Nancy Dyson

A Number Sense Intervention for Low-Income Kindergartners at Risk for Mathematics Difficulties

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 to either a number sense intervention or a business as usual contrast group. The intervention was carried out in small-group, 30-min 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.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement.

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 both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas 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.

Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children with Mathematics Difficulties.

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.

Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties.

The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as “equal,” “more,” and “less,” and associated number concepts would increase at-risk children’s vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were recruited from kindergarten classes in four schools. Participants were randomly assigned to one of three groups: a storybook number competencies (SNC) intervention, a number sense intervention, or a business-as-usual control. Interventions were carried out in groups of four children over 8 weeks (24 30-minute sessions). Findings demonstrated that the SNC intervention group outperformed the other groups on measures of mathematics vocabulary, both in terms of words that were closely aligned to the intervention and those that were not. There was no effect of the SNC intervention, however, on general mathematics measures, suggesting a need to provide the mathematics vocabulary work along with more intensive instruction in number concepts.

Catching Math Problems Early: Findings From the Number Sense Intervention Project

This chapter provides an overview of a kindergarten (ie, children 5–6 years of age) number sense intervention that was developed and tested over a 4-year period. The intervention targeted core understandings of number, number relations, and number operations in high-risk learners. Over multiple trials, we obtained moderate to strong effect sizes, relative to controls, on a measure closely aligned to the intervention topics (ie, a number sense brief screener) as well as on a test of mathematics calculation achievement. Many of the gains were still present 2 months after the intervention ended. Catching number sense weaknesses early positions children for later success in formal mathematics.