operations as opposed to more general cognitive deficits (e.g., Gersten et al., 2005; Malofeeva et al., 2004). Weak number competency is reflected in poorly developed counting procedures, slow fact retrieval, and inaccurate computation, all characteristics of the disability (Geary et al., 2000; Jordan, Hanich, and Kaplan, 2003a). Skill with number combinations is tied to fundamental number knowledge (Baroody and Rosu, 2006; Locuniak and Jordan, in press). Accurate and efficient counting procedures can lead to strong connections between a problem and its solution (Siegler and Shrager, 1984). Developmental dyscalculia, a severe form of mathematics disability that has a known neurological basis, is explained more by domain-specific impairments in number knowledge than by domain-general deficits related to memory, spatial processing, or language (Butterworth and Reigosa, 2007). Although debate continues about the underpinnings of mathematics learning disabilities and diagnostic criteria (e.g., Geary et al., 2007), weakness in number sense appears to be a common theme in the literature. This finding has instructional implications for young children’s mathematics education. Specifically, early interventions that focus on number sense have the potential to improve children’s mathematics learning outcomes.
Early number competencies serve as a foundation for learning formal mathematics (Griffin et al., 1994; Miller, 1992). Deficits in these can prevent children from benefiting from formal mathematics instruction when they enter school, regardless of whether they are associated with environmental disadvantages or with genuine learning differences or disabilities (Baroody and Rosu, 2006; Griffin, 2007). In a recent study, Jordan and colleagues (in press) found that poor mathematics achievement is mediated by low number sense regardless of children’s social class. That is, deficits in number sense are a better predictor of poor mathematics achievement than SES when all else is equal. Implications of this work suggest that children from low-income backgrounds and those with mathematics difficulties would benefit from a mathematics intervention during the early years (Jordan et al., in press).
Number competencies appear to have neurological origins, with their core components (e.g., subitization and approximate number representations) developing without much formal instruction (Berch, 2005; Dehaene, 1997; Feigenson, Dehaene, and Spelke, 2004). These early foundations provide support for learning more complex number skills involving number words, number comparisons, and counting. Children with mathematics difficulties seem to have problems with the symbolic system of number, rather than the universal analog magnitude system. Knowledge of the symbolic number system is heavily influenced by experience and instruction (Geary,