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ABSTRACT: Examined the utility of a data-based assessment process to supplement teacher judgments about mathematics test accommodations. 192 4th- and 5th-grade students with learning disabilities (LD) and 181 students (mean age 9.59 yrs) without LD completed standard and extended time computations curriculum-based measurements (CBMs); 4 concepts and applications CBMs (standard, extended time, calculators, reading text aloud); and 5 problem-solving CBMs (standard, extended time, calculators, reading text aloud, encoding). CBM scores were used to examine whether students with LD benefited differentially from accommodations; estimate "typical" accommodation boosts among nondisabled students; and award accommodations to students with LD whose boosts exceeded the "typical" boost. Teachers provided independent accommodation judgments and students with LD completed large-scale assessments with and without accommodations. The results show that students with LD, as a group, profited differentially from accommodations on problem-solving CBMs, but not on conventional CBMs; teachers over-awarded accommodations; and CBM accommodation boosts predicted differential performance on large-scale assessments and supplemented teacher judgments in important ways. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
School psychology review 10/2012; · 1.85 Impact Factor
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ABSTRACT: In a sample of 195 first graders selected for poor reading performance, the authors explored four cognitive predictors of later reading comprehension and reading disability (RD) status. In fall of first grade, the authors measured the children's phonological processing, rapid automatized naming (RAN), oral language comprehension, and nonverbal reasoning. Throughout first grade, they also modeled the students' reading progress by means of weekly Word Identification Fluency (WIF) tests to derive December and May intercepts. The authors assessed their reading comprehension in the spring of Grades 1-5. With the four cognitive variables and the WIF December intercept as predictors, 50.3% of the variance in fifth-grade reading comprehension was explained: 52.1% of this 50.3% was unique to the cognitive variables, 13.1% to the WIF December intercept, and 34.8% was shared. All five predictors were statistically significant. The same four cognitive variables with the May (rather than December) WIF intercept produced a model that explained 62.1% of the variance. Of this amount, the cognitive variables and May WIF intercept accounted for 34.5% and 27.7%, respectively; they shared 37.8%. All predictors in this model were statistically significant except RAN. Logistic regression analyses indicated that the accuracy with which the cognitive variables predicted end-of-fifth-grade RD status was 73.9%. The May WIF intercept contributed reliably to this prediction; the December WIF intercept did not. Results are discussed in terms of a role for cognitive abilities in identifying, classifying, and instructing students with severe reading problems.
Journal of learning disabilities 05/2012; 45(3):217-31. · 1.77 Impact Factor
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ABSTRACT: The focus of this article is recent CBM work that incorporates diagnostic reading assessment. The goal is to help general
and special educators tailor more effective reading instruction for developing readers. The development process for this CBM
diagnostic reading assessment is described; the resulting assessment is presented; and preliminary data on its technical features
and utility are provided.
Reading and Writing 04/2012; 20(6):553-567. · 1.44 Impact Factor
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ABSTRACT: The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across Grades 2-3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems.
Developmental Psychology 03/2012; 48(5):1315-26. · 3.21 Impact Factor
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ABSTRACT: This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures of WPS at low and high levels of complexity. Language skills were related to initial performance at both levels of complexity and did not predict growth at either level. Computational skills had an effect on initial performance in low- but not high-complexity problems and did not predict growth at either level of complexity. Attentive behavior did not predict initial performance but did predict growth in low-complexity, whereas it predicted initial performance but not growth for high-complexity problems. Nonverbal reasoning predicted initial performance and growth for low-complexity WPS, but only growth for high-complexity WPS. This evidence suggests that although mathematical structure is fixed, different cognitive resources may act as limiting factors in WPS development when the WPS context is varied.
Journal of Educational Psychology 01/2012; 104(4):1083-1093. · 3.08 Impact Factor
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ABSTRACT: The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on word-problem performance. Logistic regression was conducted to contrast two models. One relied exclusively on the fall test of math word-problem skill to predict word-problem difficulty on the spring outcome (less than the 25th percentile). The second model relied on a combination of the fall test of math word-problem skill and the fall DA to predict the same outcome. Holding sensitivity at 87.5%, the universal screener alone resulted in a high proportion of false positives, which was practically reduced when DA was included in the prediction model. Findings are discussed in terms of a two-stage process for screening students within a responsiveness-to-intervention prevention model.
Journal of learning disabilities 06/2011; 44(4):372-80. · 1.77 Impact Factor
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ABSTRACT: The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word problems in fall and then reassessed on procedural calculations and word problems in spring. Development was indexed by latent change scores, and the interplay between numerical and domain-general abilities was analyzed by multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of procedural calculations and word problems development. Yet, for procedural calculations development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for word problems development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables. Language, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive.
Developmental Psychology 11/2010; 46(6):1731-46. · 3.21 Impact Factor
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ABSTRACT: The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students' word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students' emerging algebraic reasoning.
The Elementary School Journal 06/2010; 110(4):446-463. · 1.17 Impact Factor
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ABSTRACT: The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone vs. MD with reading difficulty) and site (proximal vs. distal to the intervention developer) and then randomly assigned to control (no tutoring) or 1 of 2 variants of NC remediation. Both remediations were embedded in the same validated word-problem tutoring protocol (i.e., Pirate Math). In 1 variant, the focus on NCs was limited to a single lesson that taught strategic counting. In the other variant, 4-6 min of practice per session was added to the other variant. Tutoring occurred for 16 weeks, 3 sessions per week for 20-30 min per session. Strategic counting without deliberate practice produced superior NC fluency compared to control; however, strategic counting with deliberate practice effected superior NC fluency and transfer to procedural calculations compared with both competing conditions. Also, the efficacy of Pirate Math word-problem tutoring was replicated.
Learning and Individual Differences 04/2010; 20(2):89-100. · 1.58 Impact Factor
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ABSTRACT: This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3 intervention approaches hypothesized to be most productive for a student uses a validated protocol while monitoring student response. The more intensive stage, which is reserved for nonresponders, involves integrating the 3 intervention approaches within a skills-based diagnostic-prescriptive scheme for individualizing intervention.
Exceptional children 01/2010; 76(2):135-165. · 2.29 Impact Factor
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The Elementary School Journal 01/2010; 110:440-463. · 1.17 Impact Factor
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ABSTRACT: The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students' math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC) remediation, and to examine the transportability of the tutoring protocols. At 2 sites, 133 students were stratified on mathematics difficulty status and site and then randomly assigned to 3 conditions: control (no tutoring), tutoring on automatic retrieval of NCs (i.e., Math Flash), or tutoring on word problems with attention to the foundational skills of NCs, procedural calculations, and algebra (i.e., Pirate Math). Tutoring occurred for 16 weeks, 3 sessions per week and 20-30 min per session. Math Flash enhanced fluency with NCs with transfer to procedural computation but without transfer to algebra or word problems. Pirate Math enhanced word problem skill as well as fluency with NCs, procedural computation, and algebra. Tutoring was not differentially efficacious as a function of students' mathematics difficulty status. The tutoring protocols proved transportable across sites.
Journal of Educational Psychology 08/2009; 101(3):561-576. · 3.08 Impact Factor
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ABSTRACT: Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3(rd) graders' development of mathematics problem solving. In the fall, 122 3(rd)-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities.
Journal of Educational Psychology 11/2008; 100(4):829-850. · 3.08 Impact Factor
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ABSTRACT: The purpose of this study was to assess the effects of small-group tutoring with and without validated classroom instruction on at-risk (AR) students' math problem solving. Stratifying within schools, 119 3(rd)-grade classes were randomly assigned to conventional or validated problem-solving instruction (Hot Math [schema-broadening instruction]). Students identified as AR (n = 243) were randomly assigned, within classroom conditions, to receive Hot Math tutoring or not. Students were tested on problem-solving and math applications measures before and after 16 weeks of intervention. Analyses of variance, which accounted for the nested structure of the data, revealed the tutored students who received validated classroom instruction achieved better than tutored students who received conventional classroom instruction (ES = 1.34). However, the advantage for tutoring over no tutoring was similar whether or not students received validated or conventional classroom instruction (ESs = 1.18 and 1.13). Tutoring, not validated classroom instruction reduced the prevalence of math difficulty. Implications for responsiveness-to-intervention prevention models and for enhancing math problem-solving instruction are discussed.
Journal of Educational Psychology 02/2008; 100(3):491-509. · 3.08 Impact Factor
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ABSTRACT: The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed.
Journal of Educational Psychology 02/2008; 100(1):30-47. · 3.08 Impact Factor
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ABSTRACT: The major purposes of this study were to assess the efficacy of tutoring to remediate 3rd-grade computational deficits and to explore whether remediation is differentially efficacious depending on whether students experience mathematics difficulty alone or concomitantly with reading difficulty. At 2 sites, 127 students were stratified on mathematics difficulty status and randomly assigned to 4 conditions: word recognition (control) tutoring or 1 of 3 computation tutoring conditions: fact retrieval, procedural computation and computational estimation, and combined (fact retrieval + procedural computation and computational estimation). Results revealed that fact retrieval tutoring enhanced fact retrieval skill, and procedural computation and computational estimation tutoring (whether in isolation or combined with fact retrieval tutoring) enhanced computational estimation skill. Remediation was not differentially efficacious as a function of students' mathematics difficulty status.
Journal of research on educational effectiveness. 01/2008; 1(1):2-32.
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ABSTRACT: This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits.
Exceptional children 01/2008; 74(2):155-173. · 2.29 Impact Factor
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ABSTRACT: This study examined the efficacy of preventive 1st-grade tutoring in mathematics, estimated the prevalence and severity of mathematics disability, and explored pretreatment cognitive characteristics associated with mathematics development. Participants were 564 first graders, 127 of whom were designated at risk (AR) for mathematics difficulty and randomly assigned to tutoring or control conditions. Before treatment, all participants were assessed on cognitive and academic measures. Tutoring occurred 3 times weekly for 16 weeks; treatment fidelity was documented; and math outcomes were assessed. Tutoring efficacy was supported on computation and concepts/applications, but not on fact fluency. Tutoring decreased the prevalence of math disability, with prevalence and severity varying as a function of identification method and math domain. Attention accounted for unique variance in predicting each aspect of end-of-year math performance. Other predictors, depending on the aspect of math performance, were nonverbal problem solving, working memory, and phonological processing. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Journal of Educational Psychology 07/2005; 97(3):493-513. · 3.08 Impact Factor
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ABSTRACT: The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on 4 types of word problems. The 3 16-week conditions were contrast, SBI, and SBI with practice in sorting word problems into schemas. Students were pre- and posttested on mathematical problem-solving tests and were posttested on schema development. Students receiving SBI, with and without sorting practice, improved more than the contrast group on problem-solving measures. Concurrently, the SBI groups' schema development exceeded that of the contrast group, and schema development explained a substantial portion of unique variance in students' posttreatment problem-solving performance. Results also suggested the need for additional research testing the contribution of practice in sorting word problems. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Journal of Educational Psychology 11/2004; 96(4):635-647. · 3.08 Impact Factor
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ABSTRACT: The purpose of this study was to assess the effects of explicitly teaching for transfer by (a) broadening the categories by which students group problems requiring the same solution methods and (b) prompting students to search novel problems for these broad categories. This transfer treatment was combined with instruction on solution methods. The effectiveness of a combined treatment (transfer-plus-solution instruction) was contrasted to solution instruction alone and to teacher-designed instruction. Twenty-four 3rd-grade teachers, with 375 students, were assigned randomly to conditions. Treatments were conducted for 16 weeks. Improvement on immediate- and near-transfer measures supported the utility of solution instruction. Improvement on near- and far-transfer measures revealed the added contribution of explicitly teaching for transfer. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Journal of Educational Psychology 05/2003; 95(2):293-304. · 3.08 Impact Factor
