In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

In intervention studies, high rates of "implementation fidelity" are important markers of a study's success; however, the definition of implementation fidelity is both complex and dynamic. In this synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a…

Teachers and caregivers use children's books (i.e., trade books) to support mathematics learning in school and home settings; shared book reading offers a unique opportunity to support students' understanding of operations and schema development. No prior studies have examined the representations of addition, subtraction, multiplication, and…

This quasi-experimental study was designed to investigate the initial efficacy of a fraction-vocabulary intervention for Grade 4 students with mathematics difficulty (MD) and to explore its impact on relevant fraction competencies. Thirty-three students were assigned to either the intervention condition (n = 16) or a business-as-usual comparison…

This study examined the influence of addition and subtraction practice embedded within a word-problem intervention for Grade 3 students experiencing word-problem difficulty. Students (N = 448) were randomly assigned to one of two variants of a word-problem intervention or a business-as-usual comparison condition. Within the word-problem…

Increasingly, students must demonstrate knowledge in mathematics through mathematics writing, yet research lags in understanding how students engage in mathematics-writing tasks. Most available research on mathematics writing focuses on typically achieving students without considering students with mathematics difficulty (MD). In this study, we…

In mathematics, the keyword strategy involves identifying a keyword and using that keyword to determine the operation needed to find a word problem's solution. We analyzed 747 high-stakes released items across grades 3, 4, 5, 6, 7, and 8. Of these, 57 items did not involve written text. Of the 690 text-based items, we classified 69% as directive…

In mathematics, the keyword strategy involves identifying a keyword (e.g., "altogether") and using that keyword to determine the operation needed to find a word problem's solution. We analyzed 747 high-stakes released items across Grades 3, 4, 5, 6, 7, and 8 from the Partnership for Assessment for Readiness for College and Careers and…

As students enter the upper elementary grades, word problems become a main component of mathematics instruction, increasing in complexity as students advance through the curriculum. For students identified as emergent bilinguals with mathematics difficulty (MD), the linguistic complexity inherent in word problems may serve as a barrier to…

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (N = 76) were randomly assigned to word-problem intervention (n = 56)…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

Some elementary students may exhibit challenging externalizing or internalizing behaviors in addition to difficulty with mathematics. In this study, we explored the behavioral patterns of 441 third-grade students with and without mathematics difficulty (MD). Compared with students without MD, students with MD demonstrated higher rates of…

Some elementary students may exhibit challenging externalizing or internalizing behaviors in addition to difficulty with mathematics. In this study, we explored the behavioral patterns of 441 3rd-grade students with and without mathematics difficulty (MD). Compared to students without MD, students with MD demonstrated higher rates of externalizing…

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…