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High-quality Tier 1 instruction is frequently conceptualized as the "foundation" for other tiers of intervention within multitiered systems of support (MTSS) models. However, the vast majority of Tier 2 intervention studies do not account for Tier 1 variables when examining intervention effectiveness. The purpose of this study was to examine Tier 1 predictors, or "quality indicators," of differential responsiveness to Tier 2 mathematics intervention. Data were drawn from a large-scale data set where all teachers taught the Early Learning in Mathematics (Tier 1) core program across the academic year, and a subset of students were selected for the ROOTS (Tier 2) mathematics intervention. We examined the following Tier 1 variables: (a) classroom-level mathematics gains, (b) Tier 1 fidelity of implementation, (c) Tier 1 classroom management and instructional support, and (d) class size. Response to Tier 2 intervention was not significantly predicted by any of the Tier 1 variables examined; however, the pattern of Hedges' g effect sizes suggested that students with higher quality of Tier 1 instruction tended to benefit less from the Tier 2 ROOTS intervention. Results are discussed in the context of implications for research and practice. [For the corresponding grantee submission, see ED626857.]

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. Practitioner points: Gains in student mathematics achievement in a Tier 2 kindergarten mathematics intervention were significantly associated with the quality of interventionists' classroom management.Effective small group management techniques may be more important in intervention groups with smaller student‐to‐teacher ratios.School psychologists and other personnel involved in schoolwide processes such as Multi‐tiered Systems of Support should intentionally support instructors to use effective classroom strategies while delivering mathematics instruction, across instructional tiers of support. [ABSTRACT FROM AUTHOR]

The purpose of this quantitative systematic literature review was to identify and describe published mathematics studies from 1980 to 2021 that incorporated a self-monitoring component (k = 22 studies; N = 1,787 students). We examined specific self-monitoring procedures, instructional contexts, implementation variables, and methodological quality. For inclusion, studies needed to (a) include self-monitoring (defined as students observing, evaluating, and/or recording their behaviors), (b) include co-occurring mathematics instruction, (c) include at least one mathematics outcome measure, (d) occur in a school setting, (e) include students in Grades K–12, and (f) utilize a single-case, experimental, or quasiexperimental design. Variables of interest were coded and methodological quality was assessed using What Works Clearinghouse standards. Our findings suggest that students with and without disabilities generally benefit from embedded self-monitoring procedures across mathematical content areas and tiers of instructional support. Future research should further unpack definitions of self-monitoring and related constructs. [ABSTRACT FROM AUTHOR]

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help students represent and solve problems involving addition, subtraction, multiplication, and division with fractions while building conceptual understanding of the underlying operations. Evidence-based strategies for using number line models to teach fraction arithmetic concepts and skills are described and specific examples provided to illustrate how teachers can strategically integrate number line models with other mathematical representations to support the development of flexible understanding of fractions. [ABSTRACT FROM AUTHOR]