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More than two-thirds of middle school students do not read proficiently. Research has shown that targeted interventions using explicit instruction methods can improve reading outcomes for struggling readers. A central feature of explicit instruction is the systematic implementation of instructional interactions, but it is not clear what specific instructional interaction practices lead to stronger outcomes for middle school readers. This study used a regression discontinuity design to compare the frequency and impact of instructional interactions experienced by U.S. eighth-grade students who received a targeted reading intervention (n = 1,461) with those who did not (n = 4,292). Results indicated that students who received intervention experienced far more instructional interactions with their teachers than did students who did not. However, the association between rates of interaction and student need in the intervention group was minimal, and the relationship between the rate of instructional interactions and reading growth was mixed. Implications for intervening with struggling students in the middle grades are discussed.

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240 first-grade students with mathematics difficulties in a new geographical region. Participating students were randomized into one of three conditions: (a) 2:1 mathematics intervention group, (b) 5:1 mathematics intervention group, or (c) business-as-usual instruction. Relative to the original study, findings from the replication varied. When comparing the treatment groups to the control, results suggested positive effects on all outcome measures, including a follow-up assessment administered one year later. However, differences between the two treatment groups based on group size were not found in the mathematics outcome measures. Both groups also received commensurate levels of observed instructional interactions. Implications for unpacking contextual differences between original research and their replications as well as using future research to explore the quantity and quality of instructional interactions as ways to explain variation in findings of group size are discussed.

Effective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the relationship between classroom management and student mathematics achievement within the context of ROOTS, a validated Tier 2 kindergarten mathematics intervention taught by paraprofessionals. Results show that the quality of classroom management within the ROOTS intervention predicted gains in student mathematics achievement from pretest to posttest. These findings have critical implications for practitioners, including the importance of integrating effective classroom management techniques into Tier 2 mathematics intervention groups and supporting paraprofessionals' knowledge and use of effective classroom management.

Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics courses. However, recent research has demonstrated that utilizing effective instructional design, such as the use of a number line with systematic and explicit instruction, can result in academic progress for students with LD in mathematics. This article presents teachers with a four-step teaching sequence utilizing the number line and effective strategies for teaching students with LD in mathematics to introduce fraction-to-decimal relationships in upper elementary, a prerequisite for middle school mathematics.

Number lines can benefit students in learning an array of mathematical concepts. An area of mathematics where number lines are visibly underused is in teaching measurement concepts. For students in upper elementary grades, accurate measurements require the use of mathematical precision and coordination, including skills in fractions and decimals, operations, and magnitude. A robust knowledge of measurement holds significant value in students' development of mathematical proficiency, particularly for students with learning disabilities in mathematics. Using number lines to teach and perform mathematical processes involving measurement can build fluency and conceptual understanding for all learners, including those with learning disabilities. This article demonstrates the versatility of integrating number lines into mathematical interventions involving measurement concepts for students with learning disabilities in mathematics. Measurement content discussed includes distance, time intervals, liquid volume, and mass. Scenarios with examples of how to apply number lines to each measurement form are described.

The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of pretest variability within intervention groups using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics pretest variability within ROOTS groups predict student gains from the intervention, and is this relationship moderated by (a) intervention group size (two- vs. five-student groups), (b) quality of explicit instruction, or (c) group-level initial skill? We found that ROOTS groups with greater pretest variability on a closely aligned mathematics measure experienced smaller gains from the intervention. This association was more impactful in larger intervention groups (i.e., five-student groups compared with two-student groups) and in groups with higher quality of explicit instruction. We unpack these findings and conclude with recommendations for practice and future research.

The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these recommendations coupled with the myriad ways in which number lines can be used, little hands-on guidance has been provided how best to leverage number lines in mathematics instruction. This special series details five areas in which teachers can use number lines to support acquisition of critical mathematics concepts and skills.

This study investigated the technical characteristics of four early measurement curriculum-based measures (EM-CBMs) designed to assess concepts related to linear measurement and iteration. The sample consisted of 221 first grade students. Data were collected at two time points approximately 10 weeks apart. Reliability and concurrent and predictive validity correlations were in the low to moderate range. We discuss study results related to screening for risk status including limitations to the current work and future directions for research. Impact Statement: The importance of measurement in mathematics development is garnering increased attention. Exploring measures to screen students for risk status is critical to enable schools to allocate resources to students in need of intervention services. The findings in this manuscript represent a first exploratory attempt to develop screening measures in the area of measurement.