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This implementation project focused on supporting teachers who provide mathematics instruction and/or intervention to students with mathematics learning disabilities (MLD) and mathematics difficulties (MD). The research team worked with three schools, over three years. Instructional delivery differed across schools, primarily in setting and amount of time students received mathematics instruction. Given these various contexts, the project provided job-embedded professional development to support each school's implementation of the three key features of the project: using evidence-based curricula, using evidence-based practices, and responsive coaching. By focusing middle school intervention on algebraic reasoning--which requires a strong understanding of rational numbers, variables, and equivalence--students with MLD and MD made gains across the school year that were comparable to their peers. However, the gains were not enough to close the achievement gap between students with MLD and MD and students who are on grade-level. Given the three-year implementation of this project included two years of altered instruction due to COVID-19 restrictions, it is encouraging that students with MLD and MD made gains that were comparable to their peers. The project worked with eight teachers across the three schools and found variability among their implementation and how they preferred to work with the research team. From an implementation science perspective, one year of implementing a new innovation is likely insufficient to fully build capacity in teachers to sustain the practices learned from the JEPD. However, teachers indicated that they learned many new things related to teaching students with MLD and MD through the JEPD, which is encouraging.

Several school districts in Georgia use two teacher-administered diagnostic assessments of student knowledge of mathematics as part of their multi-tiered system of support in grades K-8: the Global Strategy Stage (GloSS; New Zealand Ministry of Education, 2012) and the Individual Knowledge Assessment of Number (IKAN; New Zealand Ministry of Education, 2011), which comes in two formats (Counting Interview and Written Assessment). However, little is known about whether two teachers using the same assessment to assess the same student on two occasions within a short period of time assign the same Stage Score (interassessor reliability) or about how useful the teachers found the assessments (consequential validity). Rather than relying on occasional testimonials from the field, decisions about using diagnostic assessments across the state should be based on psychometric data from an external source. Districts not currently using the GloSS and IKAN assessments have indicated an interest in using them, if they are proven to be reliable and valid diagnostic assessments, to assess students' understanding of mathematics and determine appropriate levels of instruction and intervention. This study found adequate interassessor reliability for the GloSS and for the IKAN Counting Interview but not for the IKAN Written Assessment. The IKAN Written Assessment requires additional attention to improve training so that reliability can be established. Teachers indicated that they found the screening data from the GloSS and IKAN assessments more useful for guiding decisions about student instruction and intervention than the screening data currently employed. Although teachers in the study's focus groups expressed strong support for both assessments, teachers reported in the study's survey that the GloSS is more useful than the IKAN because it assesses students' solution strategies, unlike most other mathematics assessments. Teachers also expressed some criticisms of both assessments; for example, they believed that the GloSS should include vocabulary familiar to students and that the IKAN Written Assessment should be untimed. [For the appendixes, see ED607586; for the study snapshot, see ED607587.]

The purpose of this brief is to present an overall picture of how well early reading interventions are working for students in Grades 1-3. Using a meta-analytic approach, this paper combines findings from several studies to determine the effectiveness of early reading interventions for students who are struggling with learning to read.

A solid foundation in fractions is a key predictor of success in algebra and more advanced mathematics, which in turn is predictive of entry into higher education and many high-paying vocations. Yet, when fractions are introduced into the mathematics curriculum in upper elementary grades (grades 4 and 5), many students demonstrate minimal growth in fractions knowledge and some students find themselves three grade levels or more behind their peers at the start of seventh grade. Identifying the best way to meet the needs of students who struggle with fractions, coupled with validating instructional approaches that address this need, is critical. This brief paper presents research findings from an experimental study utilizing a "preventative" approach to fraction intervention for fifth-grade students that emphasizes "proactively" teaching grade-level standards in conjunction with key foundations for understanding fractions concepts and procedures. Then, six recommendations for practice and policy are presented based on findings from the research study.

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.

The purpose of this efficacy study was to examine the impact of the Teacher Study Group (TSG) professional development program in vocabulary, on teacher knowledge, observed teaching practice, and student vocabulary achievement, when implemented with first grade teachers in Title 1 schools. This multi-site cluster randomized trial was implemented in 61 schools from 16 districts in four states (California, Texas, Ohio, and Illinois). The analytic sample included 182 first grade teachers and 1,680 of their students. Significant impacts were found at the teacher level for teacher knowledge (g = 0.38, p < 0.05), the "Teacher-Directed Vocabulary Instruction" scale (g = 0.93, p < 0.001), and the "Interactive Vocabulary Instruction" scale (g = 0.47, p < 0.05). No significant impacts were found at the student level on the "Woodcock-Johnson Oral Vocabulary" and "Reading Vocabulary" subtests and the "GRADE Word Meaning" subtest.

The ESEA Blueprint for Reform states that teachers need "effective, ongoing, job-embedded, professional development that is targeted to student and school needs… [and] aligned with evidence of improvements in student learning." Unfortunately, the professional development approaches advocated, though sensible and compelling in theory, have rarely been widely field-tested and evaluated using rigorous research techniques. The situation is slowly changing, but often the results have been mixed. One promising professional development effort in recent years has been the Teacher Study Group (TSG). This approach to professional development is an attempt to orchestrate several of the "best practices" in professional development--linkage to core curriculum, concreteness, establishment of collegial networks, and ongoing related activities--into a feasible model for use in elementary schools. The goal of the TSG professional development program is to enhance instruction by helping teachers integrate research-based instructional strategies into their existing curriculum. The purpose of the study is to examine the impact of the Teacher Study Group, focused on effective vocabulary instruction, on teacher knowledge, observed teaching practice, and student vocabulary achievement when implemented with first grade teachers in Title I schools. The major research questions were: (1) What is the impact of the TSG on teacher knowledge and teaching practice when compared to the professional development efforts being provided by the states and districts?; (2) What is the impact of the TSG on students' vocabulary knowledge when compared with students in classes receiving existing professional development efforts?; (3) What role does fidelity of implementation of the TSG protocols by the facilitators play in moderating the impacts of TSG on teacher and student outcomes?; and (4) What contextual factors facilitate or hinder effective implementation of the TSG? the randomized controlled study was conducted in 61 Title 1 schools (31 treatment and 30 control) from 16 school districts in four states: California, Ohio, Illinois, and Texas. The sample consisted of 182 first grade teachers (94 treatment and 88 control) and a randomly selected sample of 1811 students (940 in treatment and 871 in control). In each district, data were collected from both the TSG and control schools at the same time, by observers and testers blind to condition, to guard against bias entering the data collection process. Preliminary findings demonstrate the potential of the TSG intervention to bring about significant positive impacts at the teacher level (a proximal outcome for a professional development intervention). Tables are appended.

Randomized field trials were used to examine the impact of the Teacher Study Group, a professional development model, on first grade teachers' reading comprehension and vocabulary instruction, their knowledge of these areas, and on the corollary comprehension and vocabulary achievement of their students. The multi-site study was conducted during the 2004-2005 and 2005-2006 school years in three large urban school districts from three states: California, Pennsylvania, and Virginia. A total of 81 first grade teachers and their 468 students from 19 Reading First schools formed the analytic sample in the study. Classrooms observations of teaching practice showed significant improvements in TSG schools: TSG teachers scored 0.86 standard deviations higher on the comprehension measure and 0.58 standard deviations higher on the vocabulary measure than control teachers. TSG teachers also significantly outperformed control teachers on the teacher knowledge measure of vocabulary instruction (ES = 0.73). Confirmatory analysis of student outcomes focused on passage comprehension, reading vocabulary, and oral vocabulary; of these only the latter was marginally significant (0.44). Implications for teacher practice and future research are discussed.

The purpose of this study was to use meta-analysis to synthesize findings from randomized control trials and quasi-experimental research on instructional approaches that enhance the mathematics proficiency of students with learning disabilities. A search of the literature from January 1971 to August 2007 resulted in a total of 42 interventions (41 studies) that met the criteria for inclusion in the study. We examined the impact of four categories of instructional components: (a) approaches to instruction and/or curriculum design, (b) providing formative assessment data and feedback to teachers on students' mathematics performance, (c) providing formative data and feedback to students with LD on their mathematics performance, and (d) peer-assisted mathematics instruction. We first examined the effectiveness of each instructional component in isolation by determining unconditional stratified mean effects and heterogeneity. All instructional components except for student feedback with goal-setting and peer-assisted learning within a class resulted in significant mean effects ranging from 0.21 to 1.56. We then examined the effectiveness of these same components conditionally, using hierarchical multiple regressions. We created a model to understand instructional variables that explain significant amounts of unique variance in outcomes. Two instructional components were associated with practically and statistically important increases in effect size -- teaching students to use heuristics and explicit instruction. Limitations of the study, suggestions for future research, and applications for improvement of current practice are discussed.

The purpose of this professional development study was to examine the impact of Teacher Study Groups on the teacher practice, teacher knowledge, and student outcomes, specifically in the areas of reading comprehension and vocabulary. The multi-site study was conducted in three large urban school districts from three states: California (CA), Pennsylvania (PA), and Virginia (VA). A total of 19 Reading First schools were involved in the study (10 treatment, 9 control). The authors developed the "Reading Comprehension and Vocabulary (RCV) Observational Measure" (Gersten et al., 2007), a moderate-inference measure, to assess the quality of classroom reading instruction. The authors' findings indicate that the "RCV Observational Measure" (Gersten et al., 2007) is sensitive to the intervention, a key component of construct validity. This aspect of validity was particularly important to them in that they designed this measure to be one of several outcomes in a study of professional development for first grade teachers. The measure also has acceptable levels of inter-observer reliability and internal consistency. The "RCV Observational Measure" (Gersten et al.) presents a viable alternative to existing observational methodology that can be used to assess the quality of teacher practice in large scale up projects to yield consistently data that is objective and reliable. (Contains 2 tables and 1 figure.)

Notes that when parents or guardians are closely involved in what is occurring at school, their children benefit. Considers the importance of how best to involve families in the educational process. Notes that home-school collaboration is necessary to accomplish more general, ongoing tasks, such as completing homework. Summarizes research and practice on home-school collaboration as it relates to homework. (SG)