Search

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.

BACKGROUND: Transition-age youth (TAY) with depressive disorders struggle with finding and retaining gainful employment. Thousands of these youth enroll in the state-federal vocational rehabilitation (VR) program each year to improve their employment outcomes. However, there is a dearth of information on the factors that facilitate or impede their success in the program. OBJECTIVE: The study aims to shed light on the effects of demographic characteristics and vocational rehabilitation services on successful employment and earnings of TAY with depressive disorders in the state-federal VR program. METHOD: The sample comprised of 4,772 participants drawn from the Rehabilitation Services Administration dataset. Regression analyses were employed to examine the effects of demographic characteristics and vocational rehabilitation services on successful employment and earnings. RESULTS: Results indicated that employment outcomes varied by demographic characteristics such as race/ethnicity, severity of disability and level of education. Also, certain VR services had significant positive or negative relationships with successful employment and earnings. CONCLUSIONS: Highlighting the promise of the state-federal programs for supporting TAY with depressive disorders to successfully participate in the labor market, findings from this study expand upon the literature by suggesting practices and services for optimizing employment potentials of this population.

This article introduces the special section on adaptive interventions and sequential multiple-assignment randomized trial (SMART) research designs. In addition to describing the two accompanying articles, we discuss features of adaptive interventions (AIs) and describe the use of SMART design to optimize AIs in the context of multitiered systems of support (MTSS) and integrated MTSS. AI is a treatment delivery model that explicitly specifies how information about individuals should be used to decide which treatment to provide in practice. Principles that apply to the design of AIs may help to more clearly operationalize MTSS-based programs, improve their implementation in school settings, and increase their efficacy when used according to evidence-based decision rules. A SMART is a research design for developing and optimizing MTSS-based programs. We provide a running example of a SMART design to optimize an MTSS-aligned AI that integrates academic and behavioral interventions.

Previous studies demonstrate the positive effects of explicit mathematics intervention on the mathematics outcomes of students at risk for mathematics difficulties (MD). One such intervention was the Tier 2 Booster Intervention (T2BI), a supplemental mathematics intervention focused on whole number concepts and skills that detailed the explicit and systematic instructional design of T2BI. However, findings from past research suggest that some students do not adequately respond to this purposefully designed intervention. Against that backdrop, the focus of this study is to address this notion of minimal response to intervention by integrating a select set of validated Cognitive Learning Principles (CLPs) into T2BI and investigating the extent to which students with MD respond favorably to the resulting intervention. Employing a multiple baseline design, our results showed a functional relation between the provision of an intervention with CLPs and increasing accuracy scores on both proximal and distal measures across the four participants with MD. These findings and their broader implications using CLPs to reduce minimal response to well-designed mathematics interventions are discussed.

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...

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.

This study, which was reviewed through the Registered Report process, examined the initial efficacy of the Scientific Explorers program (Sci2) on second-grade students’ science achievement. Sci2 is grounded in the growing body of empirical research on science instruction, embedding principles of explicit instruction within a guided inquiry-based design framework. Eighteen second-grade classrooms were randomly assigned to treatment or control conditions. A cluster randomized controlled trial was employed, with 294 students nested within classrooms and classrooms nested within condition. The Sci2 program was implemented for a total of 10 lessons (5 hr) in treatment classrooms, whereas control classrooms provided business-as-usual science instruction. Overall treatment effects were observed on three of four science outcome measures. The reported effects were moderate to large, with effect sizes (Hedges’ g) ranging from 0.48 to 0.94. Moderation analyses indicated that science knowledge at pretest did not moderate Sci2’s effects. Implications for practice and research are discussed.

This study examined the cost-effectiveness of a 50-lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS. The study utilized a randomized...

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated risk for severe MD at kindergarten entry and examined whether these students improved from a category of high MD risk (i.e.

This study examined whether the efficacy of ROOTS, a 50-lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, differed by group size an...

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 mathematics intervention for elementary students (i.e., Grades 1–5). We examined implementation fidelity following recommendations made by Dane and Schneider (1998), O’Donnell (2008), and DeFouw et al. (2009) to capture a comprehensive representation of the implementation fidelity data collected and reported within mathematics intervention studies. We organized our conceptualization of implementation fidelity into four overarching categories and nine dimensions within those categories: intervention design (i.e., theories of change and logistics), fidelity of implementor (i.e., adherence, quality of delivery, dosage, and implementor knowledge or experience), student engagement, and treatment analysis (i.e., treatment differentiation and analysis of implementation fidelity). Overall, findings indicate many author teams reported adherence data and dosage data, but significantly fewer studies reported quality of delivery data, student engagement data, or treatment differentiation data. In addition, author teams were more likely to report at least one form of logistics, such as implementor support, than theories of change. Implications for research and practice are discussed.

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 issue details five areas in which teachers can use number lines to support acquisition of critical mathematics concepts and skills.

This article focuses on implementing the Science of Math through a culturally responsive framework designed to support culturally and linguistically diverse students in math classrooms. We consider the influence of (second) language acquisition and instructional environments for students in addition to specific ways to increase instructional engagement with considerations of students’ cultural identity, prior experiences, and dual language development. Key features of the culturally responsive math instruction framework for dual language learning students with and at risk for math disabilities include utilizing culturally and linguistically appropriate assessment, anti-biased contextual supports, linguistics supports within math curriculum, and sustaining home-school collaborations. Implications for applying the framework for math instruction are discussed.

Instructional interactions that occur between teachers and students around foundational mathematics topics are critical for supporting mathematical proficiency among students with mathematics learning disabilities (MLD). This study investigated whether the initial mathematics skill of 880 kindergarten students at risk of MLD predicted the quantity and quality of explicit instructional interactions (i.e., overt teacher modeling, student practice opportunities, and academic feedback) experienced during an empirically validated Tier 2 kindergarten mathematics intervention. It also examined whether the quantity and quality of such instructional interactions predicted gains in student mathematics achievement. Researchers conducted 740 direct observations of 255 intervention groups within a multiyear, randomized controlled trial. Results suggested that intervention groups with lower initial mathematics skill received higher rates of academic feedback and made more frequent errors. In addition, more frequent and higher quality academic feedback and group practice opportunities predicted increased mathematics achievement. Implications for investigating the active ingredients of mathematics interventions are discussed.

In this synthesis, we reviewed 65 studies involving elementary students (i.e., grades 1–5) identified with mathematics difficulty (MD) in which authors implemented a mathematics intervention. Of these studies, we identified 33 group designs, 9 quasi-experimental designs, and 23 single-case designs. We aimed to synthesize performance differences between students with MD with and without reading difficulty (RD). We identified three categories of students for analysis: Students with MD+RD, MD-alone, or MD-nonspecified (i.e., no reading information provided). Overall, 80% of studies included students with MD-nonspecified, and the interventions for these students demonstrated strong effects. For the limited number of studies with students with MD+RD or MD-alone, intervention effects were strong for students with MD+RD and variable for students with MD-alone. In the three studies directly comparing the performance of students with MD+RD versus MD-alone, we noted differential patterns of performance. To tailor interventions to student need, more research must be conducted to understand whether students with MD with variable reading profiles respond differentially to mathematics intervention.

The provision of high-quality early mathematics instruction and intervention is critical to ensure that all students are on track for academic success. Given this, identifying and utilizing assessments that can enable the detection of nonresponse to mathematics instruction is a critical aspect of early intervention. To this end, the current study explored the extent to which there were distinct patterns of performance on embedded assessments for intervention participants within the context of a large-scale randomized control trial of the ROOTS intervention. This study also examined how performance on embedded assessments was associated with pretest mathematics scores and residual gains on mathematics measures, and how those associations differed based on (a) the point in the intervention when students demonstrated difficulty, and (b) intervention intensity. Findings from this study suggest that participants fell into 4 distinct performance categories and performance classifications were associated with pretest measures and gains in mathematics achievement. Study results also highlight the potential relevance of instructional intensity and timely monitoring of student performance. Implications for intervention and instructional planning in the context of tiered instructional delivery models are discussed. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Well-designed mathematics instruction focused on concepts and problem-solving skills associated with measurement and data analysis can build a foundational understanding for more advanced mathematics. This study investigated the efficacy of the Precision Mathematics Level 1 (PM-L1) intervention, a Tier 2 print- and technology-based mathematics intervention designed to increase first-grade students’ conceptual understanding and problem-solving skills around the areas of measurement and data analysis. Employing a randomized controlled trial, 96 first-grade students at risk for mathematics difficulties were randomly assigned within classrooms to either a treatment (PM-L1) or a control (business-as-usual) condition. A statistically significant positive effect was found on one of five outcome measures, with the other four showing positive but nonsignificant results. Results also suggested preliminary evidence of differential response based on students’ number sense and early literacy risk status. Implications for using mathematics interventions focused on measurement and data analysis to build comprehensive, multitiered service delivery models in mathematics are discussed.

English learners (ELs) represent a rapidly growing subgroup in US schools. Yet, converging evidence suggests that a concerning number of ELs struggle to reach proficient levels in mathematics. The purpose of this multi-site randomized controlled trial was to examine the treatment effects of a Tier 2 mathematics intervention on the mathematical outcomes of kindergarten ELs with mathematics difficulties (MD). Additionally, recognizing that students differently benefit from early mathematics interventions, the study also examined whether specific student-level variables predicted ELs’ differential response to the intervention. A total of 295 ELs from 138 kindergarten classrooms participated in the study. Findings indicated overall treatment effects on five mathematics outcome measures. Results also suggested that the intervention worked equally well across a diverse sample of at-risk ELs with varying mathematics skills and English proficiency levels. Implications in terms of using principles of explicit instruction to improve the design of mathematics interventions and furthering the knowledge base of effective instruction for ELs with MD 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.

Implementation of evidence-based practices (EBPs) is paramount to students’ development of mathematics proficiency. This study investigated “practice-based evidence” of interventionists’ actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a federally funded efficacy trial involving a Tier 2 first-grade mathematics intervention to examine whether the quantity and quality of explicit mathematics instruction was associated with the mathematics outcomes of 470 first-grade students with or at risk for mathematics learning disabilities. Associations between group-level pretreatment skill levels and the quality and quantity of explicit mathematics instructional practices used in the intervention were also explored. Findings suggested significant associations between positive gains in student mathematics outcomes and (a) lower rates of incorrectly answered mathematics-focused questions, and (b) the rate in which interventionists delivered group-level practice opportunities and offered academic feedback. Significant associations were also found between initial student mathematics performance and rates of student errors and the quality of explicit instruction. Implications for using direct observation to document enacted EBPs are discussed.

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK–12 Design and Development project focused on building mathematical proficiency with the critical concepts and problem-solving skills of early measurement and data analysis among first- and second-grade students with MD. The Precision Mathematics curriculum incorporates (a) technology-based activities that offer individualized opportunities for instruction and practice and (b) hands-on activities that promote small-group instructional interactions. Our production of the first-grade Precision Mathematics intervention was grounded in the CRF, which involves a series of iterative cycles of development, implementation field-testing, analysis, and revision. Results from initial implementation studies suggest that teachers and students can feasibly implement the first-grade Precision Mathematics intervention in authentic education settings. Challenges faced in developing technology-based mathematics interventions are discussed.

This study examined the role of initial skill in moderating intervention effects of a 50-lesson mathematics intervention program, ROOTS, for at-risk kindergarten students focused on developing whole-number concepts and skills. The study utilized a randomized block design with at-risk students ( n = 592) within classrooms ( n = 60) randomly assigned to one of two treatment conditions (a small group of two to five students) or control condition. Proximal and distal measures were collected in the fall (pretest), spring (posttest), and winter of first grade (delayed posttest). Analyses examined the moderating effects of initial student achievement level on mathematics outcomes. Results indicated that initial skill moderated student outcomes but the relationship did not differ by group size. Implications for tiered mathematics instruction are discussed.

Early number skills are a critical aspect of early mathematics development. However, the constructs that comprise early number skills differ across assessments, and previous studies have proposed v...

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities and the quality of explicit instruction served as treatment intensity metrics. A total of 465 kindergarten students with mathematics difficulties from 136 intervention groups participated. Results suggested comparable performances between the 2:1 and 5:1 intervention groups on six outcome measures. Observation data indicated that student practice differed by group size. Students in the 5:1 groups received more opportunities to practice with their peers, while students in the 2:1 groups participated in more frequent and higher quality individualized practice opportunities. Implications in terms of delivering Tier 2 interventions in small-group formats and engaging at-risk learners in meaningful practice opportunities are discussed.

A primary aim of mathematics programs is to accelerate the achievement of all students, including students with or at risk for learning disabilities (LD) in mathematics. Yet research suggests that many programs fail to incorporate the instructional design and delivery principles that have been validated to meet the learning needs of students with or at risk for LD in mathematics. This article provides special education teachers with a practical guide for assessing and evaluating the extent to which mathematics programs contain validated principles of explicit mathematics instruction. An example illustrates how teachers can apply the evaluation guide and use the results to address potential instructional shortfalls of mathematics programs.

A growing body of research suggests that the effects of core mathematics instruction on student mathematics outcomes may not be uniform across different skill levels in mathematics. This study investigated the extent to which observed components of explicit mathematics instruction explained why students’ initial mathematics achievement was previously found to moderate the treatment impact of an empirically validated, core kindergarten mathematics program. Instructional components examined were as follows: (a) teacher demonstrations and explanations of mathematical concepts, (b) group and individual student practice opportunities, and (c) teacher-delivered academic feedback. Findings suggest that the rate in which teachers facilitated individual student practice opportunities during core mathematics instruction explained the program’s differential effectiveness. Implications in terms of differentiating practice opportunities for at-risk learners and utilizing classroom observation data to test potential mediating variables of academic interventions are discussed.

Accumulating research has established explicit mathematics instruction as an evidence-based teaching practice. This study utilized observation data from a multi-year efficacy trial to examine the longitudinal effects of a core kindergarten mathematics program on the use of explicit mathematics instruction among two distinct groups of teachers: one group that used standard practices in Year 1 of the efficacy trial and the core program in Year 2, and a second group that used the core program in both years. Targeted teaching practices consisted of teacher models, student practice opportunities, and teacher-provided academic feedback. Implementation of the program in Year 2 was found to increase the mean rates of teaching practices of teachers who used standard teaching practices in Year 1. Effect sizes are also suggestive of a positive impact of a second year of implementation with the core program. Implications for designing explicit mathematics programs and investigating evidence-based practices in future research are discussed.

With the increasing availability of technology and the emphasis on science, technology, engineering, and mathematics education, there is an urgent need to understand the impact of technology-mediated mathematics (TMM) interventions on student mathematics outcomes. The purpose of this study was to review studies on TMM interventions that target the mathematical outcomes of K–12 students with or at risk for mathematics learning disabilities (MLDs). A review of the literature revealed 19 studies (9 single-case and 10 group/quasi experimental designs) published between 2000 and 2016. Results suggest that TMM interventions had mainly positive results on the mathematics outcomes of students with or at risk for MLD. This study also examined the extent to which principles of explicit instruction were integrated in TMM interventions. While many of the interventions provided frequent practice opportunities with academic feedback, few complemented such practice opportunities with overt demonstrations and explanations of mathematical content. Implications for designing TMM interventions are discussed.