Mix (1999, 2001) found that infants ages 6 to 8 months detected a change in amount (contour length or area) but not a

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