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High-quality Tier 1 instruction is frequently conceptualized as the "foundation" for other tiers of intervention within multi-tiered systems of support (MTSS) models (Gersten et al., 2009). However, the vast majority of Tier 2 intervention studies do not account for Tier 1 variables when examining intervention effectiveness (Hill et al., 2012). The purpose of the current study was to examine Tier 1 predictors, or "quality indicators", of differential responsiveness to Tier 2 mathematics intervention. Data was drawn from a large-scale dataset 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: (1) classroom-level mathematics gains, (2) Tier 1 fidelity of implementation, (3) Tier 1 classroom management and instructional support, and (4) 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. [This paper will be published in the "Journal of Learning Disabilities."]

The purpose of this study was to conduct a replication study of a kindergarten mathematics intervention, ROOTS, delivered within the context of a research base core program. In the study, sixty two classrooms were randomly assigned to treatment (ROOTS) or a business as usual control. All classrooms implemented a research based core program (Early Learning in Mathematics). Participants included 163 treatment students and 145 control students nested within classrooms. Key differences between the current replication study and the original study included geographical region, instructional context, and student initial skill. In contrast to the significant positive effects (Hedges' g values of 0.30 to 0.38) found in the original study, no significant differences were found between the treatment and control conditions. Pretest skills did not moderate treatment effects. Implications for replication research and evaluating intervention efficacy are discussed. [This is the online first version of an article published in "Exceptional Children."]

This paper reports the outcomes of an experimental evaluation of "Direct Instruction Spoken English (DISE)," an English language curriculum that focuses on developing English speaking, listening, and comprehension skills in English Learners (ELs). Twenty-nine middle schools in three states were randomly assigned to teach "DISE" Level 1 or their typical English language development program. Treatment teachers received two days of training and taught daily lessons. Project staff assessed 746 sixth and seventh-grade students with a proximal measure of English language proficiency and distal measures of language and oral reading fluency. Analyses of oral English language suggested differences between intervention conditions favored the DISE condition for students who began with lower English language proficiency and accumulated when taught over two years. Differences between intervention conditions were not observed after only one year of instruction and for students with advanced levels of English language proficiency. The findings suggest that an evidence-based English oral language program that included frequent teacher demonstrations and opportunities for students to practice speaking English may improve English oral language skills for middle school students. [This is the online first version of an article published in "Journal of Education for Students Placed at Risk (JESPAR)."]

The purpose of the study was to investigate whether the districts that received ongoing training and coaching to use the Active Implementation Frameworks improved mathematics outcomes. The Active Implementation Frameworks represent five essential approaches for effective implementation of any evidence-based program or practice. One of the frameworks is a clearly defined and operationalized usable innovation, or any evidence-based practice that is easily measured for adherence to the program design. The subject of Kentucky's usable innovation is mathematics and use of the 8 mathematical teaching practices developed by the National Council of Teachers of Mathematics (NCTM, 2014). The evaluation focused on priority populations, specifically students with disabilities and Black students, and compared their outcomes to a carefully matched district that did not receive the same level of support.

This paper describes "the development and technical adequacy of the Classroom Observations of Student Teacher Interactions (COSTI) instrument," a tool for measuring the frequency and rate of explicit instructional interactions, such as those used in Direct Instruction curricula, for teaching children basic reading and math skills. "The COSTI was originally developed" to provide teachers with coaching feedback to improve their explicit reading instructional practices, "and has been shown in multiple studies to be a reliable and valid predictor of student gains in beginning reading and math skills." This paper discusses potential uses of the instrument for training and coaching across curricula with varying instructional design features, and lays out a future research agenda to further improve the "COSTI" and related observation tools for studying explicit instructional practices and their contribution to student learning. [This paper will be published in "Perspectives on Behavior Science."]

Instructional interactions that occur between teachers and students around foundational mathematics topics are critical for supporting mathematical proficiency among students with mathematics learning disabilities (MLD). This study investigated whether the initial mathematics skill of 880 kindergarten students at risk for MLD predicted the quantity and quality of explicit instructional interactions (i.e., overt teacher modeling, student practice opportunities, and academic feedback) experienced during an empirically-validated, Tier 2 kindergarten mathematics intervention. It also examined whether the quantity and quality of such instructional interactions predicted gains in student mathematics achievement. Researchers conducted 740 direct observations of 255 intervention groups within a multi-year, randomized controlled trial. Results suggested that intervention groups with lower initial mathematics skill received higher rates of academic feedback and made more frequent errors. Additionally, more frequent and higher quality academic feedback and group practice opportunities predicted increased mathematics achievement. Implications for investigating the active ingredients of mathematics interventions are discussed. [This paper was published in "Learning Disability Quarterly" v44 n1 p50-62 Feb 2021 (EJ1281644).]

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" (Green, 2008) of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a federally funded efficacy trial involving a Tier 2 first-grade mathematics intervention to examine whether the quantity and quality of explicit mathematics instruction was associated with the mathematics outcomes of 470 first-grade students with or at risk for mathematics learning disabilities. Associations between group-level pretreatment skill levels and the quality and quantity of explicit mathematics instructional practices used in the intervention were also explored. Findings suggested significant associations between positive gains in student mathematics outcomes and (a) lower rates of incorrectly answered mathematics-focused questions, and (b) the rate in which interventionists delivered group-level practice opportunities and offered academic feedback. Significant associations were also found between initial student mathematics performance and rates of student errors and the quality of explicit instruction. Implications for using direct observation to document enacted EBPs are discussed. [This paper was published in "Journal of Learning Disabilities" v54 n1 p20-35 Jan-Feb 2021 (EJ1279319).]

The purpose of this study was to examine parent-teacher congruent perceptions of middle school structures to support parent monitoring of children's behavior. We examined family educational involvement and school's communication and support to families as predictors of congruence, as well as congruence as a predictor of children following school rules and expectations. Participants were 415 teachers and 5003 parents across 40 public middle schools in the Northwest Region of the U.S. Mixed-effects regression was used to examine the cross-sectional data. School size and student eligibility of free or reduced price school lunch were included as school-level covariates. Results suggested that higher levels of teacher-reported family involvement and school communication and support to families were significantly associated with greater parent-teacher congruence. In addition, results suggested that greater parent-teacher congruence was significantly associated with higher levels of teacher-report of children following school rules and expectations. Implications for research on parent-teacher congruence and family-school collaboration are discussed at the school system level in terms of parent monitoring of children's behavior. Practical applications are reviewed for public middle schools. [This paper will be published in "Psychology in the Schools."]

We assessed the effects of a whole-school equity intervention implemented within a school-wide positive behavioral interventions and supports (PBIS) framework on racial inequities in school discipline in eight elementary schools with inequitable referrals for Black students. The intervention involved assessing patterns of racial disparities in school discipline decisions and providing professional development on adapting school-wide behavior systems to improve cultural responsiveness through concrete strategies targeting the patterns. After consent and matching on existing levels of racial inequities, half of the schools were randomly assigned to receive the intervention. Analyses showed that schools receiving the intervention had significant decreases in racial disparities in school discipline and rates of office discipline referrals for Black students, while control schools had minimal change. Results are discussed in terms of improving equity in school discipline within multi-tiered systems of support. [This paper was published in "School Psychology" v36 n6 p433-444 2021 (EJ1316009).]

This study examined whether the efficacy of a 50 lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS, differed by group size and whether initial skill moderated intervention effects by group size. The study utilized a randomized block design with at-risk students (n = 1,251) within classrooms (n = 138) randomly assigned to one of two treatment conditions (a small group of two or five students) or control condition. Proximal and distal measures were collected in the fall (pretest), spring (posttest) and winter of first grade (follow-up). Results indicated that students who received ROOTS performed better at posttest than control students (Hedges' g from 0.09 to 0.81), that impact did not vary by group size, and that initial skill moderated the impact of ROOTS compared to control student outcomes but not likely differences in group size. [This paper was published in "The Elementary School Journal" v121 n1 p125-153 2020 (EJ1270205).]

The purpose of this study was to examine middle school outreach to families about student behavior and its relationship with student school behavior, conduct problems, emotional symptoms, prosocial behavior, as well as school safety. In addition, the role of school implementation of PBIS was examined as a systems-level approach that could promote school outreach to families. Participants were 653 teachers and 12,912 students across 41 public middle schools in the Northwest region of the U.S. The longitudinal data were examined using multilevel regression models in which repeated measures at the school level were nested within schools. Residualized change in school-level outcome was modeled as a function of current and prior measures. Findings suggested teacher-report of school proactive outreach to families predicted greater teacher-report of school safety, as well as declines in student-report of conduct problems and emotional symptoms. In addition, results suggested school outreach was associated with teacher-report of student school behavior. Implications for continued research on school-home communication, as well as implications for embedding proactive school-home communication approaches in school systems and practices are discussed. [This paper was published in "School Psychology Review" v49 n4 p493-509 2020 (EJ1282622).]

This study examined the cost effectiveness of a 50 lesson mathematics intervention program focused on whole number concepts for at-risk kindergarten students, ROOTS. The study utilized a randomized block design with 1,251 at-risk students within 138 classrooms randomly assigned to one of two active treatment conditions (small groups of either two or five students) or control condition. Proximal and distal measures were collected in the fall (pretest) and spring (posttest). The costs per group per effect-size unit change varied from $216 to $736 depending on differing district scenarios and group size. The cost-effectiveness ratios per student varied from $267 to $3,201 depending on district scenario, group size, and the measure. Implications for conducting cost effectiveness evaluations and public policy are discussed. [This article was published in "School Psychology Review" v40 n4 p359-373 2020 (EJ1282375).]

This pilot study evaluated a novel professional development (PD) model designed to prepare K-12 educators in high-need, rural school districts to teach evidence-based argument writing. The PD showed teachers how to engage students in discussions about visual art using Visual Thinking Strategies to enhance students' argumentation writing. Twenty intervention teachers completed the professional development program and conducted lessons in Visual Thinking Strategies and argument writing. Intervention teachers, relative to 34 comparison teachers, improved on their perceived knowledge of critical thinking concepts, ability to teach critical thinking concepts, knowledge of concepts related to argument writing and their actual ability to perceive and analyze artistic work and understand characteristics used to convey intent and meaning (Hedges's g > 0.50). Students in the intervention condition (N = 210 in K-11) improved their argument writing skills. Given the quasi-experimental design and small sample size, these findings should be viewed with caution but suggest promise. [This paper was published in "The Elementary School Journal" 2020 (EJ1270199).]

This study utilized a partially nested randomized control design to investigate the impact of Fusion, a first grade math intervention. Blocking on classrooms, students were randomly assigned to one of three conditions: a Fusion two student group, a Fusion five student group, or a no treatment control group. Two primary research questions were examined: What was the overall impact of the Fusion intervention as compared to a business-as-usual comparison condition? and Was there a differential impact on student outcomes between the 2:1 Fusion and the 5:1 Fusion conditions? Analyses found a positive effects on four outcome measures favoring Fusion groups over control with two of the differences statistically significant. Results between Fusion groups found positive effects favoring the Fusion 2:1 group compared to the Fusion 5:1 group on all four outcome measures with two of the differences statistically significant. On a second grade follow up measure no difference was found between Fusion groups and control but a statistically significant difference was found between Fusion groups favoring the 2:1 Fusion group. Future research directions and implications for practice are discussed. [This paper will be published in the "Journal of Research on Educational Effectiveness."]

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically-validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities and the quality of explicit instruction served as treatment intensity metrics. A total of 465 kindergarten students with mathematics difficulties from 136 intervention groups participated. Results suggested comparable performances between the 2:1 and 5:1 intervention groups on six outcome measures. Observation data indicated that the intensity of student practice opportunities differed by group size. Students in the 5:1 groups received more opportunities to practice with their peers, while students in the 2:1 groups participated in more frequent and higher quality individualized practice opportunities. Implications in terms of delivering Tier 2 interventions in small-group formats and engaging at-risk learners in meaningful practice opportunities are discussed. [This paper was published in "Journal of Learning Disabilities" v52 n2 p168-180 Mar 2019 (EJ1203634). The published article was titled "Examining the Impact of Group Size on the Treatment Intensity of a Tier 2 Mathematics Intervention within a Systematic Framework of Replication."]

Student behavior problems in general-education classrooms present a major barrier to effective teaching. Behavior challenges, such as disruptions, noncompliance, and peer conflicts, reduce instructional time, whereas prosocial behaviors, such as paying attention, being ready to work, asking for help, participating in class, and completing homework, improve academic performance. Most interventions developed to address student behavior problems were not designed for general-education students in typical classrooms. The purpose of this paper is to present preliminary results from a novel intervention developed to enhance behavioral self-management skills among all upper-elementary students in general-education classrooms. "We Have Choices," a universal intervention, was designed to increase students' capacity to make appropriate behavioral choices and decrease teachers' responsibility by transferring behavior management to students. An initial randomized controlled trial with 86 fourth- to sixth-grade teachers and 2,055 students suggested that "We Have Choices" was associated with improvements in student-reported use of self-management strategies, teacher-reported student prosocial behavior, and teacher-reported self-efficacy in behavior management and instruction. Teachers gave the program high scores for social validity, suggesting a good fit for their classrooms. [This is the online version of an article published in "Psychology in the Schools."]

The purpose of this study was to investigate the incremental validity of a set of domain general cognitive measures added to a traditional screening battery of early numeracy measures. The sample consisted of 458 kindergarten students of whom 285 were designated as severely at-risk for mathematics difficulty. Hierarchical multiple regression results indicated that Wechsler Abbreviated Scales of Intelligence (WASI) Matrix Reasoning and Vocabulary subtests, and Digit Span Forward and Backward measures explained a small, but unique portion of the variance in kindergarten students' mathematics performance on the Test of Early Mathematics Ability -- Third Edition (TEMA-3) when controlling for Early Numeracy Curriculum Based Measurement (EN-CBM) screening measures (R[superscript 2][subscript change] = 0.01). Furthermore, the incremental validity of the domain general cognitive measures was relatively stronger for the severely at-risk sample. We discuss results from the study in light of instructional decision-making and note the findings do not justify adding domain general cognitive assessments to mathematics screening batteries. [This paper was published in "School Psychology Quarterly" v33 n2 p264-271 2018 (EJ1181714).]

The goal of this randomized controlled trial (RCT) was to evaluate the effectiveness of a small-group intervention in fractions for fifth-graders who are performing below grade level in mathematics. The impact of the fractions intervention was assessed on fifth-grade at-risk students' understanding of foundational fractions concepts and procedural competence with fractions. For the fractions intervention, lessons from the "TransMath"® curriculum (Level 2; Woodward & Stroh, 2015) were modified to create 52 thirty-five-minute lessons focused only on fourth- and fifth-grade level fractions content that could be used in a small-group setting. In this rigorous large-scale RCT, a sample of 1,123 students from three school districts across two U.S. states were screened at the beginning of the school year using a fractions measure developed by the research team. Two hundred and five students who scored between the 15th and the 37th percentile on the screening measure and received parental consent to participate were randomly assigned to the intervention (n = 102) and comparison (n = 103) conditions. Students in the fractions intervention condition received 35-minute tutoring sessions 3-4 times a week. Fraction instruction using the 52 "TransMath" lessons was provided by trained tutors. The comparison condition (n = 103) was business as usual instruction (i.e., core classroom fractions instruction, including intervention or support traditionally provided by the school). Results from the final analytic sample of 186 students (87 in intervention, 99 in comparison) showed that the intervention group significantly outperformed the comparison group on all outcome measures, which included an array of assessments used to measure both student understanding of foundational fractions concepts as well as procedural competence with grade-level fraction material (Hedges' g = 0.66 to 1.08; p < 0.0001).

We explore the potential of a computer-adaptive decoding game in Spanish to increase the decoding skills and oral reading fluency in Spanish and English of bilingual students. Participants were 78 first-grade Spanish-speaking students attending bilingual programs in five classrooms in Texas. Classrooms were randomly assigned to the treatment (i.e., where students played Graphogame Spanish) for 16 weeks for ten minutes per day (n = 3) versus business as usual instruction (n = 2). Results indicate that students at some risk on Spanish pseudoword reading appeared to benefit the most from playing the game. Analysis of gains suggests a potentially small, but meaningful educational effect of the game on Spanish oral reading fluency and English pseudoword reading when taking Spanish decoding skills at pretest into account. Students indicated that they enjoyed playing the game, and that the game helped them improve their reading skills. Teachers perceived the game as an engaging tool for students to use during small-group instruction or during independent time in a Response-to-Intervention approach. We discuss our mixed results in the context of using computer-adaptive games to improve the academic outcomes of bilingual students. [This is the online version of an article published in "Bilingual Research Journal." For the final version of this article, see EJ1143411.]

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during which students build a strong foundation in fractions concepts. At the same time, the National Mathematics Advisory Panel (2008) cites limited understanding of fractions as the key reason for the high failure rate in algebra courses. Longitudinal data from both the United States and the United Kingdom have demonstrated that knowledge of fractions in the elementary grades plays a powerful role in subsequent success in algebra, the gateway to math achievement in high school. Members of the Regional Educational Laboratory (REL) Southeast Improving Mathematics Instruction Research Alliance saw teachers' lack of in-depth knowledge of fractions concepts as a major challenge in their teaching these concepts to their students. Alliance members indicated that teachers would benefit from a professional development program that focused on building a deep understanding of the mathematical ideas underlying fractions and of how to apply those ideas in the classroom. This large-scale study investigates the effectiveness of such a program to help inform future district and state investments in professional development. Members of the REL Southeast Improving Mathematics Instruction Research Alliance formed a work group and selected Developing Mathematical Ideas (DMI) as the professional development program that seemed best suited to develop in-depth teacher knowledge of fractions and that could be scaled up in a large number of districts simultaneously. Developed by the Education Development Corporation, DMI is designed to help teachers think through major mathematical ideas and examine and reflect on how their students develop and understand the ideas. Teachers examine vignettes of classroom teaching and examples of student work from their own classes and from the classes of other participating teachers. Teachers also work on fractions problems designed to promote their own understanding of fractions concepts. The primary goal of the study was to assess the impact of DMI on grade 4 students' and teachers' understanding of fractions. The study was conducted during the 2014/15 school year using data from 84 schools in eight school districts in three states (Florida, Georgia, and South Carolina). Participants included 4,204 grade 4 students and 264 grade 4 teachers. Nine trained facilitators provided the professional development. The study used a randomized controlled trial, randomly assigning schools to either the treatment condition or the control condition. Teachers in schools in the treatment condition received 24 hours of DMI professional development on fractions during fall 2014. They attended eight three-hour sessions conducted over four days (two three-hour sessions per day; one day per month). In most cases substitute teachers filled in for teachers during these days; in some cases teachers preferred occasional Saturday sessions and were compensated for the additional workday. Teachers in the control condition did not receive DMI professional development but were free to participate in any type of school- or district-provided professional development in math, including fractions. About a third of teachers in the control condition indicated that they had participated in some form of professional development in fractions. The student outcome measure was the Test for Understanding of Fractions, which was administered at the end of the school year to assess students' understanding of fractions concepts and their ability to perform computations and word problems. The teacher outcome measure was the Mathematical Knowledge for Teaching: Fractions Scale (Learning Mathematics for Teaching, 2008), which was administered to all teachers at the end of the study to assess their understanding of the mathematical ideas involved in teaching fractions and their knowledge of the typical errors and misconceptions that can develop as students learn this material. Key findings include: (1) DMI did not demonstrate any impact on student proficiency in fractions. Students of teachers who participated in DMI performed at almost the same level as students of teachers who did not participate; the difference was not statistically significant (p = 0.637); and (2) The impact of DMI on teachers' knowledge of fractions was inconclusive. Teachers who participated in DMI performed 0.19 standard deviation better than teachers who did not participate, but the difference was not statistically significant (p = 0.051). Thus, DMI had nonsignificant impacts on students' proficiency in fractions and their teachers' knowledge of fractions. The finding of no impact on students' math proficiency is common in the research literature on professional development in math. The results suggest that professional development that attempts to build teachers' knowledge of the mathematical ideas underlying the K-8 curriculum, though theoretically compelling, does not always lead to improvements in student learning. The following are appended: (1) Study design and study sample; (2) Reliability of measures; (3) Online surveys; and (4) Data analysis.

This article presents the results of an evaluation of Positive Family Support, an ecological family intervention and treatment approach to parent supports and family management training developed from a history of basic and translational research. This effectiveness trial, with 41 public middle schools randomly assigned to intervention or control, examined student-, teacher-, and parent-reported outcomes, as well as math and reading scores and school attendance. Multilevel analyses suggested that for students at risk for behavior problems, immediate-intervention schools outperformed control schools on parent-reported negative school contacts for students at risk for behavior problems. Implementation, however, was hampered by several challenges, including school funding cuts, lack of staff time to provide parenting supports, and staff turnover. Given that preventive interventions are generally cost effective, it is critical that researchers continue their efforts to refine these interventions and find ways to support schools' implementation of evidence-based programs that can reduce problem behavior. This article is part of a special issue "Parental Engagement in School-Based Interventions". [This is the in press version of an article published in "Journal of School Psychology" (ISSN 0022-4405).]