Accelerating Academic Achievement (A3) Research Articles & Book Chapters

A3 Math: Research Articles

Wang, A. Y., Fuchs, L. S., Preacher, K. J., Fuchs, D., Malone, A. S., Pachmayr, R. (2019). Effects of Super Solvers Fractions Intervention for At-Risk Third Graders. Submitted for publication.

Fuchs, L. S., Malone, A. S., Preacher, K. J., Fuchs, D., Wang, A. Y., Pachmayr, R. (2019). Effects of Fourth- and Fifth-Grade Super Solvers Intervention on Fraction Magnitude Understanding and Calculation Skill. Submitted for publication.

Krowka, S. K., & Fuchs, L. S. (2017). Cognitive profiles associated with responsiveness to fraction intervention. Learning Disabilities Research & Practice32(4), 216-230.

This study examined differences in cognitive processing between 4th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or inadequate responders, using as the cut-point the control-group mean on pre-to-post improvement on the relevant measure. Between-group differences identified reasoning, concept formation, and listening comprehension related to all 3 fraction outcomes. On the number-line outcome, within-group profile analysis indicated that inadequate responders experienced low reasoning ability relative to their other forms of cognitive processing.

Fuchs, L. S., Fuchs, D., & Malone, A. S. (2017). The taxonomy of intervention intensity. TEACHING Exceptional Children50(1), 35-43.

In this article, we describe the Taxonomy of Intervention Intensity, which articulates seven principles for evaluating and building intervention intensity based upon research. The Taxonomy’s seven dimensions of intensity are strength, dosage, alignment, attention to transfer, comprehensiveness, behavioral support, and individualization. In explaining the Taxonomy, we present a case study illustrating how the Taxonomy can be used to systematize the process by which special educators and related personnel (a) set up the intensive intervention process and (b) monitor the student’s response and systematically improve the program to match the target student’s individual needs. The goal is to increase the quality of intensive intervention, improve student outcomes, and help schools design intensive intervention programs that are clearly distinguishable from less intensive (Tier 2) intervention programs.

Fuchs, L. S., Sterba, S. K., Fuchs, D., & Malone, A. S. (2016). Does evidence-based fractions intervention address the needs of very low-performing students?Journal of Research on Educational Effectiveness9(4), 662-677.

The purpose of this set of analyses, conducted on a randomized control trial examining the effects of a fourth-grade fraction intervention, was to assess the initial academic deficit severity hypothesis. With this hypothesis, at-risk students with more severe initial academic deficits are expected to profit less from intervention than do students with less severe initial academic deficits. Moderation analyses indicated that students with varying degrees of initial academic deficits benefited comparably from the intervention, such that effect sizes comparing intervention against control students were similar across the range of initial academic deficits. In a similar way, across the range of initial academic deficits, intervention students’ posttest (spring) calculation performance was normalized (one standard error of measurement above the 25th percentile of a not-at-risk normative group’s spring performance). On the most distal fractions outcome, however, normalized performance was achieved for intervention students with less severe initial academic deficits. Findings are discussed in terms of methods for judging intervention efficacy and for making individual decisions about when students should exit intervention.

Malone, A. S., Fuchs, L. S., Sterba, S. K., Fuchs, D., & Foreman-Murray, L. (2019). Does an integrated focus on fractions and decimals improve at-risk students’ rational number magnitude performance?Contemporary Educational Psychology59, 101782.

The purpose of this study was to assess whether intervention with an integrated focus on fraction and decimal magnitude provides added value in improving rational number performance over intervention focused exclusively on fractions. We randomly assigned 4th graders with poor whole-number performance to 3 conditions: (a) a business-as-usual control group, (b) a validated fraction magnitude (FM) intervention, known as Fractions FaceOff!, which included fraction applications (word problems requiring addition and subtraction) (FM+FAPP), and (c) an experimental condition using the same instruction on fraction magnitude but integrating a component on fraction-decimal magnitude (FM+DM). Cross-classified partially-nested analyses (n=225) provided that Fractions FaceOff! improves 4th-graders’ fraction understanding and applications and that integrating fraction-decimal magnitude does not provide added value over Fractions FaceOff! on fraction or decimal performance.

Wang, A. Y., Fuchs, L. S., Fuchs, D., Gilbert, J. K., Krowka, S., & Abramson, R. (2019). Embedding Self-Regulation Instruction Within Fractions Intervention for Third Graders With Mathematics Difficulties. Journal of learning disabilities, 0022219419851750.

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, meta-cognitively, and behaviorally through challenging tasks. Students (n = 69) were randomly assigned to business-as-usual control and the two versions of fractions intervention. Multilevel models, accounting for the nested structure of the data, identified a moderation effect on fraction word problems: For students receiving fractions intervention with embedded SR, response to intervention was robust across the continuum of students’ pretest word problem skill; by contrast, without SR, response to fractions intervention depended on students’ pretest word problem skill. On the remaining outcomes, results reflected stronger outcomes when fractions intervention embedded SR instruction without moderation.

A3 Math: Books & Chapters

Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2018). Learning disabilities: From identification to intervention. Guilford Publications.

Fuchs, L. S., Malone, A. S., Seethaler, P.M., Powell, S.R., Fuchs, D. (2017). Intervention to Improve Arithmetic, Word-Problem, and Fraction Performance in Students with Mathematics Disabilities in Handbook of special education. Routledge.

A3 Reading: Research Articles

Fuchs, D., Hendricks, E. Walsh, M.E., Fuchs, L.S., Gilbert, J.K., Zhang-Tracy, W., Patton, S., Davis-Perkins, N., Kim, W., Elleman, A., Peng, P. (2018). Evaluating a multi-dimensional reading comprehension program and reconsidering the lowly reputation of tests of near-transfer. Learning Disabilities Research and Practice, 00 (0), 1-13.

We conducted a 14‐week experimental study of 2 versions of a relatively comprehensive RC intervention that involved 50 classroom teachers, 15 tutors, and 116 children drawn in equal proportions from grades 3 and 5 in 13 schools in a large urban school district. Students were randomly assigned in equal numbers to the two tutoring conditions and a control group. Results indicated that students in the two tutored groups tended to perform comparably on all tests and to outperform controls (more so in grade 5 than grade 3) on near‐transfer but not far‐transfer measures of RC. This differential pattern of program effects for near‐ versus far‐transfer measures raises questions about how tests of near‐transfer and far‐transfer are conventionally understood.

A3 Reading: Book Chapters

Fuchs, D., Patton, S.A., Fuchs, L.S., Gilbert, J., Walsh, M.E., Lute, N., Yen Haga, L., Peng, P., Elleman, A. (2018). Combining reading comprehension instruction with cognitive training to provide intensive intervention to at-risk students in Kennedy, M. & Pullen, P. (Eds.)  Handbook of RTI and MTSS. (198-217).

Book Chapter from the Handbook of Response to Intervention and Multi-Tiered Systems of Support. This research was conducted by staff from the National Center on Accelerating the Academic Achievement of Students with Severe and Persistent Learning Disabilities, which is funded by Grant No. R324D130003 from the National Center on Special Education Research, Institute of Educational Sciences. We thank Wen Zhang Tracy, Nicole Davis, Emma Hendricks, and Wooliya Kim for their guidance concerning curriculum development, and we thank the administrators in the Metro-Nashville Public Schools and the classroom teachers of the children in our study for their interest and support.

Exceptional Children: Special Issue

Fuchs, D., & Fuchs, L. S. (2019). On the importance of moderator analysis in intervention research: An introduction to the special issue.

Clarke, B., Doabler, C. T., Smolkowski, K., Turtura, J., Kosty, D., Kurtz-Nelson, E., … & Baker, S. K. (2019). Exploring the Relationship Between Initial Mathematics Skill and a Kindergarten Mathematics Intervention. Exceptional Children85(2), 129-146.

This study examined the role of initial skill in moderating intervention effects of a 50-lesson mathematics intervention program, ROOTS, for at-risk kindergarten students focused on developing whole-number concepts and skills. The study utilized a randomized block design with at-risk students (n = 592) within classrooms (n = 60) randomly assigned to one of two treatment conditions (a small group of two to five students) or control condition. Proximal and distal measures were collected in the fall (pretest), spring (posttest), and winter of first grade (delayed posttest). Analyses examined the moderating effects of initial student achievement level on mathematics outcomes. Results indicated that initial skill moderated student outcomes but the relationship did not differ by group size. Implications for tiered mathematics instruction are discussed.

Fuchs, L. S., Fuchs, D., & Gilbert, J. K. (2019). Does the Severity of Students’ Pre-Intervention Math Deficits Affect Responsiveness to Generally Effective First-Grade Intervention?Exceptional children85(2), 147-162.

The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners’ initial skill levels. Students were randomly assigned to control (n = 213) and two 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 two variants, focused on number knowledge that provides the conceptual bases for arithmetic. The other five minutes provided nonspeeded conceptual practice (n = 196) or speeded strategic practice (n = 199). Contrasts tested effects of intervention (combined across variants) versus control and effects between the variants. Moderation analysis indicated no significant interactions between at-risk children’s pre-intervention mathematics skill and either contrast on any outcome. Across pre-intervention math skill, effects favored intervention over control on arithmetic and transfer to double-digit calculations and number knowledge, and favored speeded over nonspeeded practice on arithmetic.

Coyne, M. D., McCoach, D. B., Ware, S., Austin, C. R., Loftus-Rattan, S. M., & Baker, D. L. (2019). Racing Against the Vocabulary Gap: Matthew Effects in Early Vocabulary Instruction and Intervention. Exceptional Children85(2), 163-179.

We investigated whether individual differences in overall receptive vocabulary knowledge measured at the beginning of the year moderated the effects of a kindergarten vocabulary intervention that supplemented classroom vocabulary instruction. We also examined whether moderation would offset the benefits of providing Tier-2 vocabulary intervention within a multitiered-system-of-support (MTSS) or response-to-intervention framework. Participants included students from two previous studies identified as at risk for language and learning difficulties who were randomly assigned in clusters to receive small-group vocabulary intervention in addition to classroom vocabulary instruction (n = 825) or to receive classroom vocabulary instruction only (n = 781). A group of not-at-risk students (n = 741) who received classroom vocabulary instruction served as a reference group. Initial vocabulary knowledge measured at pretest moderated the impact of intervention on experimenter-developed measures of expressive vocabulary learning and listening comprehension favoring students with higher initial vocabulary knowledge. Tier-2 intervention substantially counteracted the Matthew effect for target word learning. Intervention effects on listening comprehension depended on students’ initial vocabulary knowledge. Implications present benefits and challenges of supporting vocabulary learning within an MTSS framework.

Vaughn, S., Roberts, G., Capin, P., Miciak, J., Cho, E., & Fletcher, J. M. (2019). How Initial Word Reading and Language Skills Affect Reading Comprehension Outcomes for Students With Reading Difficulties. Exceptional children85(2), 180-196.

This study examined how differences in listening comprehension and word reading at the beginning of the school year influence changes in reading comprehension for English learners (ELs) with significant reading difficulties compared to non-ELs with significant reading difficulties. The study investigated heterogeneity in response to instruction among 400 struggling readers in fourth grade (n = 183 for non-EL; n = 217 for EL) who received an intensive reading intervention. At pretest, word reading, listening comprehension, and reading comprehension were measured, and at posttest, reading comprehension was measured again. Results from moderated multiple regression analyses showed a significant three-way interaction such that reading comprehension at posttest was higher for ELs than non-ELs with similar levels of low word reading but relatively higher levels of listening comprehension. However, non-ELs outperformed ELs with similar levels of relatively high word reading and average to high listening comprehension. The findings suggest that pre-intervention skill profiles may need to be interpreted differently for ELs and non-ELs with significant reading difficulties in relation to language and literacy outcomes.

Clemens, N. H., Oslund, E., Kwok, O. M., Fogarty, M., Simmons, D., & Davis, J. L. (2019). Skill Moderators of the Effects of a Reading Comprehension Intervention. Exceptional Children85(2), 197-211.

This study utilized secondary analyses of a randomized controlled trial and investigated the extent to which prestest word identification efficiency, reading fluency, and vocabulary knowledge moderated the effects of an intervention on reading comprehension outcomes for struggling readers in sixth through eighth grades. Given that the experimental intervention included components that targeted word reading, reading fluency, and vocabulary, we hypothesized that students with lower pretest performance in those skill domains would benefit more from the intervention compared to students with relatively stronger pretest performance or students who received school-implemented (business-as-usual) intervention. Results indicated that pretest word identification efficiency and vocabulary did not moderate the effects of the intervention; however, moderation effects were observed for pretest oral reading fluency such that reading comprehension gains of students with lower pretest fluency were greater in the experimental intervention compared to students with higher pretest fluency or in the comparison condition. Reasons for the moderation effect are discussed. Findings underscore the use of moderation analyses when evaluating multicomponent interventions.

Wanzek, J., Roberts, G., Vaughn, S., Swanson, E., & Sargent, K. (2019). Examining the Role of Pre-Instruction Academic Performance Within A Text-based Approach to Improving Student Content Knowledge and Understanding. Exceptional Children85(2), 212-228.

Students with disabilities are often included in general education social studies classes, but these classes can differ in the achievement level of the overall class, including wide variation in content-related background knowledge, reading achievement, or both. The purpose of this study was to examine how background knowledge and reading achievement moderate the effects of a previously validated intervention, Promoting Adolescents’ Comprehension of Text (PACT). We examined data from a prior randomized control trial of 1,487 eighth-grade students in 85 classes that were randomly assigned at the class level to receive either PACT instructional practices or typical instructional practices using the same social studies content. Results of the current study reveal no moderating effect at the class level of either initial background knowledge or reading achievement on student content knowledge acquisition or content reading comprehension outcomes. Classes with varying levels of background knowledge and reading achievement performed similarly in PACT instruction, with benefits of the PACT instruction found on content knowledge acquisition.

Fuchs, D., Kearns, D. M., Fuchs, L. S., Elleman, A. M., Gilbert, J. K., Patton, S., … & Compton, D. L. (2019). 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. Exceptional children85(2), 229-247.

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 and reading comprehension dimensions (DF and COMP), creating DF and DF+COMP treatments to parse the value of COMP. Students (N = 125) were randomly assigned to the two active treatments and controls. Treatment children were tutored three times per week for 21 weeks in 45-min sessions. Children in DF and DF+COMP together performed more strongly than controls on word reading and comprehension. However, pretreatment word reading appeared to moderate these results such that children with weaker beginning word reading across the treatments outperformed similarly low-performing controls to a significantly greater extent than treatment children with stronger beginning word reading outperformed comparable controls. DF+COMP children did not perform better than DF children. Study limitations and implications for research and practice are discussed.

Preacher, K. J., & Sterba, S. K. (2019). Aptitude-by-treatment interactions in research on educational interventions. Exceptional Children85(2), 248-264.

 A common theme uniting articles in this special issue is a focus on aptitude-by-treatment interactions (ATIs). This timely and welcome focus allows the field to synthesize current substantive findings on ATIs in educational intervention research in both reading and math domains. In this methodological commentary, we begin by reviewing traditional approaches for detecting and reporting interactions in single-level and multilevel models. Next, we discuss some limitations of traditional approaches for theorizing about and modeling ATIs, and we suggest some solutions. These solutions include interpreting level-specific (unconflated) ATIs, understanding and ameliorating threats to adequate power for detecting ATIs, expanding focus beyond linear ATIs, and increasing the number of measurement occasions beyond two to allow use of a growth modeling framework for investigating ATIs. Incorporating some of these advances into future research can motivate new research questions about educational interventions and lead to new discoveries in the search for ATIs.