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A critical challenge for elementary mathematics teachers is meeting the learning needs of all students, especially when there is variability in students' number knowledge. Because young students' number system knowledge (NSK) contributes to future success in mathematics, NSK activities must be designed to engage all students, particularly students who have struggled to engage in mathematics, to help students build early number knowledge. In this manuscript, we describe a quick images number sense intervention implemented across five second-grade teachers and 75 students, and examine outcomes related to teacher actions and student engagement behaviors. The results of our mixed-methods study indicate that the intervention provided multiple ways for students of varying abilities to engage with and learn the content. Our results provide practical implications for teachers, and prompt questions to evaluate in future research.

Co-teaching may be a promising strategy to improve inclusive secondary mathematics education in rural schools. Professional development (PD) aids in special and general education teachers' co-teaching implementation, yet little empirical research examines how to effectively train and support co-teachers. In this study, we describe one U.S. state's PD model for secondary mathematics co-teaching, evaluate outcomes of the PD on co-teachers' behaviors and beliefs, and examine the impact of co-teaching on students' mathematics achievement. We examined data from observations, surveys, and students' pre/post assessments across nine classes within seven U.S. school districts, including three rural school districts, over 3 years. We report data from a total of 19 teachers and 281 students in sixth through ninth grades. The PD participants implemented effective co-teaching strategies and reported positive viewpoints toward co-teaching. Additionally, students with and without disabilities improved their mathematics scores. We present key findings for rural schools to guide future implementation and research.

Research on mathematics interventions for college students with learning disabilities (LD) is sparse, yet mathematics is critical for post-secondary success. Prior research indicates that many effective strategies for teaching mathematics to secondary students with LD (e.g., manipulatives and cognitive strategies) can also improve the mathematics performance of college students with LD. In this article, we summarize mathematics intervention research conducted with college students with LD, and report the findings of a pilot single-case design intervention implemented with one college student with LD, Ada. Results indicate that Ada made improvements in solving rate of change word problems following participation in a six-week intervention that incorporated an integrated Concrete-Representational-Abstract framework and a problem-solving heuristic (POD[checkmark]). Effect sizes were largest for the specific outcome of calculating the correct answer. These results provide initial directions for future research and practice to improve the mathematics performance of college students with LD.

Kindergarten reading screening measures typically identify many students as at risk who later meet criteria on important outcome measures (i.e., false positives). To address this issue, we evaluated a gated screening process that included accelerated progress monitoring, followed by a simple goal/reward procedure (skill vs. performance assessment, SPA) to distinguish between skill and performance difficulties on Phoneme Segmentation Fluency (PSF) and Nonsense Word Fluency (NWF) in a multiple baseline across students design. Nine kindergarten students scored below benchmark on PSF and/or NWF at the middle of year benchmark assessment. Across students and skills (n = 13 panels of the study), nine met/exceeded benchmark during baseline (suggesting additional exposure to the assessments was adequate), two exceeded benchmark during goal/reward procedures (suggesting adding a motivation component was adequate), and two required extended exposure to goal/reward or skill-based review to exceed the benchmark. Across panels of the baseline, 12 of 13 skills were at/above the end-of-year benchmark on PSF and/or NWF, suggesting lower risk than predicted by middle-of-year screening. Due to increasing baseline responding, experimental control was limited; however, these results suggest that simple progress monitoring may help reduce false positives after screening. Future research on this hypothesis is needed.

There are many practices that educators can use to develop self-regulated learning (SRL); however, an organizational framework for cataloging SRL supportive practices that also identifies empirical support for those practices is lacking. The purpose of this manuscript is to provide such guidance by developing the settings, exchanges, and events (SEE) framework, and guide its use. Literature review and expert feedback led us to identify three categories of SRL supportive practices including (a) creating a learning setting that is conducive to SRL, (b) fostering adaptive learning exchanges between educators and learners that foster SRL, and (c) creating events that provide opportunities to utilize SRL skills. The SEE framework is beneficial to educators because it organizes SRL supportive practices and can facilitate professional development trainings. The SEE framework can also support educational researchers interested in embedding SRL within classrooms. Specifically, the SEE framework provides an initial structure of practices that can initiate discussions among researchers and be tested and elaborated upon. Moreover, the SEE framework can assist researchers in the development of tools to support classroom observation and consultation.

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of mathematics. Combining CRA-I and explicit instructional strategies may increase students' conceptual understanding and ability to express mathematical reasoning through writing. This study included three ninth-grade students with disabilities, and employed a multiple-probe design across-participants to investigate a functional relation between an explicit instructional strategy within a CRA-I framework and high school students' with disabilities proficiency in solving rate of change problems. Results showed that all three students improved their mathematics scores (combined Tau-"U" effect size = 0.77, p < 0.001) and maintained improvements during a 1- to 7-week post-instruction phase. Implications for research and practice related to mathematics instruction and intervention specifically for students with learning disabilities are discussed.

The push toward digital curricula has quickened with the COVID-19 pandemic leading to concerns about how digital curricula programs are selected. Research indicates selection of curricula plays a primary role in student achievement. State curriculum leaders were surveyed about how they are involved in selecting PK-8 mathematics digital curricula. Results indicated while 81% were aware of the rise of digital curricula, 77% of responding states did not have state-level digital curricula selection processes.

Secondary level or Tier 2 interventions such as the Check-in Check-out (CICO) intervention effectively reduce problem behaviors of students who are non-responsive to school-wide interventions. However, some students will not be successful with Tier 2 interventions. This study investigated the effects of adding individualized function-based support for four students with disabilities who were not successful in general education settings while receiving only a secondary level intervention. Results indicated that the combination of secondary and individualized function-based interventions effectively decreased problem behavior for all participants. Teachers and students rated the interventions as acceptable and effective. Research and practice implications are discussed.

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual understanding of numbers while learning to operate with abstract symbols. In this mixed-methods study, we examined the variations and shifts in second-grade students' NSK outcomes after participating in an instructional treatment focused on building their NSK through visual representations. After receiving professional development in the instructional treatment, five classroom teachers implemented a systematically planned series of 27 visual number activities across 9 weeks. Analysis using a general linear model indicates that, based on 75 students' pretest and posttest achievement data, students made significant improvements in NSK that are most likely attributable to the instructional treatment. Additional analyses indicate that students with the lowest pretest scores made the greatest gains and the most substantial shifts in their thinking following the instructional treatment.

Check-in, check-out (CICO), an intervention implemented with students at risk for behavioral disorders, addresses minor misbehaviors by providing students with a structured means of receiving positive adult attention. CICO reduces problem behaviors and improves appropriate behaviors of students with and without behavioral disorders. Research indicates CICO may be adapted to target a range of behaviors. This article presents a six-step process for adapting CICO and applies this process to demonstrate how the intervention can be adapted to support students with academic difficulties, internalizing behavior problems, and more severe behavior problems.

Research has shown that: (1) Curriculum-based monitoring (CBM) can be easily implemented and interpreted by teachers (e.g., Fuchs, Deno, & Mirkin, 1984); (2) student outcomes have improved when teachers use CBM to inform instructional decision making (e.g., Fuchs, Fuchs, Hamlett, & Stecker, 1991); (3) reliable and valid measures have been developed that predict important student outcomes (e.g., Fuchs, Fuchs, & Maxwell, 1988; Kim, Petscher, Schatschneider, & Foorman, 2010; Wayman, Wallace, Wiley, Tichá, & Espin, 2007); and (4) CBM can be an integral component of multi-tiered systems for identifying and monitoring students' academic needs (e.g., Kovaleski, VanDerHeyden, & Shapiro, 2013; M. R. Shinn, 2007). According to the authors, using curriculum-based measurement of oral reading fluency (CBM ORF) progress-monitoring measures is an effective way to consistently evaluate students' reading performance and make data-based instructional decisions. However, educators should understand and properly control for factors that may influence variability. Working with other professionals at their schools, educators should ensure that data are collected and analyzed following the recommendations presented in this article as well as the recommendations from the publisher of the CBM ORF measure to maximize the use of CBM ORF.

Previous research on curriculum-based measurement of oral reading fluency (CBM ORF) found high levels of variability around the estimates of students' fluency; however, little research has studied the issue of variability specifically with well-designed passage sets and a sample of students who scored below benchmark for the purpose of progress monitoring. We examined the variability in oral reading fluency score slopes due to passage and student characteristics using "DIBELS Next" progress monitoring passages over 4 weeks using a hierarchical linear growth model. Participants included second-, third-, and fourth-grade students identified as at risk for reading difficulties. The results showed an average growth rate of approximately 1 correctly read word per minute per week, with considerably lower variability than shown in previous research with less controlled passage sets and/or higher performing student samples. Implications for practice are discussed, including procedural recommendations for administrators and teachers.

Check-In, Check-Out (CICO) is one of the most widely implemented Tier 2 behavior interventions in a school-wide system of Positive Behavior Interventions and Supports (PBIS). Much literature has documented implementation of CICO across individual schools or districts. The Illinois PBIS Network, currently known as the Midwest PBIS Network, has provided extensive training and technical assistance (TA) on CICO with more than 400 schools in more than 125 districts. The purpose of this descriptive study was to detail the training process for implementation of CICO across 441 schools, evaluate student success based on Daily Progress Reports (DPRs), and document fidelity and implementation on a subset of 41 elementary and 13 middle schools. Results indicated more than 80% of students earned at least 80% of their DPR points, the majority of schools implemented CICO with more than 70% fidelity, and schools were able to support between 7% and 12% of student population on CICO. Implications for practice and suggestions for future research are included.

This survey study assessed the acceptability of a variety of functional behavioral assessment (FBA) procedures (i.e., functional assessment interviews, rating scales/questionnaires, systematic direct observations, functional analysis manipulations) to a national sample of 123 special educators and a state sample of 140 school psychologists. Results indicated that special educators and school psychologists reported generally positive perceptions regarding their willingness to participate in, the appropriateness of, the usefulness of, and the feasibility of the FBA procedures. Special educators were significantly more likely to endorse the use of systematic direct observation and functional analysis manipulation strategies than school psychologists, although no differences were found regarding the social desirability of FBA procedures for individuals exhibiting mild and severe problem behaviors. School psychologists were also more likely than special educators to express concerns about the amount of time that can be entailed in FBA procedures. We discuss implications for practice and future research.

The purpose of this systematic literature review was to summarize outcomes of the Check-in Check-out (CICO) intervention across elementary and secondary settings. Twenty-eight studies utilizing both single subject and group (experimental and quasi-experimental) designs were included in this review. Median effect sizes across the eight group studies were small (median "d" = 0.37; range, -0.15 to 0.60) for studies reporting Cohen's "d" or similar effect sizes and large (0.23; range, 0.13 to 0.32) for studies reporting "R"[superscript 2] type effect sizes favoring the implementation of CICO. For single subject design studies, the overall median PND across 20 studies was 68% (range, 0 to 100%), indicating CICO is questionably effective but approaching the effectiveness criterion (= 70% PND) suggested by Scruggs and Mastropieri (1998). Implications for practice are discussed along with suggestions for future research.

Kindergarten reading screening measures typically identify many students as at risk who later meet criteria on important outcome measures (i.e., false positives). To address this issue, we evaluated a gated screening process that included accelerated progress monitoring, followed by a simple goal/reward procedure (skill vs. performance assessment, SPA) to distinguish between skill and performance difficulties on Phoneme Segmentation Fluency (PSF) and Nonsense Word Fluency (NWF) in a multiple baseline across students design. Nine kindergarten students scored below benchmark on PSF and/or NWF at the middle of year benchmark assessment. Across students and skills (n = 13 panels of the study), nine met/exceeded benchmark during baseline (suggesting additional exposure to the assessments was adequate), two exceeded benchmark during goal/reward procedures (suggesting adding a motivation component was adequate), and two required extended exposure to goal/reward or skill-based review to exceed the benchmark. Across panels of the baseline, 12 of 13 skills were at/above the end-of-year benchmark on PSF and/or NWF, suggesting lower risk than predicted by middle-of-year screening. Due to increasing baseline responding, experimental control was limited; however, these results suggest that simple progress monitoring may help reduce false positives after screening. Future research on this hypothesis is needed. [ABSTRACT FROM AUTHOR]

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for improving the word problem-solving performance of students with disabilities. This multiple-probe, multiple-baseline, single-case design study evaluated the effects of an intervention that included an integrated, concrete-representational-abstract teaching framework with an embedded problem-solving strategy (POD Check) on students’ rate-of-change word problem-solving performance. The intervention was delivered virtually via video conferencing technology. Four middle- and high-school students with or at risk of mathematics learning disabilities in the Intermountain West participated in the intervention. Results indicate evidence of a functional relation between the intervention and students’ word problem-solving performance, and effects were maintained 2–4 weeks after the intervention. The findings of this study provide implications for mathematics intervention research and practice for students with learning disabilities. [ABSTRACT FROM AUTHOR]

There are many practices that educators can use to develop self‐regulated learning (SRL); however, an organizational framework for cataloging SRL supportive practices that also identifies empirical support for those practices is lacking. The purpose of this manuscript is to provide such guidance by developing the settings, exchanges, and events (SEE) framework, and guide its use. Literature review and expert feedback led us to identify three categories of SRL supportive practices including (a) creating a learning setting that is conducive to SRL, (b) fostering adaptive learning exchanges between educators and learners that foster SRL, and (c) creating events that provide opportunities to utilize SRL skills. The SEE framework is beneficial to educators because it organizes SRL supportive practices and can facilitate professional development trainings. The SEE framework can also support educational researchers interested in embedding SRL within classrooms. Specifically, the SEE framework provides an initial structure of practices that can initiate discussions among researchers and be tested and elaborated upon. Moreover, the SEE framework can assist researchers in the development of tools to support classroom observation and consultation. [ABSTRACT FROM AUTHOR]

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of mathematics. Combining CRA-I and explicit instructional strategies may increase students' conceptual understanding and ability to express mathematical reasoning through writing. This study included three ninth-grade students with disabilities, and employed a multiple-probe design across-participants to investigate a functional relation between an explicit instructional strategy within a CRA-I framework and high school students' with disabilities proficiency in solving rate of change problems. Results showed that all three students improved their mathematics scores (combined Tau- U effect size = 0.77, p <.001) and maintained improvements during a 1- to 7-week post-instruction phase. Implications for research and practice related to mathematics instruction and intervention specifically for students with learning disabilities are discussed. [ABSTRACT FROM AUTHOR]

The push toward digital curricula has quickened with the COVID-19 pandemic leading to concerns about how digital curricula programs are selected. Research indicates selection of curricula plays a primary role in student achievement. State curriculum leaders were surveyed about how they are involved in selecting PK–8 mathematics digital curricula. Results indicated while 81% were aware of the rise of digital curricula, 77% of responding states did not have state-level digital curricula selection processes. [ABSTRACT FROM AUTHOR]

Check-in, check-out (CICO), an intervention implemented with students at risk for behavioral disorders, addresses minor misbehaviors by providing students with a structured means of receiving positive adult attention. CICO reduces problem behaviors and improves appropriate behaviors of students with and without behavioral disorders. Research indicates CICO may be adapted to target a range of behaviors. This article presents a six-step process for adapting CICO and applies this process to demonstrate how the intervention can be adapted to support students with academic difficulties, internalizing behavior problems, and more severe behavior problems. [ABSTRACT FROM AUTHOR]

Previous research on curriculum-based measurement of oral reading fluency (CBM ORF) found high levels of variability around the estimates of students’ fluency; however, little research has studied the issue of variability specifically with well-designed passage sets and a sample of students who scored below benchmark for the purpose of progress monitoring. We examined the variability in oral reading fluency score slopes due to passage and student characteristics using DIBELS Next progress monitoring passages over 4 weeks using a hierarchical linear growth model. Participants included second-, third-, and fourth-grade students identified as at risk for reading difficulties. The results showed an average growth rate of approximately 1 correctly read word per minute per week, with considerably lower variability than shown in previous research with less controlled passage sets and/or higher performing student samples. Implications for practice are discussed, including procedural recommendations for administrators and teachers. [ABSTRACT FROM AUTHOR]