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Multiple measures assessment (MMA) is an alternative placement system that involves the consideration of alternative measures of students' performance--such as high school grades or GPA--in addition to or in place of standardized test scores to better place students. While the evidence for MMA is strong, placement reform has yet to spread to many colleges and states. Moreover, despite growing support for MMA, many colleges may not be implementing the most promising MMA systems, and some may shift back to standardized testing in the post-pandemic environment. CAPR has sought to assist colleges and states nationwide with the adoption and implementation of MMA practices that place more students--and allow more students to be successful--in college-level courses. As part of these efforts, CAPR worked with colleges in Arkansas and Texas to adopt and expand MMA. The findings in this report are derived from interviews with personnel from 12 two- and four-year public colleges in those states that went through considerable effort to improve their placement systems and to make them sustainable on a large scale. The study focused on three questions: What was the design of the MMA system at each college? How were colleges adopting MMA practices and what were key facilitators and hindrances? And what was the average cost of implementation? The authors found that adoption of MMA at each study college required collaboration among institutional leaders, administrators, faculty members, and advisors. The report highlights the roles of key actors in the adoption of MMA and the important role that state context and policies played in implementation. It also describes challenges that colleges had to overcome during implementation, such as obtaining staff buy-in, managing student data, and ensuring sufficient staffing.

Let $\ell$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\ell$-torsion point, then there has been significant work done on characterizing the $\ell$-divisibility of the global Tamagawa number of $E$. In this paper, we consider elliptic curves that are $\ell$-isogenous to elliptic curves with an $\ell$-torsion point and study the $\ell$-divisibility of their global Tamagawa numbers.

Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional Chern-Simons, this gives rise to a diamond correspondence of theories. In this work we extend this framework to incorporate models realised through gaugings. As well as describing a higher-dimensional origin of coset CFTs, by choosing the details of the reduction from higher dimensions, we obtain rich classes of two-dimensional integrable models including homogeneous sine-Gordon models and generalisations that are new to the literature., Comment: 44 pages

Let $G$ be a finite group and $\rho:G \to \GL(V)$ a finite dimensional representation of $G$. We say that $\rho$ is unisingular if $\det(1-\rho(g)) = 0$ for all $g \in G$. Building on previous work in \cite{cullinan}, we consider the symmetric groups $S_n$ and prove that certain families of Specht modules are always unisingular as well as raise new questions for future study.

Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the complex group algebra C[G] and admits a direct-sum decomposition into simple Lie algebras based on the ordinary character theory of G. In this paper we review the known results on L[G] and related Lie algebras, as well as introduce a conjecture on a characteristic p analog L_p[G], with a focus on when p divides the order of G.

In this supplement, the cost to implement and operate the Dana Center Mathematics Pathways (DCMP) program across the participating colleges is presented separated into primary cost categories based on program components describing what portion of spending went to training, teacher time in class, teacher time outside of class, advisement, technology, curriculum materials, and general administration. These costs are shown in Supplement Table 1 for the start-up phase. In addition to costs incurred by the college, costs incurred by the Dana Center are quantified in Supplement Table 2. The ongoing cost of the intervention to colleges was calculated based on an estimation of DCMP program costs, the cost of the traditional developmental math sequence, and the cost of college credits attempted. These resources include direct instructional costs, as well as the usual advising services, administration, and other student services. The ongoing costs for the operation of the program during one academic year are presented in Supplement Table 3.

At community colleges and open-enrollment universities, most first-year students take placement exams in English and mathematics to determine whether they are ready for college-level courses. But large-scale studies have indicated that these test scores misplace substantial numbers of students--in other words, for many students, the test score does not accurately reflect their ability to succeed in college-level courses. This fact means that many students are taking these courses when they do not need them, using up valuable time and money. To improve placement accuracy, hundreds of colleges across the country have begun implementing a strategy called multiple measures assessment (MMA), a placement approach that uses alternative indicators including high school grade point average instead of or in addition to a single test score to improve placement accuracy. Both corequisite remediation and MMA have been shown to get more students into college-level courses quickly and to help more students pass those courses. This brief summarizes findings from two surveys that show both corequisite and MMA practices are on the rise nationally, making it even more important to understand how best to implement these two practices together. This brief also introduces a study that will provide rigorous evidence related to that question.

Following up on a previous impact and cost study of the Dana Center Mathematics Pathways (DCMP) model, which used an individual-level randomized controlled trial, this study assesses the costs and cost-effectiveness of the program on longer-term college progress and college attainment. The version of DCMP included in this study diversified the developmental and college-level math course content, separating the content into distinct pathways that better aligned with students' career interests. It also streamlined the developmental math sequence into a one-semester developmental course for all students, regardless of placement level, and implemented an evidence-based curricula and pedagogy to engage students in active problem solving pertinent to real-life situations. The study, which included 1,411 students across four Texas community colleges and ten campuses, found that DCMP saves students money and may be cost-effective when used as part of a larger strategy to improve student success.

Multiple measures assessment (MMA) has gained considerable momentum over the past decade as an alternative to traditional test-based procedures for placing incoming students into developmental or college-level coursework in math and English at broad-access colleges. Compared to standardized tests, which measure student performance at a single point in time, MMA (which often emphasizes high school GPA as a measure) provides a more holistic picture of students' academic preparation. Despite positive impacts on student outcomes that have been found by recent research on MMA, questions remain about whether the positive effects of MMA are sustained over time. This study--a follow-up to prior research using the same sample of students--employs a randomized controlled trial to investigate whether algorithmic MMA placement used at seven State University of New York (SUNY) community colleges led to better student outcomes, for up to four and a half years after randomization, than a system based on test scores alone. Nearly 13,000 incoming students who arrived at the seven colleges in fall 2016, spring 2017, and fall 2017 took placement tests and were randomly assigned to be placed using either the status quo method (business-as-usual group) or the alternative, algorithmic MMA method (program group). Using this sample, we estimate the overall treatment effects on placement into, enrollment in, and completion of college-level math and English as well as effects on other outcomes. We conduct similar analyses on race/ethnicity, Pell recipient status, and gender subgroups. We also descriptively examine the proportion of program group students who were bumped up (i.e., their placement changed from a developmental course placement to a college-level course placement) and bumped down (i.e., their placement changed from a college-level course placement to a developmental course placement) by the MMA algorithm, and we perform a cost-effectiveness analysis. We find that the MMA method used at the colleges improved access to and success in college-level courses and that lower cut scores in English rather than math are associated with larger and longer lasting impacts on completion of college-level coursework. While MMA improved outcomes among student subgroups, it had little to no impact on gaps in outcomes between subgroups. We also find that bumped-up students had substantially better outcomes in both math and English, while bumped-down students had substantially worse outcomes. Our results suggest that increased access to college-level courses is the driving factor in the positive outcomes experienced by program group students and that placement into standalone developmental courses can have detrimental effects on student outcomes. In the discussion of the study's results, we make recommendations for adopting MMA at colleges. Implemented together with other initiatives to support students, MMA can be a first step on the path to success for incoming students. [For the accompanying research brief, see ED632528.]

The Texas Higher Education Coordinating Board (THECB) seeks to improve student outcomes by promoting a variety of student success efforts. These efforts include direct programs with well-defined target populations and program participants, offering specific student support services following a program model, and indirect programs aimed at providing faculty and staff members professional development or at improving campus facilities. MDRC led an implementation study of student success programs across the state that were funded by a grant from the U.S. Department of Education, Education Stabilization Fund Program Governor's Emergency Education Relief (GEER II) Fund. This fund was a COVID-19 recovery initiative, allowing recipients great flexibility in the use of grants, evident in the findings below. A total of nearly $12 million in grants was disbursed to 59 institutions of higher education in Texas. This report presents: (1) implementation research findings from the 59 institutions; (2) highlights research findings from previously conducted, rigorous evaluations of student support programs; and (3) offers recommendations for future research and practice.

This appendix is a supplement to the report "Possible Ways of Increasing College Access Among Adults from Underserved Backgrounds: A Study of College Transition Text-Based Messaging." It provides additional information about the study of Text Ed--the messaging strategy evaluated for its ability to increase college enrollment and Free Application for Federal Student Aid completion rates among clients of Education Opportunity Centers. This includes details about the Text Ed messages, how the study was designed and conducted, detailed impact and implementation analyses, and exploratory analyses to further elucidate the findings and suggest avenues for future study. The content of the appendix is referenced as applicable within the main report. This document presents the following four appendixes that accompany the study: (1) Additional Details on Text Ed; (2) Additional Information About How the Study was Designed and Implemented; (3) Supplemental Tables for the Impact Analysis; and (4) Detailed Implementation Analysis. [For the full Evaluation Report, see ED628025. For the Study Highlights, see ED628026.]

Applying to college and securing financial aid are complex processes that can be barriers to college enrollment, particularly for individuals not entering directly after high school. These adults can seek out support from various organizations, including the U.S. Department of Education-funded Educational Opportunity Centers (EOCs), which operate from offices located within select colleges and community-based organizations. The EOCs primarily target their help to adults with low incomes and those who are potential first-generation college-goers. This study examines whether adding low-cost, text-based messaging can help EOCs more effectively work with their clients to increase clients' completion of the Free Application for Federal Student Aid (FAFSA) and college enrollment. About 3,500 EOC college-intending clients from 18 EOCs across the country were randomly divided into two groups: one received regular EOC services, and the other received EOC services plus a set of personalized, pre-programmed text messages focused on how to secure financial aid, complete key college enrollment steps, and navigate other potential barriers to college entry. The study compared the two groups to determine the effectiveness of the college transition text messaging. Key findings include: (1) Adding personalized text messaging to existing EOC services did not increase clients' rates of college enrollment or FAFSA completion; and (2) Although many clients completed important college-going tasks such as applying to college and submitting the FAFSA, 4 out of every 10 clients did not enroll in college. [For the Study Highlights, see ED628026. For the appendix, see ED628028.]

Increasingly, obtaining a job that pays family-sustaining wages means getting a college degree or other postsecondary credential. However, according to the 2021 U.S. Census, only 31.5 percent of Texans ages 25 and older have a bachelor's degree or higher. The Texas Higher Education Coordinating Board (THECB)--the highest authority in the state regarding public higher education--has therefore set out a strategic plan to increase that percentage. Specifically, the plan calls for 60 percent of Texans ages 25 to 64 to have a postsecondary credential "of value" by 2030. THECB seeks to improve student outcomes by promoting a variety of student success interventions, particularly corequisite models. To meet this goal, THECB is giving grants to colleges across the state to fund student success programs: programs designed to help more students stay in college and earn degrees, particularly students of color, students from lower-income backgrounds, and students who need additional assistance to make satisfactory academic progress (that is, to earn enough credits to keep their federal financial aid). This brief summarizes some of the information THECB and its partners will use in that effort. It describes best practices and programs with proven effectiveness--the information that policymakers and practitioners need to consider in designing and promoting student success programs. The findings are based on MDRC's 20-year history conducting rigorous evaluations in postsecondary education as well as research and evaluations by other researchers. [This brief was funded by a grant from the U.S. Department of Education, Education Stabilization Fund Program Governor's Emergency Education Relief Fund, as part of the THECB Student Success Acceleration Program Implementation Grants.]

At the 3 GeV ring of the MAX IV Laboratory, a fourth generation ring-based synchrotron light source, an asymmetric influence of the sign of the amplitude-dependent tune shift (ADTS) on the transverse mode-coupling instability (TMCI) has been observed. Measurements of the instability, in dedicated single-bunch experiments at low chromaticity, revealed a significant dependence of the dynamics of the instability above threshold on the sign of the ADTS. While for a negative sign of the ADTS the crossing of the instability does not lead to a loss of beam current, a positive sign results in the loss of 40% or more of the beam current at the threshold. In order to investigate the observed asymmetry, systematic measurement of beam dynamics above the threshold have been conducted in combination with particle tracking simulations with mbtrack2 and theoretical calculations of the Landau damping due to the ADTS. The findings point towards an influence of the Landau damping in combination with the low synchrotron frequency, which indicates that this effect could become relevant in future low-emittance electron storage rings., Comment: 13 pages, 15 figures

We provide evidence for a conjecture of Yamamura that the truncated logarithmic polynomials \[ F_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n} \] have Galois group $S_n$ for all $n \geq 1$., Comment: 9 pages. Submitted for publication

Let $E$ and $E'$ be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq E'(\F_{p^2})$. Our main result is an explicit formula for the proportion of anomalous primes for any such pair of elliptic curves. We consider both the CM case and the non-CM case., Comment: 29 pages

Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory., Comment: 38 pages, 1 figure

In response to research raising concerns about developmental placement, new placement systems and curricular models designed to increase the number of students placed into entry-level college courses have emerged in recent years. These systems aim to more accurately identify students who may benefit from some type of developmental instruction and those who are ready for entry-level college courses. This brief presents the findings of CAPR's exploratory study of informed self-placement (ISP), a placement system in which colleges provide information about placement policies, available courses, and other relevant topics to engage students as active participants in their own placement. ISP, which is also called guided self-placement or directed self-placement, is of interest because it does not rely solely, if at all, on standardized test scores, which research shows are not reliable predictors of performance in college. Moreover, many colleges adopted ISP during the COVID-19 pandemic, when this study began, because they experienced difficulty administering standardized tests and were seeking placement methods that could be easily used in a virtual setting. The study examined course enrollment and completion trends among students placed using ISP practices and sought to document varied approaches to ISP. The researchers collected demographic and outcome data on students' math and English course enrollments and completions over the last five academic years at three Nevada colleges offering associate and bachelor's degrees. They also interviewed assessment and placement scholars and representatives of higher education systems and institutions currently implementing some form of ISP. This brief provides a taxonomy of various placement systems, shares descriptive data on course enrollment and completion, and identifies important equity and access considerations for states and institutions interested in implementing ISP. Although more research is needed to understand the causal impacts of ISP on student outcomes, the data suggest that ISP has the potential to improve students' access to college-level coursework.

Research suggests that using only standardized placement test scores to determine which new college students should take developmental coursework is inadequate, as many students may be unnecessarily assigned to developmental courses. These courses generally take one or more semesters to complete, delaying entry into college-level coursework, and students earn no credit toward a credential for completing them. MDRC and the Community College Research Center recently completed two experimental studies of multiple measures assessment (MMA), in which colleges use high school GPA and other measures in addition to placement test scores to assign incoming students to either developmental or college-level courses in math and English. Overall, results from both studies indicate that student outcomes improve under MMA as compared to status quo placement based on test scores alone. In this brief, we explain what we have learned from these studies.

Let $\ell$ be a prime number and let $E$ and $E'$ be $\ell$-isogenous elliptic curves defined over a finite field $k$ of characteristic $p \ne \ell$. Suppose the groups $E(k)$ and $E'(k)$ are isomorphic, but $E(K) \not \simeq E'(K)$, where $K$ is an $\ell$-power extension of $k$. In a previous work we have shown that, under mild rationality hypotheses, the case of interest is when $\ell=2$ and $K$ is the unique quadratic extension of $k$. In this paper we study the likelihood of such an occurrence by fixing a pair of 2-isogenous elliptic curves $E$, $E'$ over ${\mathbf{Q}}$ and asking for the proportion of primes $p$ for which $E(\mathbf{F}_p) \simeq E'(\mathbf{F}_p)$ and $E(\mathbf{F}_{p^2}) \not \simeq E'(\mathbf{F}_{p^2})$.

Colleges throughout the United States are evaluating the effectiveness of their strategies to place entering students into college-level or developmental education courses. Developmental, or remedial, courses are designed to advance the reading, writing, and math skills of students who are deemed academically underprepared for college-level courses. Placements have traditionally been determined through standardized placement testing; however, through evaluating additional types of placement tests, high school transcripts, and evaluations of student motivation, multiple measures assessments (MMAs) are becoming an increasingly popular tool to place students with greater nuance. Colleges must decide what measures to include, and how to combine them. This study was developed to add to the understanding of the implementation, cost, and efficacy of an MMA system using locally determined rules. As part of a randomized controlled trial, the study team evaluated MMA programs and observed 17,203 student performances across five colleges in Minnesota and Wisconsin over the course of the fall 2018, spring 2019, and fall 2019 semesters. This report examines the impacts of MMA on math and English gatekeeper course completion and college-level credit accumulation three semesters after students' initial placement. This report also analyzes the predictive utility of high school GPA, placement tests, and the noncognitive assessments used by the study colleges.

The Krawtchouck polynomials arise naturally in both coding theory and probability theory and have been studied extensively from these points of view. However, very little is known about their irreducibility and Galois properties. Just like many classical families of orthogonal polynomials (e.g. the Legendre and Laguerre), the Krawtchouck polynomials can be viewed as special cases of Jacobi polynomials. In this paper we determine the Newton Polygons of certain Krawtchouck polynomials and show that they are very similar to those of the Legendre polynomials (and exhibit new cases of irreducibility). However, we also show that their Galois groups are significantly more complicated to study, due to the nature of their coefficients, versus those of other classical orthogonal families.

In this paper we build on the work of \cite{kaber} where it was shown that the one-parameter family of Gegenbauer Polynomials (GP) exhibit a Gibbs Phenomenon at a jump discontinuity. We show that the one-parameter family of Generalized Laguerre Polynomials (GLP) also exhibit a Gibbs Phenomenon. Among many differences, a major one is that the GLP are orthogonal on a non-compact subset of $\R$, while the GP are orthogonal on $[-1,1]$. Our strategy follows that of \cite{kaber} and we use entirely elementary methods to arrive at our result. As a special case we show that the Hermite Polynomials also possess a Gibbs Phenomenon. We conclude with a numerical example exhibiting the rate of convergence to the Gibbs constant and a conjectured identity for special values of the GLP.

Postsecondary education is widely seen as a necessity in the modern economy. Yet students at community colleges often face steep odds when it comes to completing a degree. Community colleges serve many low-income and first-generation students as well as students of color, all of whom must contend with many obstacles to success. At the same time, two-year colleges are severely underfunded, and therefore are unable to provide the level of personal support that many students require. MDRC and the Detroit Regional Chamber partnered in 2016 to create the Detroit Promise Path (DPP), an evidence-based student services program designed to help more Detroit high school graduates--among the nation's most underserved students--enroll and persist in college, accumulate credits, graduate, and potentially transfer to a four-year program. DPP builds on an existing scholarship program called the Detroit Promise, launched in 2013, which covers community college tuition and fees for up to three years of attendance. At the heart of DPP are campus coaches who help students acclimate to college, proactively reach out to them with help and reminders about tasks and deadlines, and offer a sympathetic ear to young people who may be grappling with personal challenges--all with the goal of keeping them in school and on track to graduate. This executive summary presents an overview of findings from MDRC's randomized controlled trial evaluation of DPP at five Detroit community colleges. [Additional funding for this report was provided by the Michigan Education Excellence Foundation. For the full report, see ED611769.]