preschool children ages 3 and 4 to correctly judge whether more small objects or more large ones would fit in a designated space. In pretest trials, the children incorrectly chose the larger object, but after six demonstration trials of watching the experimenter place objects of the two sizes, one by one, into two identical containers, they performed significantly better on posttest trials. These results identify the difficulties very young children have with understanding units and suggest that preschoolers (ages 2 years, 9 months to 4 years, 7 months) benefit from instructional intervention highlighting the relation between unit size and number. Thus, young children show some understanding of fundamental mathematical concepts that are relevant to measurement if given the opportunity to explore these concepts in interactive, supportive contexts.

Scaling and Proportion

Children demonstrate early use of fundamental skills related to measurement and proportional reasoning in their use of maps. A critical factor for success in map use is scaling, which is related to measurement and proportional thinking. Scaling refers to the ability to code distance and understand how distance on a map corresponds to distance in the real world (Huttenlocher et al., 1999). Newcombe and Huttenlocher (2000, 2005) review the hierarchical nature of spatial coding, suggesting that various systems of coding spatial location are available, and their use depends on a mix of factors (e.g., cue salience in the external environment, complexity of movements required for action by the viewer). Furthermore, the availability of these systems appears as early as 6 months for both externally referenced and viewer-centered systems, which is much earlier than is predominantly reported in the literature. In relation to map use, children not only need to code locations in space but also to accommodate changes in scale, which requires a form of measurement (e.g., comparing the distance between two locations on a map and the corresponding distance between two locations in the real world). Scaling has been assumed to involve proportional reasoning and therefore to occur much later in development, between ages 10 and 12 (Piaget and Inhelder, 1967). However, evidence of early success using maps by children ages 3 to 6 indicates that scaling, at least in these cases, may represent a precursor to more precise measurement and is accomplished using spatial coding (Huttenlocher et al., 1999; Sandberg and Huttenlocher, 2001; Stea et al., 2004).

REGULATING BEHAVIOR AND ATTENTION

Infants’ and young children’s mathematical development also takes place in the context of cognitive and behavior regulation, which when



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