Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing "mathematical" predictors, whether their predictive contributions are direct or indirectly mediated…

The aim of this study was to analyze the joint, relative, and unique predictive value of students' prior knowledge of mathematics (knowledge of fractions and ability to divide natural numbers) and general cognitive ability (fluid intelligence and working memory) upon general mathematics achievement in the last year of primary school. Seventy-five…

Background: Mastering fractions seems among the most critical mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and…

Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. Aims: To examine the extent to which…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

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…

Background: Prior research with adults and children suggests that inhibitory control may have a role to play in learning counterintuitive fractions and decimals that are inconsistent with whole number knowledge. However, there is little research to date with primary school-aged children at the early stages of fraction and decimal instruction that…

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…

Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we…

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of…