Early number sense is a strong predictor of later success in school mathematics. A disproportionate number of children from low-income families come to first grade with weak number competencies, leaving them at-risk for a cycle of failure. The present study examined the effects of an 8-week number sense intervention to develop number competencies of low-income kindergartners (n = 121). The intervention purposefully targeted whole number concepts related to counting, comparing, and manipulating sets. Children were randomly assigned either to a number sense intervention or a business as usual contrast group. The intervention was carried out in small group, 30-minute sessions, 3 days per week for a total of 24 sessions. Controlling for number sense at pretest, the intervention group made meaningful gains relative to the control group at immediate as well delayed posttest on a measure of early numeracy. Intervention children also performed better than controls on a standardized test of mathematics calculation at immediate posttest.

Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to one of three groups (n = 44 in each group): a number sense intervention group, a language intervention group, or a business as usual control group. Accounting for initial skill level in mathematical knowledge, children who received the number sense intervention performed better than controls at immediate post test, with meaningful effects on measures of number competencies and general math achievement. Many of the effects held eight weeks after the intervention was completed, suggesting that children internalized what they had learned. There were no differences between the language and control groups on any math-related measures.

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children ( N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

Domain general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that attention problems and executive functioning both were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance while executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense.

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