Chapter 8: The Impact of Method on Assessing Young Children’s Everyday Mathematical Experiences¹

Many children arrive at school with an impressive understanding of mathematics. As Baroody, Lai, and Mix (2006) pointed out in a recent review of the literature on children’s development of a sense of number, “mathematical learning begins early, very early” (p. 196). Although there is still a good deal of debate at precisely when this learning starts (see, for example, Baroody, 2004; Mix, Huttenlocher, & Levine, 2002; Starkey, Spelke, & Gelman, 1990; Wynn, 1998), it is clear that by age 3 or 4 children have had a great deal of mathematical experiences (for reviews, see Baroody et al., 2006; Ginsburg, Cannon, Eisenband, & Pappas, 2006; Ginsburg, Klein, & Starkey, 1998). Ginsburg and his colleagues were thus led to state that we have “a rich understanding of the ways in which children construct an informal knowledge of mathematics in the everyday environment” (1998, pp. 401–402). However, as Hannula (2005) pointed out with regard to number, “nearly all our knowledge of young children’s number recognition skills is based on studies that explicitly direct children’s attention to the aspect of number” (p. 11). The same is true of the other areas of mathematics, with a relative dearth of research focusing on how much, and under what conditions, young children play with mathematical shapes, talk about time, estimate distance, and so on in the course of their typically occurring everyday activities. Our focus in this chapter will be on this type of informal mathematics that occurs during the course of preschool-aged children’s typically occurring everyday activities, rather than what can be seen in laboratory or other controlled conditions. As we will show, however, the methods used to assess children’s involvement in everyday mathematics heavily influence the apparent extent of their involvement.