Chapter 2: Rethinking the Starting Point for Mathematics Learning

The assumption that counting is at the very core of mathematical development, or at least of the development of numerical knowledge, is so pervasive as to go almost unquestioned. Neuroscientists such as Dehaene (1997) and Butterworth (1999) have posited that the brain has built-in mechanisms for precisely enumerating small collections, and also for obtaining approximate numerical information about large ones. A number of developmental psychologists, similarly, have posited a preverbal form of counting that is already operational in the first year of life and that has important isomorphisms with verbal counting (Gelman, 1991, 1998; Wynn, 1992; Xu, 2003). Mathematics curricula for early childhood have always targeted counting and related numerical skills as key instructional foci (although the standards formulated by the National Council of Teachers of Mathematics, 2003, are much broader than that), and that emphasis is also reflected in the content of standardized tests of young children’s mathematics abilities (e.g., Ginsburg & Baroody, 2003).