Comorbid Word Reading and Mathematics Computation Difficulty at Start of First Grade.

The purpose of this analysis was to describe cognitive processes associated with comorbid difficulty between word reading (WR) and mathematics computation (MC) at the start of first grade among children selected for WR and MC delays. A sample of 234 children (mean age 6.50 years, = 0.

Modeling variability in treatment effects for cluster randomized controlled trials using by-variable smooth functions in a generalized additive mixed model.

Variability in treatment effects is common in intervention studies using cluster randomized controlled trial (C-RCT) designs. Such variability is often examined in multilevel modeling (MLM) to understand how treatment effects (TRT) differ based on the level of a covariate (COV), called TRT COV. In detecting TRT COV effects using MLM, relationships between covariates and outcomes are assumed to vary across clusters linearly.

Severe Pandemic Learning Loss and the Promise of Remotely Delivered Intervention in Students With Comorbid Reading and Mathematics Learning Difficulty.

Analyses were conducted with second graders, drawn from an ongoing multi-cohort randomized controlled trial (RCT), who had been identified for RCT entry based on comorbid reading comprehension and word-problem solving difficulty. To estimate pandemic learning loss, we contrasted fall performance for 3 cohorts: fall of 2019 (pre-pandemic; = 47), 2020 (early pandemic, when performance was affected by the truncated preceding school year; = 35), and 2021 (later pandemic, when performance was affected by the truncated 2019 to 2020 school year plus the subsequent year's ongoing interruptions; = 75). Across the 2 years, declines (standard deviations below expected growth) were approximately 3 times larger than those reported for the general population and for students in high-poverty schools.

Modelling multilevel nonlinear treatment-by-covariate interactions in cluster randomized controlled trials using a generalized additive mixed model.

A cluster randomized controlled trial (C-RCT) is common in educational intervention studies. Multilevel modelling (MLM) is a dominant analytic method to evaluate treatment effects in a C-RCT. In most MLM applications intended to detect an interaction effect, a single interaction effect (called a conflated effect) is considered instead of level-specific interaction effects in a multilevel design (called unconflated multilevel interaction effects), and the linear interaction effect is modelled.

Connections between Mathematics and Reading Development: Numerical Cognition Mediates Relations between Foundational Competencies and Later Academic Outcomes.

We examined longitudinal relations between 1-grade cognitive predictors (early nonverbal reasoning, processing speed, listening comprehension, working memory, calculation skill, word-problem solving, word-reading fluency, attentive behavior, and numerical cognition) and 2-grade academic outcomes (calculations, word-problem solving, and word reading) in 370 children ( = 6.55 years, = 0.33 years at the start of the study) who were identified as at-risk or not-at-risk for mathematics disability.

Comorbidity in Reading Comprehension and Word-Problem Solving Difficulties: Exploring Shared Risk Factors and Their Impact on Language Minority Learners.

The purpose of this study was threefold: to examine unique and shared risk factors of comorbidity for reading comprehension and word-problem solving difficulties, to explore whether language minority (LM) learners are at increased risk of what we refer to as (reading comprehension and word-problem solving difficulties), and to examine the profiles of at-risk LM learners compared with at-risk non-LM learners. At-risk (LM = 70; non-LM = 89) and not-at-risk (LM = 44; non-LM = 114) students were evaluated on foundational academic (word reading, calculation), behavioral (behavioral attention), cognitive (working memory, processing speed, nonverbal reasoning), and language (vocabulary, listening comprehension) measures in English. Results indicated listening comprehension was the only shared risk factor for higher order comorbidity.

Bringing Data-Based Individualization to Scale: A Call for the Next-Generation Technology of Teacher Supports.

The purpose of this narrative synthesis of the curriculum-based measure (CBM) instructional utility literature is to deepen insight into the supports required to enrich teachers' instructional decision-making within curriculum-based measuredata-based individualization (CBM-DBI) in ways that enhance the learning outcomes of students with intensive intervention needs, including students with learning disabilities. We begin by summarizing a recent meta-analysis of CBM-DBI studies focused on academic outcomes. We then reconsider studies from that meta-analysis to further explore the supports required to enrich teachers' instructional decision-making within CBM-DBI and improve student learning.

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 1 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 1 grade. Children (n=391; mean age = 6.

Language-Related Longitudinal Predictors of Arithmetic Word Problem Solving: A Structural Equation Modeling Approach.

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10 to 9.02 years).

Is "Response/No Response" Too Simple a Notion for RTI Frameworks? Exploring Multiple Response Types With Latent Profile Analysis.

We conducted a secondary analysis of data from a randomized control trial to explore this question: Does "response/no response" best characterize students' reactions to a generally efficacious first-grade reading program, or is a more nuanced characterization necessary? Data were collected on 265 at-risk readers' word reading prior to and immediately following program implementation in first grade and in spring of second grade. Pretreatment data were also obtained on domain-specific skills (letter knowledge, decoding, passage comprehension, language) and domain-general skills (working memory, non-verbal reasoning). Latent profile analysis of word reading across the three time points with controls as a local norm revealed a group ( = 45) with mean word-reading scores of 0.

Improving Language Comprehension to Enhance Word-Problem Solving.

The focus of this article is the role of language comprehension within word-problem solving (WPS). The role of the language comprehension in WPS is explained, and an overview of research illustrating language comprehension's contribution to WPS is described. Next, an innovative intervention that embeds WP-specific language comprehension instruction within a validated form of schema-based WP intervention is described, and the methods and results of a randomized controlled trial assessing the added value of embedding WP-specific language comprehension instruction are outlined.

Do the Processes Engaged During Mathematical Word-Problem Solving Differ Along the Distribution of Word-Problem Competence?

Conventional research methods for understanding sources of individual differences in word-problem solving (WPS) only permit estimation of average relations between component processes and outcomes. The purpose of the present study was instead to examine whether and if so how the component processes engaged in WPS differ along the spectrum of WPS performance. Second graders ( = 1,130) from 126 classrooms in 17 schools were assessed on component processes (reasoning, in-class attentive behavior, working memory, language comprehension, calculation fluency, word reading) and WPS.

Are Individual Differences in Response to Intervention Influenced by the Methods and Measures Used to Define Response? Implications for Identifying Children With Learning Disabilities.

Response to intervention (RTI) has been promoted for nearly 20 years as a valid supplement to or alternative method of learning disability (LD) identification. Nevertheless, important unresolved questions remain about its role in disability identification. We had two purposes when conducting this study of 229 economically and racially diverse poor readers in Grades 4 and 5 in 28 public elementary and middle schools in Nashville.

Dynamic Assessment for Identifying Spanish-Speaking English Learners' Risk for Mathematics Disabilities: Does Language of Administration Matter?

We examined dynamic assessment's (DA's) added value over traditional assessments for identifying Spanish-speaking English learners' (ELs) risk for developing mathematics disabilities, as a function of the language of test administration (English vs. Spanish), type of math outcome, and EL's language dominance. At the start of first grade, ELs ( = 368) were randomly assigned to English-DA or Spanish-DA conditions, were assessed on static mathematics measures and domain-general (language, reasoning) measures in English, and completed DA in their assigned language condition.

Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency.

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N = 200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing, number comparison, memory skills, and processing and articulation speed in the spring of Grade 1 and on reading and arithmetic fluency in the fall of Grade 2. RAN and verbal counting were strongly associated, and a constructed latent factor, serial retrieval fluency (SRF), was the strongest unique predictor of the shared variance.

Embedding Self-Regulation Instruction Within Fractions Intervention for Third Graders With Mathematics Difficulties.

The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering belief that intellectual and academic abilities can be developed) along with SR processes in which students set goals, self-monitor, and use strategies to engage motivationally, metacognitively, and behaviorally through challenging tasks.

Connections Between Reading Comprehension and Word-Problem Solving via Oral Language Comprehension: Implications for Comorbid Learning Disabilities.

In this article, we discuss the approach adopted within the Vanderbilt University Learning Disabilities Innovation Hub, which focuses on students with higher-order comorbidity: students with concurrent difficulty with reading comprehension and word-problem solving. The aim of the Hub's Research Project is to test what we refer to as the higher-order comorbidity hypothesis: that language comprehension plays a critical role in reading comprehension and word-problem solving. In the Hub's study, we test the hypothesize that language comprehension offers a coordinated approach for improving both outcomes and that this approach thus provides direction for understanding higher-order comorbidity and support for the validity of reading comprehension and word-problem solving comorbidity as a learning disabilities subtyping framework.

Does the Severity of Students' Pre-Intervention Math Deficits Affect Responsiveness to Generally Effective First-Grade Intervention?

The purpose of this analysis was to assess whether effects of 1-grade mathematics intervention apply across the range of at-risk learners' initial skill levels. Students were randomly assigned to control (=213) and 2 variants of intervention (n=385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16 weeks), 25 minutes were identical in the 2 variants, focused on number knowledge that provides the conceptual bases for arithmetic.

Using Moderator Analysis to Identify the First-Grade Children Who Benefit More and Less from a Reading Comprehension Program: A Step Toward Aptitude-by-Treatment Interaction.

Because of the importance of teaching reading comprehension to struggling young readers and the infrequency with which it has been implemented and evaluated, we designed a comprehensive first-grade reading comprehension program. We conducted a component analysis of the program's decoding/fluency (DF) and reading comprehension (COMP) dimensions, creating DF and DF+COMP treatments to parse the value of COMP. Students ( = 125) were randomly assigned to the 2 active treatments and controls.

A Longitudinal Analysis of the Trajectories and Predictors of Word Reading and Reading Comprehension Development Among At-Risk Readers.

This study explored the developmental trajectories and predictors of word reading and reading comprehension among young at-risk readers. In fall of first grade, 185 students identified as at-risk for reading difficulties were assessed on measures of domain-specific skills (phonological awareness, letter knowledge, and vocabulary), domain-general skills (working memory, nonverbal reasoning, and processing speed), and word reading and reading comprehension. Word reading and reading comprehension were assessed again in spring of grades 1-4.

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

We present first-grade, second-grade, and third-grade impacts for a first-grade intervention targeting the conceptual and procedural bases that support arithmetic. At-risk students (average age at pretest = 6.5) were randomly assigned to three conditions: a control group (n = 224) and two variants of the intervention (same conceptual instruction but different forms of practice: speeded [n = 211] vs.

Response-To-Intervention in Finland and the United States: Mathematics Learning Support as an Example.

Response to Intervention (RTI) was accepted in the early 2000s as a new framework for identifying learning difficulties (LD) in the U.S. In Finland, a similar multi-tiered framework has existed since 2010.

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension.

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes.

Cognitive and Linguistic Predictors of Mathematical Word Problems With and Without Irrelevant Information.

The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working memory capacity, and processing speed; in the spring, they were tested on a word-problem measure that included items with versus without irrelevant information.