Evaluating a gated screening approach for identifying risk in kindergarten mathematics.

The purpose of the present study was to examine the diagnostic accuracy of different universal screening approaches for identifying mathematics difficulties in kindergarteners. We used extant data from 2,010 kindergarten students from 23 schools across two states. First, we identified the diagnostic accuracy of two individual screeners: (a) a set of three curriculum-based measures (CBM) and (b) a diagnostic measure, the Number Sense Brief (NSB). Then, we determined the diagnostic accuracy of a gated screening approach considering both the CBM and NSB. The criterion measure was a norm-referenced mathematics achievement test. The results indicated that area under the curve values met or exceeded .80 for both individual screeners; however, the number of false positives was high. The gated screening approach yielded fewer false positives at the expense of increasing false negatives. Directions for future research and the practical implications of the results for screening in kindergarten mathematics are discussed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Measuring Instructional Interactions During Reading Instruction for Students Receiving Intervention in Middle School.

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 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.

Proficiency With Number Concepts and Operations: Replicating the Efficacy of a First-Grade Mathematics Intervention.

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.

Examining Interactions Across Instructional Tiers: Do Features of Tier 1 Predict Student Responsiveness to Tier 2 Mathematics Intervention?

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.

A Synthesis of the Conceptualization and Measurement of Implementation Fidelity in Mathematics Intervention Research.

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.

Multitiered Systems of Support, Adaptive Interventions, and SMART Designs.

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.

Using Direct Observation to Document "Practice-Based Evidence" of Evidence-Based Mathematics Instruction.

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.

Kindergarteners at Risk for Severe Mathematics Difficulties: Investigating Tipping Points of Core Mathematics Instruction.

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., <10th percentile) to a lower risk of MD (i.e., norm-referenced performance at or above the 10th, 20th, 30th, and 40th percentiles) between the fall and spring of kindergarten. Differential response to the program based on the classroom-level proportion of students with severe MD was also explored. A total of 795 kindergarteners with severe MD from 122 classrooms were included in the analyses. Results suggested students with severe MD in treatment classrooms improved from fall to spring at a greater rate than their control peers. Treatment students also demonstrated higher rates of improvement from below the 10th percentile to a performance at or above the 20th, 30th, and 40th percentiles across the school year. No evidence of differential efficacy of the program by the classroom-level proportion of students with severe MD was found. Implications for using explicit mathematics programs to thwart the onset of severe MD among academically vulnerable students are discussed.

A Synthesis of Elementary Mathematics Interventions: Comparisons of Students With Mathematics Difficulty With and Without Comorbid Reading Difficulty.

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.

Exploring the utility of assessing early mathematics intervention response via embedded assessment.

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).

Student Practice Opportunities in Core Mathematics Instruction: Exploring for a Goldilocks Effect for Kindergartners With Mathematics Difficulties.

Opportunities for practice play a critical role in learning complex behaviors. In the context of explicit mathematics instruction, practice facilitates systematic opportunities for students with mathematics difficulties (MD) to learn new mathematics content and apply such knowledge and skills to novel mathematics problems. This study explored whether there is an optimal amount of student practice that teachers should provide in core mathematics instruction to maximize the mathematics achievement of kindergarten students with MD, a so called "Goldilocks effect," as opposed to simply "more is better." Results from observation data collected in a large-scale efficacy trial supported the latter rather than the former. Specifically, we found that three individual practice opportunities for every explicit teacher demonstration of mathematical content was associated with increased mathematics achievement for students with MD relative to fewer practice opportunities. Implications for facilitating frequent student practice opportunities during core mathematics instruction and designing professional development for teachers who work with students with MD are discussed.

Examining the Impact of Group Size on the Treatment Intensity of a Tier 2 Mathematics Intervention Within a Systematic Framework of Replication.

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.

Examining the Efficacy of a Tier 2 Kindergarten Mathematics Intervention.

This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. Gain scores of at-risk intervention students were significantly greater than those of control peers, and the gains of at-risk treatment students were greater than the gains of peers not at risk, effectively reducing the achievement gap. Implications for Tier 2 mathematics instruction in a response to intervention (RtI) model are discussed.