Heads-to-Toes task asks children to do the opposite of what the instructor tells them. So, for example, if the instructor asks the children to touch their head, they are to touch their toes. This task measures behavioral regulation (a component of self-regulation), in that it requires children to employ inhibitory control, attention, and working memory. The researchers found that behavioral regulation scores significantly predicted emergent math scores. The researchers conclude that “strengthening attention, working memory, and inhibitory control skills prior to kindergarten may be an effective way to ensure that children also have a foundation of early academic skills” (p. 956). Espy and colleagues (2004) specifically studied the roles of working memory and inhibitory control with almost 100 preschoolers. They found that both components of executive function contributed to the children’s mathematical proficiency, with inhibitory control being the most prominent. Passolunghi and colleagues (2007) studied 170 6-year-olds in Italy. They examined the roles of working memory, phonological ability, numerical competence, and IQ in predicting math achievement. They found that working memory skills significantly predicted math learning at the beginning of elementary school (primary school in Italy).


This chapter underscores that young children have more mathematics knowledge, in terms of number and spatial thinking, than was previously believed. Very early in life, infants can distinguish between larger set sizes, for example 8 versus 16 items, but their ability to do so is only approximate and is limited by the ratio of the number of items in the sets. The set size limitation is thought to reflect one of the two core systems for number (Feigenson, Dehaene, and Spelke, 2004; Spelke and Kinzler, 2007). Furthermore, young infants’ early knowledge of quantity is implicit, in that they do not use number words, which means that learning number words and relating them to objects is one of the major developmental tasks to occur during early childhood.

Toddlers and preschool children move from the implicit understanding of number seen during infancy to formal number knowledge. Spoken number words, written number symbols, and cultural solution methods are important tools that support this developmental progression.

Young children also learn about space, including shapes, locations, distances, and spatial relations, which also go through major development during the early childhood years. Children’s acquisition of spatial language plays an important role in the development of spatial categories and skills. In addition to learning about number and shape, early childhood also includes development of measurement, which is a fundamental aspect of mathematics that connects geometry and number. Young children’s understanding of measurement begins with length, which is perceptually based,

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