Prevention: Necessary But Insufficient? A 2-Year Follow-Up of an Effective First-Grade Mathematics Intervention

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.

Exploring academic and cognitive skills impacting retention and acquisition of word-problem knowledge gained during or after intervention

In the present study, we investigated the impact of a word-problem intervention in retention and acquisition of knowledge after the intervention ended. We based analyses upon Grade 4 students experiencing mathematics difficulty (average age at pretest = 8.77) who received one of two variants of a word-problem intervention (with [n = 111] vs. without [n = 110] embedded pre-algebraic reasoning instruction) and students within a business-as-usual condition (BaU [n = 127]) separately. Findings revealed that students who received the intervention not only tended to retain less, but they also showed more active knowledge acquisition after the intervention ended. Furthermore, word-problem intervention altered the contributions of some prior knowledge and skills on both retention and acquisition.

Triangulating on developmental models with a combination of experimental and nonexperimental estimates

Plausible competing developmental models show similar or identical structural equation modeling model fit indices, despite making very different causal predictions. One way to help address this problem is incorporating outside information into selecting among models. This study attempted to select among developmental models of children's early mathematical skills by incorporating information about the extent to which models forecast the longitudinal pattern of causal impacts of early math interventions. We tested for the usefulness and validity of the approach by applying it to data from three randomized controlled trials of early math interventions with longitudinal follow-up assessments in the United States (Ns = 1,375, 591, 744; baseline age 4.3, 6.5, 4.4; 17%-69% Black). We found that, across data sets, (a) some models consistently outperformed other models at forecasting later experimental impacts, (b) traditional statistical fit indices were not strongly related to causal fit as indexed by models' accuracy at forecasting later experimental impacts, and (c) models showed consistent patterns of similarity and discrepancy between statistical fit and models' effectiveness at forecasting experimental impacts. We highlight the importance of triangulation and call for more comparisons of experimental and nonexperimental estimates for choosing among developmental models. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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.

Predicting Risk for Comorbid Reading and Mathematics Disability Using Fluency-Based Screening Assessments

The first purpose of this study was to examine the prevalence of risk for comorbid reading and mathematics disabilities (RMD) at start of first grade, when measured in a representative sample of 3,062 students with first-grade fluency measures (word reading; computation). The second purpose was to examine the utility of these measures for predicting RMD status within a sample of 577 students when RMD status was assessed at the end of second grade in terms of reading and math accuracy. When set at or below the 16^th percentile, first-grade risk for RMD was two times more common than chance; at or below the 7^th percentile, it was five times more common. Logistic regression showed that the two first-grade fluency measures accurately distinguished students with and without RMD in second grade; however, when cut scores were set to capture 85% of students with RMD, false positives were high. Overall, the results provide support for the use of fluency measures as an initial gating procedure in first grade, but additional gating steps appear necessary in the screening process to reduce false positives.

Closing the Word-Problem Achievement Gap in First Grade: Schema-Based Word-Problem Intervention with Embedded Language Comprehension Instruction

The main purpose of this study was to test the effects of word-problem intervention, with versus without embedded language comprehension instruction, on at-risk 1st graders' word-problem performance. We also isolated the need for a structured approach to word-problem intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n=391; mean age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based word-problem intervention with embedded language instruction, the same word-problem intervention but without language comprehension instruction, structured number knowledge intervention without a structured word-problem component, and a control group. Each intervention included 45 30-min sessions. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based word-problem intervention at 1st grade, with both word-problem conditions outperforming the number knowledge condition and the control group. Yet, word-problem performance was significantly stronger for the schema-based condition with embedded language comprehension instruction compared to the schema-based condition without language comprehension instruction. Number knowledge intervention conveyed no word-problem advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to word-problem intervention; the efficacy of schema-based instruction at 1st grade; and the added value of language comprehension instruction within word-problem intervention. Results also provide causal evidence on the role of language comprehension in word-problem solving.

Persistence and Fade-Out of Educational-Intervention Effects: Mechanisms and Potential Solutions

Some environmental influences, including intentional interventions, have shown persistent effects on psychological characteristics and other socially important outcomes years and even decades later. At the same time, it is common to find that the effects of life events or interventions diminish and even disappear completely, a phenomenon known as fadeout. We review the evidence for persistence and fadeout, drawing primarily on evidence from educational interventions. We conclude that 1) fadeout is widespread, and often co-exists with persistence; 2) fadeout is a substantive phenomenon, not merely a measurement artefact; and 3) persistence depends on the types of skills targeted, the institutional constraints and opportunities within the social context, and complementarities between interventions and subsequent environmental affordances. We discuss the implications of these conclusions for research and policy.