Fractions are an important mathematical concept for elementary students. However, students with mathematics learning disabilities (MLD) struggle with learning fractions. Research has demonstrated that concrete-representational-abstract (CRA) instruction is an effective practice for students with learning and developmental disabilities. Here we…

Fractions are an important mathematical concept for both more advanced mathematical concepts and daily living activities (e.g., cooking) and thus are important for all students to learn. In this study, researchers explored the use of the virtual-abstract (VA) instructional sequence to teach three middle school students with disabilities three…

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in…

This study's first purpose was to investigate effects of a fourth- and fifth-grade "next-generation" fraction intervention, which included six enhancements over a previously validated fraction intervention, designed to address career- and college-readiness standards. The study's second purpose was to assess effects of the next-generation…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

The purpose of the systematic review of mathematics intervention syntheses was to identify patterns and gaps in content areas, instructional strategies, effect sizes, and definitions of learning disabilities (LD), mathematics LD (MLD), and mathematics difficulty (MD). Using rigorous inclusion criteria, we evaluated 36 syntheses that included 836…

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: "Referent units," "Reversibility," "Partitioning and iterating," and…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students' understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related…

When designing professional development for math teachers, teacher confidence, math anxiety, and student performance are factors to consider. St. Lucie Public Schools in Florida has seen a decline in performance in fifth-grade mathematics, where students are first asked to showcase their knowledge on operations for fractions. As a curriculum…

This article provides results from a study examining the impact of a self-regulated strategy development (SRSD) intervention on the fraction calculations of three Grade 5 male students with or at-risk for emotional or behavioral disorders using a multiple-baseline across students, single-case design. The teacher-led SRSD Fractions intervention…

This qualitative semi-structured interview study investigated how the opportunity to learn with productive struggle emerges in a teacher's beliefs, anticipation, planning, teaching, and response to struggle in learning mathematics. In this study, the experiences of student struggle in the teaching and learning of fractions was investigated through…

Mathematics instruction can work to open or constrain children's opportunities to learn, and the busy, interactive nature of instruction makes it challenging for researchers to identify patterns in high-quality opportunities to learn. While researchers have documented how whole-group discussions and small-group work can contribute to such…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

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…