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The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. It describes the progressions of learning within each course and provides content supports that include broad ideas about effective instruction as well as practical instructional strategies. Math teachers, coaches, and leaders are encouraged to use these materials collaboratively to support ongoing instruction and the growth of individual teaching practice. The content is organized by the following topics in Algebra I, including: (1) Standards for Mathematical Practice; (2) Algebra I: Number and Expressions; (3) Algebra I: Functions; (4) Algebra I: Linear Relationships; (5) Algebra I: Systems of Linear Equations and Inequalities; (6) Algebra I: Quadratic and Exponential Relationships; and (7) Algebra I: Data Analysis and Statistics

Since 2011, the Alaska Performance Scholarship (APS) has awarded Alaska students who excel in high school with more than $100 million in scholarships to help cover the cost of in-state postsecondary education. This report covers: (1) APS Eligibility & Use; (2) High School Outcomes; (3) Postsecondary Outcomes; and (4) Alaska Residency and Workforce Outcomes. [This report was prepared by McKinley Research Group (MRG). For "Alaska Performance Scholarship Outcomes Report 2022. APS: Fall 2011-2021," see ED621314.]

This report outlines key data elements related to the Western Undergraduate Exchange (WUE), Western Regional Graduate Program (WRGP), and Professional Student Exchange Program (PSEP) for the 2022-23 academic year and is a core resource for policymakers, institutional leaders, counselors and other stakeholders across the region. This report contains participation and migration statistics for each program, shared in aggregate and by each Western Interstate Commission for Higher Education (WICHE) state and territory. There are also summaries that provide reference points for for students and their families, school counselors and academic advisors, institutional leaders and enrollment management staff, and policymakers. [For the 2021-22 report, see ED622643.]

This report provides an overview of kindergarten readiness of six Baltimore City Public Schools (City Schools) kindergarten cohorts from the 2016-17 to the 2021-22 school year. This report is accompanied by the Annual Digest of City Schools Kindergarten Statistics, 2022 Edition (Baltimore Education Research Consortium [BERC], 2022), which provides detailed summary tables and descriptive statistics on kindergarten readiness and outcomes over time and is the source data for the visualization and interpretation found in this report. By understanding children's kindergarten experiences, we hope that the stakeholders can collectively identify needs and opportunities for early childhood services and programming for our youngest children and their families. Early childhood is a complex developmental period, and descriptions of children's kindergarten readiness through the use of only one measure can be difficult. While the core of this report provides descriptive aggregate statistics on children's measured performance on the Maryland State Department of Education's Kindergarten Readiness Assessment (KRA), we also provide a "multi-dimensional" understanding of kindergarten readiness and outcomes by including an examination of kindergarten attendance and early literacy skill development as measured by the Dynamic Indicators of Basic Early Literacy Skills (DIBELS). To better understand differences across students, we also examine these kindergarten indicators by gender, race and ethnicity, English language learner (ELL) status, special education status, and prior care. We acknowledge that these are not the only ways to measure or represent successful kindergarten experiences. However, we hope that the analyses in this report help researchers, practitioners, and policymakers use various indicators in exploring children's kindergarten success. Young children, their families, and educators experienced unprecedented challenges during the COVID-19 pandemic. In this report, we highlight children's kindergarten experiences during the pandemic and the recovery period. We compare the most recent year data with the pre-COVID data to analyze what has changed after the pandemic. Finally, we maintain the results on the relationships between kindergarten indicators and 3rd grade outcomes for the two earliest cohorts of kindergartners in this report (2014--15 and 2015--16).

Much of the policy debate emerging from concerns over student debt has focused on the structure and operation of income-driven repayment (IDR). As the number of available IDR plans and the share of borrowers enrolling in these plans has increased, the system has become more confusing and difficult to navigate. IDR has not prevented default problems, as early supporters hoped, or silenced the voices arguing that student debt is destroying the lives of too many borrowers.1 As demands for reducing the loan amounts borrowers must repay get stronger, it is useful to examine the logic behind IDR, the repayment system's strengths and weaknesses, and the reforms that could create a more sustainable and equitable public policy framework. This report reviews the history of support for IDR among policy experts and the gradual and haphazard development of current policies and analyzes potential reforms. It looks at proposals from other observers and analyze of the impacts of alternative approaches on borrowers in different circumstances and taxpayers, discussing the pros and cons of various modifications to the current system.

Head Start is a national program that helps young children from families with low income get ready to succeed in school. It does this by working to promote their early learning and health and their families' well-being. The Head Start Family and Child Experiences Survey (FACES) provides national information about Head Start programs and participants. This report includes information on the FACES 2019 study design, and presents key findings from the study's spring 2020 data collection. The purpose of this report is to (1) provide information about the FACES 2019 study, including the background, design, methodology (including the impact of COVID-19 on data collection), assessments, and analytic methods; and (2) report detailed descriptive statistics (averages, response ranges, and percentages) and related standard errors (the estimate of the standard deviation of each statistic; see accompanying technical appendix for standard errors) in a series of tables. In total, 165 programs, 318 centers, and 590 classrooms participated in the study in spring 2020. The tables provide information from separate surveys of program directors, center directors, and teachers.

We examined whether students were accurate in predicting their test performance two testing contexts (low-stakes and high-stakes). The sample comprised U.S. high school students enrolled in an advanced placement (AP) statistics course during the 2017-2018 academic year (N=209; M[subscript age]=16.6 years). We found that even two months before taking the AP exam, a high stakes summative assessment, students were moderately accurate in predicting their actual scores ([kappa][subscript weighted]=0.62). When the same variables were entered into models predicting inaccuracy and overconfidence bias, results did not provide evidence that age, gender, parental education, number of math classes previously taken, or course engagement accounted for variation in accuracy. Overconfidence bias differed between students enrolled at different schools. Results indicated that students' predictions of performance were positively associated with performance in both low- and high-stakes testing contexts. The findings shed light on ways to leverage students' self-assessment for learning.

Drasgow, Levine, and Zickar (1996) suggested a statistic based on the Neyman-Pearson lemma (e.g., Lehmann & Romano, 2005, p. 60) for detecting preknowledge on a known set of items. The statistic is a special case of the optimal appropriateness indices of Levine and Drasgow (1988) and is the most powerful statistic for detecting item preknowledge when the assumptions underlying the statistic hold for the data (e.g., Belov, 2016; Drasgow et al., 1996). This paper demonstrated using real data analysis that one assumption underlying the statistic of Drasgow et al. (1996) is often likely to be violated in practice. This paper also demonstrated, using simulated data, that the statistic is not robust to realistic violations of its underlying assumptions. Together, the results from the real data and the simulations demonstrate that the statistic of Drasgow et al. (1996) may not always be the optimum statistic in practice and occasionally has smaller power than another statistic for detecting preknowledge on a known set of items, especially when the assumptions underlying the former statistic do not hold. The findings of this paper demonstrate the importance of keeping in mind the assumptions underlying and the limitations of any statistic or method. [This paper will be published in "Applied Psychological Measurement."]

The Council on Postsecondary Education (Council) is charged with guiding the reform efforts envisioned by state policy leaders in the Kentucky Postsecondary Education Improvement Act of 1997 and is Kentucky's statewide postsecondary and adult education coordinating agency. To gain better insight into economic conditions and workforce trends, specifically within three targeted sectors, the Council partnered with Emsi, a labor market analytics firm serving higher education, economic and workforce development, talent acquisition, and site selection. In this report, Emsi focuses on the Education sector by providing an overview of education occupations and industries through traditional labor market information and a job postings analysis, conducting a program demand gap analysis of Kentucky institutions' education program offerings, and analyzing migration patterns and other qualitative characteristics that help explain why Kentucky education alumni stay in or migrate out of the state. Emsi also provides an environmental scan of the state's economy to provide context for the Education sector. Data around the Education sector are provided for the state and, where pertinent, by region. The regions are based on Kentucky's Workforce Planning Regions (WPRs). In addition, data for the city of Louisville and its surrounding counties, which comprise the Kentuckiana Local Workforce Area (LWA), are shown distinct from the Central WPR.

On average, Florida students earn only half of the points possible in the statistics content area of the state's annual mathematics assessment. Leaders in Broward County Public Schools, a large, diverse, urban school district, viewed changes to statistics curriculum and instruction as one way to address this issue. This study randomly assigned 40 middle schools in the district to either implement a replacement curriculum unit with four days of teacher professional development in probability and statistics or continue with their practice-as-usual instruction in probability and statistics. The replacement unit supported teaching and learning of all the probability and statistics standards in the grade 7 course description. The replacement unit with the associated professional development, called the Supporting Teacher Enactment of the Probability and Statistics Standards program, improved student understanding of statistics and statistics instruction. The magnitude of the effect on student understanding was 23 percent of 1 standard deviation, which is comparable to an increase of 9 percentile points for an average student. [For the appendixes, see ED610168. For the study snapshot, see ED610167.]

These are the appendixes for the report "Effects of an Inquiry-Oriented Curriculum and Professional Development Program on Grade 7 Students' Understanding of Statistics and on Statistics Instruction." This cluster-randomized controlled trial compared the Supporting Teacher Enactment of the Probability and Statistics Standards (STEPSS) program--a 20-day curriculum unit designed to support teaching and learning of the state curriculum standards for statistics and probability in grade 7, along with four days of professional development for teachers--with practice-as-usual probability and statistics instruction and teacher professional development. The two primary outcomes of interest were student understanding of statistics and classroom instruction in statistics. Two appendices are included in the document: (1) About the study; and (2) Study data and data analysis. [For the full report, see ED610166. For the study snapshot, see ED610167.]

Factor analysis is often used to model scales created to measure latent constructs, and internal structure validity evidence is commonly assessed with indices like SRMR, RMSEA, and CFI. These indices are essentially effect size measures and definitive benchmarks regarding which values connote reasonable fit have been elusive. Simulations from the 1990s suggesting possible benchmark values are among the most highly cited methodological papers across any discipline. However, simulations have suggested that fixed benchmarks do not generalize well -- fit indices are systematically impacted by characteristics like the number of items and the magnitude of the loadings, so fixed benchmarks can confound misfit with model characteristics. Alternative frameworks for creating customized, model-specific benchmarks have recently been proposed to circumvent these issues but they have not been systematically evaluated. Motivated by two empirical applications where different methods yield inconsistent conclusions, two simulation studies are performed to assess the ability of three different approaches to correctly classify models that are correct or misspecified across different conditions. Results show that dynamic fit indices and equivalence testing both improved upon the traditional Hu & Bentler benchmarks and dynamic fit indices appeared to be least confounded with model characteristics in the conditions studied. [This paper was published in "Multivariate Behavioral Research" v58 n1 p195-219 2023.]

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational knowledge and skills required for success in advanced math courses. This leaves educators to determine which students are ready for Algebra I in grade 8 and which are not. To inform strategies that address this challenge, this study examined whether student knowledge in five math domains in grade 7 was associated with Algebra I achievement in grade 8. It found that students' scores in all five domains were associated with Algebra I achievement. The "expressions and equations" domain had the strongest association. The association between the "number system" domain and Algebra I achievement was stronger for English learner students than for non English learner students. The associations between the five grade 7 domains and Algebra I achievement did not significantly differ for students who were receiving special education services and those who were not. [For the full report, see ED606821; for the appendixes, see ED606833; for the study snapshot, see ED606836.]

These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational knowledge and skills required for success in advanced math courses. This leaves educators to determine which students are ready for Algebra I in grade 8 and which are not. To inform strategies that address this challenge, this study examined whether student knowledge in five math domains in grade 7 was associated with Algebra I achievement in grade 8. It found that students' scores in all five domains were associated with Algebra I achievement. The "expressions and equations" domain had the strongest association. The association between the "number system" domain and Algebra I achievement was stronger for English learner students than for non English learner students. The associations between the five grade 7 domains and Algebra I achievement did not significantly differ for students who were receiving special education services and those who were not. Four appendixes are included: (1) Literature review; (2) Methods; (3) Supporting analysis; and (4) Other analyses using proficiency groups as the dependent variable. [For the full report, see ED606821; for the study brief, see ED606835; for the study snapshot, see ED606836.]

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational knowledge and skills required for success in advanced math courses. This leaves educators to determine which students are ready for Algebra I in grade 8 and which are not. To inform strategies that address this challenge, this study examined whether student knowledge in five math domains in grade 7 was associated with Algebra I achievement in grade 8. It found that students' scores in all five domains were associated with Algebra I achievement. The "expressions and equations" domain had the strongest association. The association between the "number system" domain and Algebra I achievement was stronger for English learner students than for non English learner students. The associations between the five grade 7 domains and Algebra I achievement did not significantly differ for students who were receiving special education services and those who were not. [For the appendixes, see ED606833; for the study brief, see ED606835; for the study snapshot, see ED606836.]

Adult numeracy is key to improving citizens' lives and supporting the development of jobs markets, economies and societies around the globe. However, its importance is all too often overlooked, in terms of both numeracy education (for adults and in schools) and monitoring of skill levels by credible direct assessment. The UNESCO Institute for Lifelong Learning (UIL) has published a policy brief to support the assessment and development of adult numeracy worldwide. Recent changes in the world of work, such as jobs growth in the information and service sectors, mean that today's workers need adequate numeracy skills in order to adapt (Jonas, 2018). Numeracy competency is also linked to important aspects of individual well-being, such as health and active citizenship (OECD, 2019). The COVID-19 pandemic has further highlighted the prime importance of numeracy skills. The public's ability to understand and analyse the large volumes of statistical information and projections that are being circulated via media channels has become crucial to the success of national measures aimed at reducing infection rates and easing the social and economic consequences of the pandemic. Existing data, however, suggests that many adults do not have sufficient numeracy skills. The Programme for the International Assessment of Adult Competencies (PIAAC), for example, notes that a large percentage of the adult population -- 30 to 60 per cent in middle-income countries and 10 to 40 per cent in high-income countries -- have low or very low levels of numeracy proficiency (OECD, 2019). Furthermore, many countries have no data on which to base an assessment of their existing numeracy gaps. The UIL policy brief highlights these challenges and recommends: (1) adopting a long-range national strategy focusing on adult numeracy that involves the use of direct numeracy measures (distinct from literacy); (2) investing in the development of national capacities to measure and improve adult numeracy skills; and (3) developing a creative and scalable monitoring approach that reflects the respective country's demographic and linguistic diversity. [This policy brief is based on joint contributions by Iddo Gal and UIL staff.]

The Adaptive Learning in Statistics (ALiS) Project tested the implementation of an adaptive learning platform at nine colleges in Maryland. The platform served as a textbook replacement to introduce course concepts inside and outside of the classroom, and instructors used in-class time to reinforce statistics concepts as part of a flipped classroom approach. This report describes study results from the 2017/18 academic year. The Urban Institute evaluation compared course satisfaction and learning outcomes (course grade, pass rates, and statistics competency) of students who completed introductory statistics in class sections with the ALiS approach against the outcomes for students enrolled in "business as usual" introductory statistics sections. We find that the ALiS intervention was effective at four-year colleges relative to business as usual. Students at community colleges in ALiS sections did not show significant differences in any of the measures of performance relative to students in business-as-usual sections but were less satisfied with the course than their peers in other sections. When all students are aggregated in the analysis, the results showed very modest improvements in student grades and statistics competency, no difference in passing with a C or better, and a lower level of satisfaction. This study adds to the body of research on adaptive learning approaches by highlighting the important roles of pedagogy, course curriculum, and course structure in the experience of students completing college-level, technology-mediated coursework.

The report provides a portrait of science and engineering (S&E) higher education in the United States, including trends over time and comparisons with other nations. S&E fields, as defined in this report, include astronomy, chemistry, physics, atmospheric sciences, earth sciences, ocean sciences, mathematics and statistics, computer sciences, agricultural sciences, biological sciences, psychology, social sciences, and engineering. At the doctoral level, the medical and health sciences are included under S&E because the doctoral-level data correspond to the doctor's-research/scholarship degree level, which includes research-focused degrees. The report is divided into four main sections. The first section provides an overview of the U.S. higher education system, with special emphasis on several types of institutions, and on distance and online education. This section also provides information on sources of aid for undergraduate and graduate S&E education, with a focus on the federal government's role. The second section looks at trends over time in S&E degree awards at the undergraduate and graduate levels, highlighting patterns by field. The third section focuses on the demographic attributes of S&E degree recipients, including sex and race and ethnicity. It examines trends by degree level and field. The final section focuses on international S&E higher education. This section provides data on students on temporary visas who study or earn degrees in the United States. It also benchmarks the United States with other nations in terms of S&E degrees awarded.