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Music has been called the temporal art par excellence. Yet, as this paper explains, it is also the atemporal art par excellence. The contradiction is, however, only apparent, and a result of viewing music from two possible perspectives. That it has these two perspectives is the focus of this paper. In particular, the way in which these two aspects of music allow it to function as a kind of conduit between transcendent and immanent; immaterial and material. This can help explain the power of music to touch places deep in the soul (the part of us that transcends matter and time), that other forms of art struggle to reach. A somewhat similar debate occurs in looking at mathematics from an ontological point of view. In particular the treatment of the real numbers. There are curious properties of real numbers that seem to put them, like music, in the realm of the transcendent: in terms of the amount of information to specify them, one requires infinite computer time since there is no repeating pattern to their decimal expansions. One must simply evolve the sequence, working through it, despite the fact that it might have a perfectly situated home in Platonia. In other words, bringing them into this world demands a temporal element. We explore these and other links to a variety of issues in physics, ultimately arguing for dual-aspect monism., Comment: To appear in K. Cunio, K. Parry, and D. Rickles (eds.), Harmony of the Spheres: New Essays. ANU Press

The "Blueprint for Maryland's Future," passed by the 2021 Maryland General Assembly, requires that a college and career readiness (CCR) standard be set for Maryland public school students that "certifies that by the end of 10th grade, and not later than the end of 12th grade, a student has the requisite literacy in English and math to be successful in first-year, credit-bearing coursework at a Maryland community college or open enrollment postsecondary institution" (Blueprint for Maryland's Future Act, 2021, p. 9). The Maryland State Department of Education (MSDE) contracted with the American Institutes for Research® (AIR®) to conduct the empirical study required by the "Blueprint" and to explore additional possible measures of student readiness for college and career success. This report addresses the study's four objectives: (1) identify knowledge and skills required to be college and career ready; (2) assess the alignment between Maryland's College and Career Ready Academic Content Standards and postsecondary expectations; (3) assess how well the interim CCR standard and alternative specifications of the standard predict postsecondary progress; and (4) identify potential areas of bias within assessments used to determine CCR.

Online credit recovery will likely expand in the coming years as school districts try to address increased course failure rates brought on by the coronavirus pandemic. Some researchers and policymakers, however, raise concerns over how much students learn in online courses, and there is limited evidence about the effectiveness of online credit recovery. This article presents findings from a multisite randomized study, conducted prior to the pandemic, to expand the field's understanding of online credit recovery's effectiveness. Within 24 high schools from a large urban district, the study randomly assigned 1,683 students who failed Algebra 1 or ninth grade English to a summer credit recovery class that either used an online curriculum with in-class teacher support or the school's business-as-usual teacher-directed class. The results suggest that online credit recovery had relatively insignificant effects on student course experiences and content knowledge, but significantly lower credit recovery rates for English. There was limited heterogeneity in effects across students and schools. Non-response on the study-administered student survey and test limit our confidence in the student experience and content knowledge results, but the findings are robust to different approaches to handling the missing data (multiple imputation or listwise deletion). We discuss how the findings add to the evidence base about online credit recovery and the implications for future research. [This paper will be published in "Journal of Research on Educational Effectiveness."]

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks for a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein ``structureless structures'' are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model., Comment: 20 pages

Stephen Wolfram has recently outlined an unorthodox, multicomputational approach to fundamental theory, encompassing not only physics but also mathematics in a structure he calls The Ruliad, understood to be the entangled limit of all possible computations. In this framework, physical laws arise from the the sampling of the Ruliad by observers (including us). This naturally leads to several conceptual issues, such as what kind of object is the Ruliad? What is the nature of the observers carrying out the sampling, and how do they relate to the Ruliad itself? What is the precise nature of the sampling? This paper provides a philosophical examination of these questions, and other related foundational issues, including the identification of a limitation that must face any attempt to describe or model reality in such a way that the modeller-observers are included

Use of online credit recovery is a growing trend across the country, with the hope that expanding credit recovery options through online courses will help students get back on track toward graduation (e.g., Atkins, Brown, & Hammond, 2007; Gemin, Pape, Vashaw, & Watson, 2015). But expanded use of online credit recovery for high school students has outpaced the research. The authors conducted a multisite study to test a blended-learning model for credit recovery, where the main curriculum is provided through an online program and an in-class teacher provides more individualized instructional support. The authors present findings on the implementation and initial outcomes for two cohorts of students who enrolled in an Algebra 1 or English 9 credit recovery course the summer immediately after their first year of high school. The authors address three main research questions to describe how implementation of the online classes differed from the schools' business-as-usual (BAU) teacher-directed approach to credit recovery, and provide preliminary evidence about the short-term effects of the online approach: (1) How did the "instructional features" of the online classes compare to the BAU classes?; (2) How did "students' experiences" in the online classes compare to the BAU classes?; and (3) How did students' "proximal outcomes" (content knowledge and credit recovery) in the online classes compare to the BAU classes? The findings suggest that implementation of the online classes produced limited instructional contrast with the BAU condition and may have unintentionally altered grading practices. Potentially as a result, fewer students recovered the course credit in the online classes than the control classes. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

It will be presented in this chapter a historical account of the consistent histories interpretation of quantum mechanics based on primary and secondary literature. Firstly, the formalism of the consistent histories approach will be outlined. Secondly, the works by Robert Griffiths and Roland Omn\`es will be discussed. Griffiths' seminal 1984 paper, the first physicist to have proposed a consistent-histories interpretation of quantum mechanics, followed by Omn\`es' 1990 paper, were instrumental to the consistent-histories model based on Boolean logic. Thirdly, Murray Gell-Mann and James Hartle's steps to their own version of consistent-histories approach, motivated by a cosmological perspective, will then be described and evaluated. Gell-Mann and Hartle understood that spontaneous decoherence could path the way to a concrete physical model to Griffiths' consistent histories. Moreover, the collective biography of these figures will be put in the context of the role played by the Santa Fe Institute, co-founded by Gell-Mann in 1984 in Santa Fe, New Mexico, where Hartle is also a member of the external faculty., Comment: To appear in: Olival Freire Junior (Ed.), Oxford Handbook of the History of Interpretations of Quantum Physics, Oxford University Press

Background: Over the past decade, schools across the United States increasingly turned to online learning (Gemin, Pape, Vashaw, & Watson, 2015; Queen & Lewis, 2011). While many espouse the promise of online credit recovery (OCR) courses, the abrupt shift to online learning during the COVID-19 pandemic renewed concerns about theses courses' effectiveness as tools for equitable outcomes (Tate & Warschauer, 2022). These concerns are exacerbated by a dearth of rigorous and mixed evidence about the effectiveness of OCR courses (Viano, 2018). A correlational study of OCR in Florida found that students in online courses were more likely to earn a C or better than students in face-to-face courses (Hughes, Zhou & Petscher, 2015). A study of North Carolina high school students who failed a course found that students who enrolled in OCR were more likely to graduate but had lower test scores than students who repeated the face-to-face version of the course (Viano & Henry, 2020). In addition, Heinrich et al. (2019) found that in a large urban midwestern district "online course-taking is not benefiting students or reflecting real learning" (p. 2,174). To date, there have been two randomized controlled trials of OCR. The first study found that students who took an OCR course in Chicago were less likely to earn credit and learned less than students who took a face-to-face course (Heppen et al., 2017), but found no statistically significant differences in longer-term outcomes, including high school graduation (Rickles et al., 2018). The second study found that students who took an OCR course in a large, urban school district were, on average, less likely to earn credit for ninth grade English than students who took a teacher-directed course but found no statistically significant differences in credit recovery rates in Algebra 1 or in content knowledge across both subject areas (Rickles et al., in press). Purpose: This paper builds off the second randomized study to examine how OCR affects longer-term high school outcomes relative to the business-as-usual (BAU) teacher-directed credit recovery classes. We address the following research questions: (1) What was the impact of taking OCR on students' credit accumulation over four years of high school?; (2) What was the impact of taking OCR on students' probability of on-time high school graduation?; (3) How did the longer-term effects of OCR vary across sites?; and (4) How did students' prior academic performance and engagement moderate the longer-term effects of OCR? Intervention: The intervention for this study was an Algebra 1 or English 9 online curriculum for the credit recovery course, where an online provider supplied the main course content and curriculum, and the school provided the credentialed in-class teacher who could supplement the digital instruction. The BAU classes primarily relied on traditional teacher-directed instruction, where teachers had latitude in the curriculum and instructional materials for the class. For both the intervention and BAU conditions, students took the class within a standard classroom during the district's 5-week summer session. Key characteristics of the online learning model tested in this study are presented in Exhibit A.1. The theory of action for the study is presented in Exhibit A.2. Population and Setting: The analyses in this paper are based on 613 students in 28 Algebra 1 classes across 13 high schools and 1,124 students in 70 English 9 classes across 19 high schools, all within a large urban district. All students entered 9th grade in the 2017-18 school year (Cohort 1) or the 2018-19 school year (Cohort 2) and failed their Algebra 1 and/or at least one semester of their English 9 course and enrolled in a credit recovery course the summer between their 9th and 10th grade year. For both cohorts, the credit recovery classes took place before the COVID-19 pandemic. Exhibit A.3 presents descriptive statistics and baseline equivalence for the Algebra 1 and English 9 student samples. Research Design: Students were randomly assigned to take their credit recovery course in an online class (treatment) or a BAU class (control). Random assignment took place within blocks defined by school, course, and cohort. In some schools, blocks were further defined by which semesters of the course the students failed during their 9th grade year. Data Collection and Analysis: We utilized extant district student background and course data for all analyses in this paper. Measures are described in Exhibit A.4. All analyses were conducted separately for Algebra and English. We estimated average treatment effects for the intent-to-treat student sample using regression models that control for student characteristics and randomization blocks. For the analysis of between-site heterogeneity, we estimated site-specific treatment effects by adding site-by-treatment interaction terms (fixed effects) to the main impact model specification. For the student-level moderator analysis we estimated separate moderation models for two indicators of prior academic performance (8th grade assessment scores and 9th grade GPA) and an indicator of school engagement (9th grade attendance). Findings: We are conducting analyses for this paper and therefore do not currently have findings to present. We expect to have full results by August 2023. Conclusions: The findings will provide needed evidence about the relative effectiveness of OCR to keep students on track toward graduation over time and obtain a high school degree. While earlier results from this study indicate that the online classes were more difficult to pass but may have improved short-term content knowledge for certain students in certain subject areas, it is not clear whether those proximal effects had implications for students' progress toward graduation. To help interpret the findings, the paper will use data from a larger sample of the district's students, focus group data from participating teachers, and interview data from students who took credit recovery during the pandemic to help situate the impact findings within the broader context of teaching, learning, and high school progression during the pandemic. Within this context, findings about the longer-term effects of OCR should inform future efforts to address the needs of students who fall behind early in their high school career.

Enrollment in eighth-grade algebra doubled from the 1990s to 2012 (National Center for Education Statistics, 2013) as research demonstrated that Algebra I operates as a "gateway" to advanced mathematics courses in high school (Adelman, 2006), and that students who succeed in Algebra I in middle school have more success in mathematics throughout high school. However, prior work was heavily prone to selection bias, focusing on high-performing students. Other work examines outcomes of taking eighth-grade algebra for students with different levels of readiness and highlights negative effects for average or lower performing students (e.g., reduced test scores [Loveless, 2008], decreased likelihood of passing geometry by Grade 11 and Algebra II by Grade 12 [Clotfelter, Ladd, & Vigdor, 2013]). However, these studies have important limitations; they focus on district(s) within one state and/or only examine short-term outcomes,and no study examines graduation outcomes among average and lower-performing students. Given rapid expansion of access to eighth-grade algebra, the need to examine short- and longer-term outcomes for "all" students is urgent. To address this gap, the authors conducted an exploration study to examine the following research questions in two distinct districts: (1) What is the "impact" of placement into eighth-grade algebra on short-term outcomes (attendance, math course performance) across the transition to high school, and on longer-term high school milestones (completing math course requirements, graduation)?; and (2) To what extent do "impacts" of placement into eighth-grade algebra vary for students with different levels of prior readiness? Although placement in eighth-grade algebra may initially result in lower math course performance in eighth-grade, the authors observed consistently positive, and no negative impacts for students in high school. Positive impacts on course performance and graduation were sometimes larger for students who did not attain the highest prior math course grades or test scores, and positive impacts on completion of math course requirements before eleventh grade were larger for higher performing students. Relatively few students with the lowest math course grades or test scores in seventh grade took algebra in eighth grade, limiting generalizability for these students. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

Educator performance evaluation systems are a potential tool for improving student achievement by increasing the effectiveness of the educator workforce. For example, recent research suggests that giving more frequent, specific feedback on classroom practice may lead to improvements in teacher performance and student achievement. This report is based on a study that the U.S. Department of Education's Institute of Education Sciences conducted on the implementation of teacher and principal performance measures that are highlighted by recent research, as well as the impact of providing feedback based on these measures. As part of the study, eight districts were provided resources and support to implement the following three performance measures in a selected sample of schools in 2012-13 and 2013-14: (1) Classroom practice measure; (2) Student growth measure; and (3) Principal leadership measure. Within each district, schools were randomly assigned to implement the performance measures (the treatment group) or not (the control group). No formal "stakes" were attached to the measures--for example, they were not used by the study districts for staffing decisions such as tenure or continued employment. Instead, the measures were used to provide educators and their supervisors with information regarding performance. Such information might identify educators who need support and indicate areas for improvement, leading to improved classroom practice and leadership and boosting student achievement. This is the second of two reports on the study. The first focused on the first year of implementation, describing the characteristics of the educator performance measures and teachers' and principals' experiences with feedback. This report examines the impact of the two-year intervention, as well as implementation in both years. The main findings are: (1) The study's measures were generally implemented as planned; (2) The study's measures provided some information to identify educators who needed support, but provided limited information to indicate the areas of practice educators most needed to improve; (3) As intended, teachers and principals in treatment schools received more frequent feedback with ratings than teachers and principals in control schools; and (4) The intervention had some positive impacts on teachers' classroom practice, principal leadership, and student achievement. This report is a summary to the full report. [For the full report, "The Impact of Providing Performance Feedback to Teachers and Principals. NCEE 2018-4001," see ED578873. For the first year report, "Early Implementation Findings from a Study of Teacher and Principal Performance Measurement and Feedback: Year 1 Report. NCEE 2017-4004," see ED569983. For the first year report executive summary, "Early Implementation Findings from a Study of Teacher and Principal Performance Measurement and Feedback: Year 1 Report. Executive Summary. NCEE 2017-4003," see ED569982.]

Educator performance evaluation systems are a potential tool for improving student achievement by increasing the effectiveness of the educator workforce. For example, recent research suggests that giving more frequent, specific feedback on classroom practice may lead to improvements in teacher performance and student achievement. This report is based on a study that the U.S. Department of Education's Institute of Education Sciences conducted on the implementation of teacher and principal performance measures that are highlighted by recent research, as well as the impact of providing feedback based on these measures. As part of the study, eight districts were provided resources and support to implement the following three performance measures in a selected sample of schools in 2012-13 and 2013-14: (1) Classroom practice measure; (2) Student growth measure; and (3) Principal leadership measure. Within each district, schools were randomly assigned to implement the performance measures (the treatment group) or not (the control group). No formal "stakes" were attached to the measures--for example, they were not used by the study districts for staffing decisions such as tenure or continued employment. Instead, the measures were used to provide educators and their supervisors with information regarding performance. Such information might identify educators who need support and indicate areas for improvement, leading to improved classroom practice and leadership and boosting student achievement. This is the second of two reports on the study. The first focused on the first year of implementation, describing the characteristics of the educator performance measures and teachers' and principals' experiences with feedback. This report examines the impact of the two-year intervention, as well as implementation in both years. The main findings are: (1) The study's measures were generally implemented as planned; (2) The study's measures provided some information to identify educators who needed support, but provided limited information to indicate the areas of practice educators most needed to improve; (3) As intended, teachers and principals in treatment schools received more frequent feedback with ratings than teachers and principals in control schools; and (4) The intervention had some positive impacts on teachers' classroom practice, principal leadership, and student achievement. [For the executive summary to this report, "The Impact of Providing Performance Feedback to Teachers and Principals. Executive Summary. NCEE 2018-4000," see ED578874. For the first year report, "Early Implementation Findings from a Study of Teacher and Principal Performance Measurement and Feedback: Year 1 Report. NCEE 2017-4004," see ED569983. For the first year report executive summary, "Early Implementation Findings from a Study of Teacher and Principal Performance Measurement and Feedback: Year 1 Report. Executive Summary. NCEE 2017-4003," see ED569982.]

This paper describes and demonstrates a new online resource developed to help researchers proactively plan for student attrition: the Student Attrition Lookup Tool (SALT). With SALT, researchers can access student mobility estimates for different student and school subpopulations and for different transition periods from kindergarten to grade 12. The paper has three main objectives: (1) describe the data and methods behind SALT; (2) demonstrate how to navigate SALT; and (3) demonstrate how to use student attrition benchmarks in a power analysis. The paper is primarily intended for applied researchers planning school-based studies that follow students over time. SALT is based on four longitudinal data sets from the National Center for Education Statistics (NCES). With the four NCES surveys, the authors constructed analytic files to examine student mobility across six transition periods. Since applied researchers increasingly utilize data from district or state student information systems, the authors estimated three types of student mobility rates (for each transition period) to reflect three different levels of data coverage: (1) any mobility (left baseline school/outside school data); (2) left the district, state, or public school system (outside district data); and (3) left the state or public school system (outside state data, including dropouts). [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

Background: Over the past 20 years, much has been written about the merits and limitations of matching methods, particularly propensity score matching (see, e.g., Stuart, 2010 for a review of matching approaches), and the myriad ways matching can be implemented to identify a comparison group that is similar to the treatment group on observable characteristics. However, relatively little methodological work focuses on using matching methods with multilevel data structures that are common in education research. For example, with students nested within schools, a study might use (a) a multisite design when the study includes multiple schools and treatment assignment is at the student level, or (b) a cluster design when treatment assignment is at the school level. Over the past 15 years, some studies have addressed matching for a multisite design (e.g., Arpino & Cannas, 2016; Lee, Nguyen, & Stuart, 2021; Rickles & Seltzer, 2014) and some studies have addressed matching for a cluster design (e.g., Pimentel, Page, Lenard, & Keele, 2018; Zubizarreta & Keele, 2017). Under both designs, a critical complication is the extent to which, and the way in which, the matching method should account for possible confounding at different levels of the data structure (e.g., student-level and school-level). We are aware of no study, however, that has addressed matching for a multisite cluster design that may include confounding factors at three levels. Such a design is common in education research, where, for example, students are the unit of analysis, classes or teachers are the unit of treatment assignment, and classes/teachers are nested within schools. Throughout this paper, we use the terms unit to refer to the level of analysis (e.g., students at level 1), cluster to refer to the level of treatment assignment (e.g., teachers at level 2), and site to refer to the top level of nesting (e.g., schools at level 3). Purpose: This paper addresses the lack of information and guidance about matching in a multisite cluster design by comparing how different matching methods perform within this design, as well as discussing the trade-offs of different matching approaches under different data conditions. The paper is primarily intended for applied researchers planning observational studies of interventions at the classroom/teacher level or the school level, and an interest in student-level outcomes. The findings will also inform needs for future methodological work on matching methods for multisite cluster designs. Setting/Population: Our analysis is based on an empirical data example and a simulation study. For the empirical example, we use data from an evaluation of an alternative teacher training program in a Southeastern metropolitan area, where some teachers of grade 4-8 students entered teaching through this alternative program (treatment condition) and other teachers did not (comparison condition). These data allow us to demonstrate how different matching methods function when estimating the effect of a teacher-level treatment on student achievement. For the simulation study, we generated data to mimic a three-level design with outcomes at level 1 and treatment at level 2. The data generation process is outlined in Table 1. To test the performance of matching methods under different study contexts, we generate data for 16 conditions (see Table 2) based on the level 2 and level 3 sample size, as well as the amount of outcome variance at level 2 and level 3. These parameters were selected because they are the most likely to affect the relative performance of the matching approach (see, e.g., Arpino & Cannas, 2016; Rickles & Seltzer, 2014). The values for the parameters were based on the empirical data example to reflect real world values. Research Design: We examine 12 different matching methods that cover the range of approaches currently available to address multisite designs or cluster designs separately (see Table 3). Matching methods for multisite designs differ in the extent to which they prioritize within-site versus between-site matching. Within-site matching is desirable because it ensures that matched units are equivalent on observed and unobserved site-level covariates but may not produce balance on unit-level covariates, or may exclude a lot of treatment units if there is limited common support among units in the same site. Between-site matching allows for a larger pool of matches, but if an unobserved site-level characteristic influences both the treatment and outcome of interest, it can bias the estimated causal effect. Within-group matching is a compromise between within- and between-site matching by creating groups (or strata) of similar sites and exact matching within those groups. Matching methods for cluster designs differ based on whether and how the matching process accounts for unit-level and/or cluster-level covariates. We will examine all 12 combinations of matching approaches on our three-level study design, using different matching specifications tailored for each method (e.g., propensity score estimation, optimal matching, caliper setting). For all the methods, we pair matching with regression-based covariate adjustment to follow best practices. Results: Our results will compare the relative performance of the methods along four dimensions: (1) match rates at all levels, (2) covariate balance at all levels, (3) mean treatment effect estimation bias, and (4) root mean squared error. We hypothesize that approaches that directly account for the unit-level and cluster-level covariates and within-site matching will have better covariate balance and lower bias compared to other approaches when cluster-level and site-level factors are stronger confounders (larger inter-class correlations) and the sample size is larger, but may result in worse match rates (and generalizability) than other approaches. Conversely, we hypothesize that approaches focused only on the unit-level or cluster-level covariates and that allow for between-site matches will perform better than other approaches when cluster-level and site-level factors are relatively weak confounders (smaller inter-class correlations) and the sample size is smaller. Conclusions: This paper addresses a limitation in current matching literature by providing researchers with information about different matching approaches for a multisite cluster observational study, as well as things to consider when selecting an approach. The findings will help applied researchers select an appropriate matching approach for a common three-level design found in education.