mathematical development (e.g., Barth et al., 2005; Butterworth, 2005; Dehaene, 1997; but see Holloway and Ansari, 2008, and Rips, Bloomfield, and Asmuth, 2008, for contrasting views). We examine two domains that are foundational to mathematics in early childhood: (1) number, including operations, and (2) spatial thinking, geometry, and measurement.

  • What are some of the important developmental changes in mathematical understandings in these domains that occur during the preschool years?

  • What is the relation of mathematical development to more general aspects of development needed for learning mathematics, such as the ability to regulate one’s behavior and attention?

EVIDENCE FOR EARLY UNDERSTANDING OF NUMBER

Preverbal Number Knowledge

Delineating the starting points of knowledge in important domains is a major goal in developmental psychology. These starting points are of theoretical importance, as they constrain models of development. They are also of practical importance, as a basic tenet of instruction is that teaching that makes contact with the knowledge children have already acquired is likely to be most effective (e.g., Clements et al., 1999). Thus, it is not surprising that infant researchers have been actively mapping out the beginnings of preverbal number knowledge—knowledge that appears to be shared by humans from differing cultural backgrounds as well as with other species, and thus part of their evolutionary endowment (e.g., Boysen and Berntson, 1989; Brannon and Terrace, 1998, 2000; Brannon et al., 2001; Cantlon and Brannon, 2006; Dehaene, 1997; Dehaene, Dehaene-Lambertz, and Cohen, 1998, Meck and Church, 1983). A large body of research has examined a set of numerical skills, including infants’ ability to discriminate between different set sizes, their ability to recognize numerical relationships, and their ability to understand addition and subtraction transformations. The study of numerical knowledge in infants represents a major departure from previously held views, which were heavily influenced by Piaget’s (1941/1965) number conservation findings and stage theory. These older findings showed that children do not conserve number in the face of spatial transformations until school age, and they led many to believe that before this age children lack the ability to form concepts of number (see Mix, Huttenlocher, and Levine, 2002, for a review). Although Piaget recognized that children acquire some mathematically relevant skills at earlier ages, success on the conservation task was widely regarded as the sine qua non of numerical understanding.



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