This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.

Learning relational categories-whose membership is defined not by intrinsic properties but by extrinsic relations with other entities-poses a challenge to young children. The current work showed 3-, 4-to 5-, and 6-year-olds pairs of cards exemplifying familiar relations (e.g., a nest and a bird exemplifying home for) and then tested whether they could extend the relational concept to another category (e.g., choose the barn as a home for a horse). It found that children benefited from (a) hearing a (novel) category name in a relational construction and (b) comparing category members. The youngest group-3-year-olds-learned the category only when given a combination of relational language and a series of comparisons in a progressive alignment sequence.

Previous reseach has documented that basic-level object categories provide an initial foundation for mapping adjectives to object properties. Children ranging from 21 months to 3 years can successfully extend a novel adjective (e.g., transparent) to other objects sharing a salient property if the objects are all members of the same basic-level category; if the objects are members of different basic-level categories, they fail to extend adjectives systematically (R. S. Klibanoff & S. R. Waxman, 2000a; S. R. Waxman & D. B. Markow, 1998). The present study proposed that the process of comparison is instrumental in children's ability to move beyond this foundation. To promote comparison, 2 target objects were introduced to 3-year-olds. In Experiment 1, the targets had contrastive properties (e.g., 1 transparent and 1 opaque object); in Experiment 2, the targets had consistent properties (e.g., 2 transparent objects). The results of both experiments illustrate that comparison--a general psychological process--operates in conjunction with naming to support the extension of novel adjectives to properties of objects from diverse basic-level categories.

Two experiments examined 3- and 4-year-old children's ability to map novel adjectives to object properties. Sixty-four children were introduced to a target (e.g., a bumpy object), and asked to choose between (1) a matching test object (e.g., a different bumpy object), and (2) a contrasting test object (e.g., a smooth object). Four-year-olds successfully extended novel adjectives from the target to the matching test object whether these objects were drawn from the same, or different, basic level categories. In contrast, 3-year-olds' extensions were more restricted. They successfully extended novel adjectives if the target and test objects were drawn from the same basic level category but failed to do so if the objects were drawn from different basic level categories (Experiment 1). However, if 3-year-olds (n = 20) were first permitted to extend a novel adjective to objects within the same basic level category, they were subsequently able to extend that novel adjective broadly to objects from different basic level categories (Experiment 2). Thus, basic level object categories serve as an initial foundation in the process of mapping novel adjectives to object properties.

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