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This study explores opportunity to learn (OTL) during mathematics activities for a nine-year-old student girl with difficulty in mathematics. We conducted a teaching experiment comprising 15 instructional sessions. To better understand the student's OTL, our qualitative analysis focused on how she student demonstrated self-regulation in response to instructional delivery (i.e., explicit instruction and cognitively demanding tasks) and feedback (i.e., corrective, affirmative, and pressing). The student's self-regulatory behaviors indicated a highly graduated, student-centered structure with affirmative, mathematizing feedback supported mathematics learning, while other components of instructional delivery and forms of feedback did not. Thus, we provide an illustration of self-regulation as an indicator of OTL rather than as something to remediate. We argue individualized support can be facilitated by integrating instructional practices from the fields of special education and mathematics education and expanding perspectives on self-regulation, rather than holding singular commitments to particular disciplinary practices and perspectives.

In this study, we examined the relationship of special education teachers' performance on the Recognizing Effective Special Education Teachers (RESET) Explicit Instruction observation protocol with student growth on academic measures. Special education teachers provided video-recorded observations of three instructional lessons along with data from standardized, curriculum-based academic measures at the beginning, middle, and end of the school year for the students in the instructional group. Teachers' lessons were evaluated by external, trained raters. Data were analyzed using many-faceted Rasch measurement (MFRM), correlation, and multiple regression. Teacher performance on the overall protocol did not account for statistically significant variance in student growth beyond that of students' beginning of the year academic performance. Teacher performance on an abbreviated protocol comprised of items that had average or higher item difficulties on the MFRM analysis accounted for an additional 4.5% of variance beyond that of beginning of the year student performance. Implications for further research are discussed. [For the Grantee Submission to this article, see ED607655.]

This study describes the development and initial psychometric evaluation of the Recognizing Effective Special Education Teachers (RESET) observation instrument. The study uses generalizability theory to compare two versions of a rubric, one with general descriptors of performance levels and one with item-specific descriptors of performance levels, for evaluating special education teacher implementation of explicit instruction. Eight raters (four for each version of the rubric) viewed and scored videos of explicit instruction in intervention settings. The data from each rubric were analyzed with a four facet, crossed, mixed-model design to estimate the variance components and reliability indices. Results show lower unwanted sources of variance and higher reliability indices with the rubric with item-specific descriptors of performance levels. Contributions to the fields of intervention and teacher evaluation are discussed.

In this study, we developed an Explicit Instruction special education teacher observation rubric that details the elements of explicit instruction and tested its psychometric properties using many-facet Rasch measurement (MFRM). Video observations of classroom instruction from 30 special education teachers across three states were collected. External raters (n = 15) were trained to observe and evaluate instruction using the rubric and assigned scores of "implemented," "partially implemented," or "not implemented" for each of the items. Analyses showed that the item, teacher, lesson, and rater facets achieved high psychometric quality for the instrument. Implications for research and practice are discussed.

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this teaching experiment was to explore a diverse learner's understandings about equipartitioning and relational reasoning. Across eleven 45-min individualized sessions, the equipartitioning learning trajectory (EPLT) served as the framework for investigating the student's thinking and learning. Findings illustrate how a student's actual trajectory can be focused on developing a many-to-one meaning for fractions and relational reasoning, rather than strictly adhering to the sequence of proficiencies hypothesized by the EPLT. Further, the student's engagement with cognitive elements which characterize mental activity reveals ways instruction might be tailored to support a student's relational reasoning. Implications include a more nuanced perspective on individual learning of equipartitioning and important considerations for educators who support relational reasoning in diverse learners.

Researchers and practitioners alike often look to meta-analyses to identify effective practices to use with students with disabilities. The number of meta-analyses in special education has also expanded in recent years. The purpose of this systematic review is to evaluate the quality of reporting in meta-analyses focused on mathematics interventions for students with or at risk of disabilities. We applied 53 quality indicators (QIs) across eight categories based on recommendations from Talbott et al. to 22 mathematics intervention meta-analyses published between 2000 and 2020. Overall, the meta-analyses met 61% of QIs and results indicated that meta-analyses most frequently met QIs related to providing a clear purpose (95%) and data analysis plan (77%), whereas meta-analyses typically met fewer QIs related to describing participants (39%) and explaining the abstract screening process (48%). We discuss the variation in quality indicator scores within and across the quality categories and provide recommendations for future researchers.

In this study, we examined the scoring and generalizability assumptions of an explicit instruction (EI) special education teacher observation protocol using many-faceted Rasch measurement (MFRM). Video observations of classroom instruction from 48 special education teachers across four states were collected. External raters (n = 20) were trained to observe and evaluate instruction using the protocol. The results of this study suggest that the scoring rule is appropriate, in that the three-point scale allows for a meaningful way to differentiate various levels of quality of implementation of EI across teachers. Raters consistently scored easier items with higher scores, and more difficult items with a lower score. Additionally, the MFRM results for the rater facet suggest that raters can consistently apply the scoring criteria, and that there is limited rater bias impacting the scores. Implications for research and practice are discussed. [For the corresponding grantee submission, see ED607677.]

In this study, we compared the results of 27 special education teachers' evaluations using two different observation instruments, the Framework for Teaching (FFT), and the Explicit Instruction observation protocol of the Recognizing Effective Special Education Teachers (RESET) observation system. Results indicate differences in the rank-ordering of teachers depending on which instrument was used. Overall scores on RESET were higher on average than those on FFT. Item-level analyses showed that across 125 correlations, 73 were significant, low-moderate, and 52 were nonsignificant. Implications for research and practice are discussed. [For the grantee submission, see ED607673.]