The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is…

When a student struggles with a mathematics task, adults may rephrase or expand initial task instructions to clarify instructions or scaffold problem solving. Yet expanded instructions may not benefit all children, especially children with a mathematics learning disability (MLD). Here, we explore whether expanded instructions differentially affect…

The present study analyzed the relationship between domain-general abilities and fraction knowledge in fifth grade, and investigated the mediating role of division competence in that relationship. Children (n = 175) were assessed in fourth grade on domain-general abilities (selective attention, working memory, fluid intelligence) and on division…

We analyzed the effects of a game-based, supplemental fraction curriculum on fourth and fifth grade students' fraction knowledge, engagement, and STEM interest. Students with and without disabilities with intersecting identities (e.g., race, disability status, gender) comprised the sample. Results indicate significant differences in fraction…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined…

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…

A number of studies have demonstrated links between linguistic knowledge and performance in math. Studies examining these links in first language speakers of English have traditionally relied on correlational analyses between linguistic knowledge tests and standardized math tests. For second language (L2) speakers, the majority of studies have…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…

The purpose of the present study was to reveal the developmental pathway from third grade cognitive competencies to sixth grade conceptual and procedural fraction knowledge through the intervening whole numerical skills at fifth grade. The study used empirical data that come from 536 students in nine schools across two Delaware public school…