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There Is Nothing So Practical as a Good Theory
Children from low-income families begin school with less mathematical knowledge than peers from middle-income backgrounds. This discrepancy has long-term consequences: Children who start behind usually stay behind. Effective interventions have therefore been sought to improve the mathematical knowledge of preschoolers from impoverished backgrounds. Some curriculum-based interventions have met with impressive success; two disadvantages of such interventions, however, are that they are quite costly in terms of the time and resources they require and their multifaceted lessons make it impossible to determine why they work. In this chapter, we describe a theoretical analysis that motivated the development of a simple, brief, and inexpensive intervention that involved playing a linear number board game. Roughly an hour of playing this game produced improvements in numerical magnitude comparison, number line estimation, counting, numeral identification, and ability to learn novel arithmetic problems by preschoolers from low-income backgrounds. The gains were greater than those produced by playing a parallel nonnumerical game or engaging in other numerical activities. Detailed analyses of learning patterns indicated that this theoretically motivated, game-based intervention exercises most of its effects by enhancing and refining children's representations of numerical magnitudes.