# Browsing by Author "Fuchs, Lynn S."

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Item Cognitive and behavioral attention in children with math difficulties(Child Neuropsychology, 2013) Gold, Alanna B.; Ewing-Cobbs, Linda; Cirino, Paul T.; Fuchs, Lynn S.; Stuebing, Karla K.; Fletcher, Jack M.Show more Cognitive assessments and behavioral ratings of attention were used to examine the relation of inattention to math performance in children. Third grade students with math difficulties (MD; n = 17) and math and reading difficulties (MDRD; n = 35) were administered the Attentional Network Test (ANT), as well as achievement and intelligence measures. Strengths and Weaknesses of ADHD-Symptoms and Normal-Behavior-IV (SWAN-IV) Inattention ratings were collected from teachers. Two comparison groups were also recruited: a typically achieving group (n = 23) and a group that responded to a math-tutoring intervention (responders; n = 54). On the ANT, children with MD and MDRD did not perform significantly different than typically achieving children or responders on measures of alerting and orienting attention and executive control. All subgroups did demonstrate performance patterns that were expected on the ANT. However, performance across blocks of the task was inconsistent, suggesting poor reliability. There were no relations between ANT performance and SWAN-IV behavioral inattention scores, though behavioral ratings of inattention correlated significantly with math performance. Children with MD and MDRD may have more difficulty with distraction and attention to detail in contextual situations, as opposed to impulsive responding in these settings. The lack of relation between cognitive attention and math performance may suggest that either the ANT does not assess the relevant attention constructs associated with math difficulties or may parallel studies of attention deficit/hyperactivity disorder (ADHD) in which cognitive and behavioral assessments are weakly related.Show more Item Cognitive and mathematical profiles for different forms of learning difficulties(Journal of Learning Disabilities, 2015-03) Cirino, Paul T.; Fuchs, Lynn S.; Elias, John T.; Powell, Sarah R.; Schumacher, Robin F.Show more The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive measures (e.g., working memory and language) and on mathematics measures of foundational numerical competencies, computation, and problem solving. Results revealed expected level differences among groups in both domains: NoLD outperformed RD, and MD outperformed MDRD. Profile differences were noted among pairs of subgroups on cognitive measures. On mathematics measures, profile differences were noted between RD and other subgroups, but not between MD and MDRD subgroups. The most discriminating cognitive measures were processing speed and language; the most discriminating mathematics measures depended on the subgroups being compared. Results were further evaluated according to more severe (< 10th percentile) criteria for MD and RD, which generally affected level differences more than the profile patterns. Results have implications for understanding comorbid MD and RD and for conceptualizing core deficits in MD.Show more Item Do word-problem features differentially affect problem difficulty as a function of students' mathematics difficulty with and without reading difficulty?(Journal of Learning Disabilities, 2009-03) Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas; Cirino, Paul T.; Fletcher, Jack M.Show more This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed.Show more Item Does calculation or word-problem instruction provide a stronger route to pre-algebraic knowledge?(Journal of Educational Psychology, 2014-12) Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.Show more The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to prealgebraic knowledge. Participants were 1,102 children in 127 second-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) and prealgebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to prealgebraic knowledge.Show more Item Effects of a multitier support system on calculation, word problem, and prealgebraic performance among at-risk learners(Exceptional Children, 2015-01) Powell, Sarah R.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.Show more The focus of the present study was enhancing word problem and calculation achievement in ways that support prealgebraic thinking among second-grade students at risk for mathematics difficulty. Intervention relied on a multitier support system (i.e., responsiveness to intervention, or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to one of three conditions: calculation RTI, word problem RTI, or business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word problem outcomes, word problem RTI enhanced proximal word problem outcomes as well as performance on some calculation outcomes, and word problem RTI provided a stronger route than calculation RTI to prealgebraic knowledge.Show more Item Effects of fact retrieval tutoring on third-grade students with math difficulties with and without reading difficulties(Learning Disabilities Research and Practice, 2009-02) Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas; Cirino, Paul T.; Fletcher, Jack M.Show more The purpose of this study was to assess the efficacy of fact retrieval tutoring as a function of math difficulty (MD) subtype, that is, whether students have MD alone (MD-only) or have concurrent difficulty with math and reading (MDRD). Third graders (n = 139) at two sites were randomly assigned, blocking by site and MD subtype, to four tutoring conditions: fact retrieval practice, conceptual fact retrieval instruction with practice, procedural computation/estimation instruction, and control (no tutoring). Tutoring occurred for 45 sessions over 15 weeks for 15-25 minutes per session. Results provided evidence of an interaction between tutoring condition and MD subtype status for assessment of fact retrieval. For MD-only students, students in both fact retrieval conditions achieved comparably and outperformed MD-only students in the control group as well as those in the procedural computation/estimation instruction group. By contrast, for MDRD students, there were no significant differences among intervention conditions.Show more Item Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties(Journal of Learning Disabilities, 2009-12) Raghubar, Kimberly P.; Cirino, Paul T.; Barnes, Marcia A.; Ewing-Cobbs, Linda; Fletcher, Jack M.; Fuchs, Lynn S.Show more Errors in written multi-digit computation were investigated in children with math difficulties. Third-and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low average achievement in math, and no learning difficulties. Math fact errors were related to the severity of the math difficulties, not to reading status. Contrary to predictions, children with poorer reading, regardless of math achievement, committed more visually based errors. Operation switch errors were not systematically related to group membership. Teacher ratings of behavioral inattention were related to accuracy, math fact errors, and procedural bugs. The findings are discussed with respect to hypotheses about the cognitive origins of arithmetic errors and in relation to current discussions about how to conceptualize math disabilities.Show more Item Intensive intervention for students with mathematics disabilities: Seven principles of effective practice(Learning Disability Quarterly, 2008-05) Fuchs, Lynn S.; Fuchs, Douglas; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.Show more The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for students in the primary grades: number combinations and story problems. We then focus on seven principles of effective intervention. First, we describe a validated, intensive remedial intervention for number combinations and another for story problems. Then, we use these interventions to illustrate the first six principles for designing intensive tutoring protocols for students with mathematics disabilities. Next, using the same validated interventions, we report the percentage of students whose learning outcomes were inadequate despite the overall efficacy of the interventions and explain how ongoing progress monitoring represents a seventh, and perhaps the most essential, principle of intensive intervention. We conclude by identifying issues and directions for future research in the primary and later grades.Show more Item Predicting development of mathematical word problem solving across the intermediate grades(Journal of Educational Psychology, 2012-11) Tolar, Tammy D.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.Show more 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.Show more Item Prediction and stability of mathematics skill and difficulty(Journal of Learning Disabilities, 2012-05) Martin, Rebecca B.; Cirino, Paul T.; Barnes, Marcia A.; Ewing-Cobbs, Linda; Fuchs, Lynn S.; Stuebing, Karla K.; Fletcher, Jack M.Show more The present study evaluated the stability of math learning difficulties over a 2-year period and investigated several factors that might influence this stability (categorical vs. continuous change, liberal vs. conservative cut point, broad vs. specific math assessment); the prediction of math performance over time and by performance level was also evaluated. Participants were 144 students initially identified as having a math difficulty (MD) or no learning difficulty according to low achievement criteria in the spring of Grade 3 or Grade 4. Students were reassessed 2 years later. For both measure types, a similar proportion of students changed whether assessed categorically or continuously. However, categorical change was heavily dependent on distance from the cut point and so more common for MD, who started closer to the cut point; reliable change index change was more similar across groups. There were few differences with regard to severity level of MD on continuous metrics or in terms of prediction. Final math performance on a broad computation measure was predicted by behavioral inattention and working memory while considering initial performance; for a specific fluency measure, working memory was not uniquely related, and behavioral inattention more variably related to final performance, again while considering initial performance.Show more Item Remediating computational deficits at third grade: A randomized field trial(Journal of Research on Educational Effectiveness, 2008-03) Fuchs, Lynn S.; Powell, Sarah R.; Hamlett, Carol L.; Fuchs, Douglas; Cirino, Paul T.; Fletcher, Jack M.Show more 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.Show more Item Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial(Journal of Educational Psychology, 2009-08) Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.; Zumeta, Rebecca O.Show more 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.Show more Item The effects of strategic counting instruction, with and without deliberate practice, on number combination skill among students with mathematics difficulties(Learning and Individual Differences, 2010-04) Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.Show more 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 versus MD with reading difficulty) and site (proximal versus 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.Show more Item The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge(Developmental Psychology, 2016-01) Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.Show more The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes.Show more