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…

Purpose: Most literature has focused solely on either knowledge about number sense or understanding of fractions. To fill the research gap, this study examined pupils' abilities in both number sense and fractions. In particular, it investigated Year 4 and Year 5 pupils' use of strategies in developing their fraction sense. Methodology: This study…

Fractions are foundational concepts for more advanced mathematics as well as used throughout daily living, for all students, including students with disabilities. This study explored the virtual-abstract (VA) instructional sequence with regard to the acquisition and maintenance of fraction behaviors for three middle school students with mild…

In an effort to expand our knowledge base pertaining to pre-K-8 prospective teachers' understanding of fractions, the present study was designed to extend the work on fractions schemes and operations to this population. One purpose of our study was to validate the fractions schemes and operations hierarchy with the pre-K-8 prospective teacher…

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4…

Ratio-proportion is one of the topics that middle school students have difficulty in comprehending. This study aims to determine the learning difficulties that seventh-grade students face while learning about ratio-proportion. Three commonly used strategies to solve ratio-proportion problems are buildup, unit ratio and cross-multiplication. The…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N=435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

The purpose of this study was to examine distinct latent classes of middle grades mathematics teachers with respect to reasoning about fractions. Survey response data came from a nationwide sample of 990 in-service middle grades mathematics teachers. The survey focused on four components of reasoning about fractions in terms of quantities:…

Many students fall below benchmarks in the area of fractions computation, particularly students with disabilities. Self-regulated strategy development (SRSD) is one strategy with proven effectiveness for improving outcomes for students with disabilities, although very few studies have applied SRSD to the area of mathematics. In this study, we used…

The teaching and learning fractions is one of the most problematic areas in primary school mathematics. A large number of studies have engaged paper-and-pencil test to measure students' instrumental understanding about fractions but few have sought to learn about children's fraction sense. This paper reports a study that investigated fraction…

As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit…

Historically, secondary students with emotional behavioral disorders (EBD) have made poor progress in mathematics putting them at risk for school failure and placement in an alternative setting. Two under studied areas essential to success in mathematics are fractions and algebra. The purpose of this study was to test the effects of a…

Proficiency with fractions is one of the most significant predictors of later mathematics achievement. However, there are currently no meta-analyses that assess the literature base on fractions for students with or at risk for disabilities using quality indicators. We applied the 2014 Council for Exceptional Children Standards for Evidence-Based…

Competence with fractions is foundational to acquiring more advanced mathematical skills. However, achieving competency with fractions is challenging for many students, especially for those with mathematics learning difficulties who often lack foundational skill with whole numbers. Teaching fractions is also challenging for many teachers as they…

The study has two primary purposes. The first was to examine the efficacy of the "Super Solvers" Fractions Intervention (SSFI) for third-grade students at risk for mathematics learning disabilities (MLD). The second was to test the added value of embedding self-regulation instruction into the SSFI. Students were randomly assigned to a…