All citizens need a broad understanding of mathematics to function in today’s society, but mathematics proficiency rates in the United States are low (Ginsburg, Leinwand, Anstrom, & Pollock, 2005; Kilpatrick, Swafford, & Findell, 2001). International comparisons indicate that children in the United States perform worse in mathematics, and their lagging mathematics development is evident as early as preschool (Cross, Woods, & Schweingruber, 2009; Sarama & Clements, 2009; Starkey, Klein, & Wakeley, 2004). Importantly, children who live in poverty and who are members of linguistic and ethnic minority groups demonstrate significantly lower levels of mathematics achievement than their majority, middle-class peers (Clements & Sarama, 2011; Denton & West, 2002; National Assessment of Educational Progress [NAEP], 2013). Moreover, the achievement gap is wider in the United States than in any other country in the world (Akiba, LeTendre, & Scribner, 2007). Given that early mathematics knowledge is a stronger predictor of later mathematics achievement than even intelligence or memory abilities (Krajewski, 2005) and that children who begin with the lowest achievement levels show the lowest mathematics growth from Kindergarten to the third grade (Bodovski & Farkas, 2007), such achievement gaps in mathematics are pernicious (Claessens, Duncan, & Engel, 2009; Clements & Sarama, 2011; Horn, 2005; National Mathematics Advisory Panel [NMAP], 2008).
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