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We replicated a study of a kindergarten mathematics intervention, ROOTS, delivered in the context of a research-based core program. We randomly assigned 62 classrooms to treatment (ROOTS) or a business-as-usual control. All classrooms implemented the research-based core program (Early Learning in Mathematics). Participants included 163 treatment students and 145 control students nested within classrooms. Key differences between the current replication study and the original study included geographical region, instructional context, and student initial skill. In contrast to the significant positive effects (Hedges’s g values of .30 to .38) found in the original study, no significant differences were found between the treatment and control conditions in this study (Hedges’s g values of –.09 to .12) Pretest skills did not moderate treatment effects. We discuss these results’ implications for replication research and evaluating intervention efficacy.

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 samp...

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students ( n = 198) were assigned to the treatment or control condition at the school level. Proximal and distal measures of math proficiency were collected in the fall (pretest) and spring (post-test). Analyses examined initial student achievement as a moderator of mathematics outcomes. Results indicated that intervention outcomes were not moderated by initial skill. Implications for tiered mathematics instruction and future mathematics intervention research are discussed.

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.

This pilot study examined the promise of a Tier 2 Grade 6 intervention program for students at risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting Algebra Readiness program consisted of 93 lessons across four strands focused on key concepts and applications of fractions. Measures of mathematics achievement were collected at pretest and posttest. Feasibility and usability data indicated favorable impressions by users and strong levels of implementation fidelity. Gain scores of treatment students were significantly greater than those of control peers on two of four proximal measures of mathematics achievement. Positive nonsignificant effects were found on additional proximal and distal measures. Implications for educators delivering instruction for at-risk students in multitier service delivery models are discussed.

Being able to understand, interpret, and critically evaluate data is necessary for all individuals in our society. Using the PreK-12 Guidelines for Assessment and Instruction in Statistics Education-II (GAISE-II; Bargagliotti et al., 2020) curriculum framework, the current paper outlines five evidence-based recommendations that teachers can use to build understanding of statistical investigation and data analysis for students with mathematics difficulties, including: (1) Explicitly teach important vocabulary related to statistical investigation and data analysis, (2) Introduce the steps and purpose of statistical investigation, (3) Guide students through the statistical investigation process, (4) Link investigative questions to word problem types to solve, and (5) Build understanding of variability throughout.

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.