A solid understanding of fractions is the cornerstone for acquiring proficiency with rational numbers and paves the way for learning advanced mathematical concepts, such as algebra. Fraction difficulties limit not only students' educational and vocational opportunities but also their ability to solve everyday problems. Students who exit 6th grade…

Efforts to increase moderate to vigorous physical activity (MVPA) in school-aged children are associated with improved health, cognitive, and academic outcomes. However, questions remain about whether similar benefits are observed in early childhood. We hypothesized that motor competence, not MVPA, would be related to improved cognitive and…

The focus of this article is the well documented association between low working memory capacity and difficulty with mathematical word-problem solving. We begin by describing a model that specifies how various cognitive resources, including working memory, contribute to individual differences in word-problem solving and by then summarizing…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude "comparison" and "estimation." Adults with higher…

Children's cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control is critical for developing both the relational representations necessary to reason and the ability to…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…

The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multi-component fraction…