Improving the Numerical Understanding of Children From Low-Income Families

Children from low-income backgrounds enter school with much less mathematical knowledge than their more affluent peers. These early deficits have long-term consequences; children who start behind generally stay behind. This article describes how a theoretical analysis of the development of number sense gave rise to an intervention that reduces this gap by producing large, rapid, and broad improvements in the mathematical competence of low-income preschoolers. Roughly, an hour of playing a simple, inexpensive, linear number board game produces gains in numerical magnitude comparison, number line estimation, counting, and numeral identification. Reasons for these large gains are discussed. KEYWORDS—number; low income; intervention; mathematics; board games When children begin school, their mathematical knowledge already varies greatly. These early differences have long-term consequences. Children’s mathematical knowledge in kindergarten predicts their math achievement test scores in elementary school, middle school, and even high school (Duncan et al., 2007; Stevenson & Newman, 1986). The relationship between early and later mathematical knowledge is roughly twice as strong as that between early and later reading achievement (Duncan et al., 2007). This research was supported by Department of Education IES Grants R305H020060 and R305H050035. Thanks to Geetha Ramani, who collaborated on the research, and to the Allegheny and Westmoreland County Intermediate Unit Head Start classrooms that participated. Correspondence concerning this article should be addressed to Robert S. Siegler, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213; e-mail: [email protected]. a 2009, Copyright the Author(s) Journal Compilation a 2009, Society for Research in Child Development Volume 3, Number The stability of individual differences in mathematical knowledge makes it especially unfortunate that children from lowincome families begin school with much less mathematical knowledge than their wealthier peers. This early achievement gap is evident on a wide range of foundational tasks: counting from one, counting up or down from numbers other than one, recognizing written numerals, adding, subtracting, and comparing numerical magnitudes (Ginsburg & Russell, 1981; Jordan, Kaplan, Olah, & Locuniak, 2006; Jordan, Levine, & Huttenlocher, 1994; Starkey, Klein, & Wakeley, 2004). These differences in mathematical knowledge between preschoolers from more and less affluent backgrounds reflect differences in environmental support for learning. Middleincome parents engage in a broader range of explicitly mathematical activities with their children, and engage in these activities more frequently, than do low-income parents (Clements & Sarama, 2007; Starkey et al., 2004). Parents who engage in more numerical activities generally have children with greater mathematical knowledge (Blevins-Knabe & Musun-Miller, 1996). These findings highlight the importance of identifying activities that can substantially improve the numerical knowledge of preschoolers from low-income backgrounds and that can be promoted for widespread use. Over the past few years, Geetha Ramani and I have applied a theoretical analysis of the development of understanding of numerical magnitudes to generate and test the effects of one such activity. The activity is simple and inexpensive, yet it produces large improvements on a broad range of numerical skills and knowledge in roughly 1 hr. I first describe the theoretical analysis that led to the intervention, and then examine evidence for its effectiveness. THEORETICAL BACKGROUND Number sense is an important part of mathematical competence (e.g., National Mathematics Advisory Panel, 2008). However, there is little agreement on what number sense is—as with