In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

We examined the associations of cognitive skills, math-related emotions and beliefs, and gender with responses to an arithmetic fluency intervention. Elementary school children with dysfluent arithmetic skills (N=69) participated in an arithmetic fluency intervention (with and without self-efficacy support) implemented in small groups in schools…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

The majority of college students are not ready for college-level math courses, which, when completed, have been shown to increase graduation and transfer rates. To address this problem, the Math My Way (MMW) program was developed to integrate module-based curriculum and mastery learning approaches. The program is based on Seidman's retention…

This paper reports the results from one of a series of related, collaborative studies carried out in Sandy Bay, Tasmania, Australia, in 1979 and 1980, examining how young children acquire the skills to represent and solve addition and subtraction problems. The purpose of this study was to relate children's cognitive processing capabilities and…