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An ongoing debate in K-12 education policy has been between the "reform" agenda, including charter schools and school vouchers, and advocates of traditional public schools, led by educator unions. A similar split has emerged in higher education, particularly community colleges. Using California as an example, this paper: 1) summarizes the evolution of the current political divide between advocates of the "completion and success" agenda and faculty-led opponents, including the major reforms involved, 2) discusses the claims that leading organizations on each side have made, including their policy priorities, and 3) argues that the two sides share do share some areas of mutual agreement. The paper concludes by noting future policy considerations that could complicate reform efforts.

Following up on an individual-level randomized controlled trial of a Dana Center Math Pathways (DCMP) model, this study assessed longer-term impacts on students' math completion, academic progress, and academic attainment. The version of the DCMP that was assessed in this study diversified the developmental and college-level math course content that students take, separating it into distinct pathways that better aligned with their career interests. It also streamlined developmental math sequences into a one-semester developmental course for all students, regardless of placement level, and implemented evidence-based curricula and pedagogy to engage students in active problem solving that was pertinent to real-life situations. The study, which followed 1,411 students from four Texas community colleges and ten campuses, found that, in the five years after random assignment, program group students were consistently more likely to successfully complete their first college-level math courses than control group students. The study did not find impacts after five years on the number of overall college credits that students accrued or on the likelihood that students attained a credential or transferred to a four-year college.

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.]

We provide evidence from a randomized controlled trial on the effectiveness of a novel, 100-percent online math tutoring program, targeted at secondary school students from highly disadvantaged neighborhoods. The intensive, eight-week-long program was delivered by qualified math teachers in groups of two students during after-school hours. The intervention significantly increased standardized test scores (+0.26 SD) and end-of-year math grades (+0.48 SD), while reducing the probability of repeating the school year. The intervention also raised aspirations, as well as self-reported effort at school.

Reading has been at the forefront of early-grade educational interventions, but addressing the educational needs of students in math early on is also critical given that early gaps in math skills widen further over the course of schooling. In this study, we examine the effects of Kentucky's Math Achievement Fund -- a unique state-level program that combines targeted interventions, peer-coaching, and close collaboration among teachers to improve math achievement in grades K-3 -- on student outcomes and the costs associated with this policy. We find significant positive effects of the program not only on math achievement, but also on test scores in reading and non-test outcomes including student attendance and disciplinary incidents. The benefits exist across racial/ethnic groups and students from different socioeconomic statuses, and they are slightly higher for racial minorities. These findings, along with the cost estimate of the program, suggest that this program could provide a cost-effective blueprint to address the educational needs of students in math in early grades.

A very small number of young people enter youth custody between age 16 and 18 (about 4 in 1000 males), yet the consequences are severe. They spend an average of 7 months in youth custody and such incarceration has been related to negative outcomes in the longer term even if they can establish themselves in the labour market. In this paper, we evaluate whether there is a relationship between GCSE qualifications in English and maths and the probability of youth custody using administrative data in England. We are hindered in this because the majority of young people who end up in youth custody are not entered or fail their GCSEs in these subjects. Although regression results are consistent with educational achievement being a factor in why people end up in youth custody, they strongly suggest that both non-entry/low achievement and youth custody are correlated with severe vulnerabilities which are partially picked up by the explanatory variables available in administrative data (in particular indicators for special needs, disadvantage and being from some ethnic minority groups). Another interesting insight is that for many, problems only emerge (or at least become evident) in early or middle adolescence. [This paper forms part of a larger project funded by the Nuffield Foundation "Youth custody: Educational influences and labour market consequences."]

There is little evidence of how differentiated instruction is being implemented, if at all, in low- and middle-income contexts, which often have unique challenges such as availability of resources and large class sizes. In this paper, we present the results of a qualitative study in eight multigrade preprimary classrooms in Kenya. We used classroom observations and teacher interviews to understand how teachers approached differentiation during language and mathematics lessons, including understanding why teachers were making the moves we observed. All teachers differentiated instruction to some extent in our findings, and we provide detailed descriptions of the ways that teachers adapted content to fit the needs of their students. We also provide recommendations, including how to support teachers in creating activities that are appropriate for different abilities of students in the same classrooms, and suggest next steps for research in this area.

This paper discusses the purpose and content of the WIDA Framework for Equitable Instruction (FEI). The FEI is an instruction-focused resource designed to promote the equitable engagement in disciplinary learning and language development of multilingual learners. It complements the WIDA English Language Development Standards Framework in that it offers guidance on how educators can design learning environments that promote language growth in the context of disciplinary learning. The paper details the approach to language instruction reflected in the FEI and describes its four key principles. The paper also discusses the different components of the FEI: cross-disciplinary teacher actions that promote equitable learning and language practices, as well as discipline-specific teacher actions, student actions, language functions, and language trajectories. The paper concludes with guidance on how educators can use the FEI to strengthen their instructional practices for multilingual learners. The appendices offer discipline-specific illustrations of the framework's components and a glossary.

This analysis uses the case of the Better Math Teaching Network (BMTN) to explore whether individuals participating in a networked improvement community (NIC) experienced common developmental trajectories on known dimensions of engagement. The analysis included quantitative data from annual network member surveys and qualitative data from annual member interviews. Evidence suggests potential developmental trajectories on three key dimensions of network participation: (1) learning how to engage in a network; (2) learning to use the tools of improvement science; and (3) learning to take up the theory of improvement. Additional findings show preliminary variations based on participant characteristics such as teaching tenure, whether they participated in the network with a colleague they knew prior to joining the network or with a school-based colleague, the context of their school, and how student centered they were at the outset of their participation.

In the United States, the prevailing high school mathematics course sequence begins with a year of Algebra I, followed by a year of geometry and a year of Algebra II. Educators and others have raised concerns about the extent to which this sequence, which prioritizes the mastery of algebra, is appropriate for the longer-term education and career goals of students who do not intend to pursue STEM degrees in college. These concerns have impelled educators and policymakers to reexamine the prominence of algebra in high school mathematics curricula and to consider new approaches that provide students with more mathematics course options better aligned with their academic and career goals. In this paper, we explore existing approaches to high school mathematics curricula as well as new developments in the field. To start, we discuss a range of high school mathematics course sequences that are currently offered across the country and look at some of the systemic challenges embedded within the traditional paradigm. Then we explore federal and state changes to the provision of high school mathematics in the early 21st century, which we follow with a look at the influence of postsecondary institutions on high school math curricula. We then introduce short case studies of innovative high school math reforms that are occurring in five states. We conclude the paper by considering the Charles A. Dana Center's new initiative, Launch Years, and how this project works to reimagine high school mathematics and its relationship to postsecondary education and careers.

Innovation in instructional technology has contributed to the rapid implementation of technology-driven instructional platforms, particularly in developmental math coursework. Prior research has shown that instructional environment and classroom experience influence student development and outcomes. Consequently, when courses transition to technology-driven instruction, a logical concern on the part of faculty and administrators is the effect on the quality of the academic experience among students. Under a hybrid emporium model, students primarily receive instruction from a computer-based platform rather than from a faculty member delivering content in front of the classroom. This paper examines how students experience a newly adopted, hybrid emporium model for developmental math coursework. We conducted focus groups with students at six public colleges in Tennessee and find that students enrolled in hybrid emporium developmental math courses reported that the instructional model contributes to lowered barriers to math by increasing cognitive and social accessibility. In spite of prior academic challenges, students perceived math content and their faculty to be more accessible in the computer-driven model than in traditional lecture classes. We discuss these findings in light of recent research suggesting technology-driven instruction does not improve math performance.

Adult proficiency in numeracy in the United States lags that of other developed nations, and the nonselective institutions that dominate the higher education sector struggle to address the learning needs of the sizeable proportion of students who enroll in their institutions and are deemed academically underprepared in mathematics. Research on curriculum and pedagogy in developmental (or remedial) mathematics indicates that typical teaching approaches emphasize memorization, often at the expense of the kinds of conceptual understanding that prepare students for college-level mathematics and the numeracy demands of the workforce. This paper examines CUNY Start, an innovative pre-matriculation developmental education program developed by The City University of New York (CUNY) that reimagines the design and implementation of remedial instruction to better serve students with weak academic preparation. Using data from interviews, classroom observations, an instructor survey, and curricular materials, this paper describes four key features of the CUNY Start mathematics instructional approach, paying particular attention to how these features differ from traditional developmental education. These features are: (1) the use of a highly detailed curricular document as a primary resource for instructors; (2) an emphasis on real-world contexts and number relationships, which serve as the instructional starting point (rather than rules and procedures); (3) a pedagogical approach that elicits student talk and discussion through questioning; and (4) explicit attention to students' organizational and study skills. This paper also elaborates on the processes, structures, and resources built into CUNY Start that support its implementation. This paper is part of an ongoing random assignment evaluation of CUNY Start undertaken with MDRC that so far finds that the program has significant positive effects on students achieving college readiness in mathematics (longer-term effects will also be estimated). This evidence strongly suggests that CUNY Start's structures, processes, and resources enable instructors to teach mathematics in a different way that may boost student achievement.

This paper looks at the popularity of after-school mathematics by focusing on the Kumon and Russian School of Mathematics models. In 1954, Toru Kumon, a high school math teacher in Japan, designed a series of math worksheets to help improve the test scores of his son Takeshi, a second grader. Toru's goal was to teach Takeshi how to learn independently through the worksheets and improve his calculation skills prior to reaching high school. By working every day on the problems, Takeshi was able to reach the level of differential and integral calculus when he was just a few months into the sixth grade. The Kumon model is based on four elements: (1) Individualized instruction; (2) Self-learning; (3) Small-step worksheets; and (4) Kumon instructors. Parents who want to give their children a head start in math before elementary school can enroll them in Kumon as young as age 3. From that age they can stay with the program through high school or until they complete the program. In the U.S. alone, Kumon has grown from more than 182,000 students and nearly 1,300 centers in 2008 to more than 279,000 students and more than 1500 centers in 2018. While the Kumon method involves repeating mathematical processes until students over-learn them to automaticity, the Russian School of Mathematics (RSM) promotes itself as believing in just the opposite. The RSM model was founded by Inessa Rifkin in 1997 with Irina Khavinson, a friend, educator, and fellow Russian immigrant, after concluding that her son Ilya was not receiving the same mathematics education that she received as a student in the Soviet Union. Their goal was to translate their own experiences with specialized Russian math programs into a school that offered the same opportunity to American children. Two decades later about 25,000 students are enrolled with RSM today, in 40 locations in 11 states and Canada. Russian School of Mathematics students attend a classroom once per week for varying lengths of time, depending on grade: 90 minutes for kindergarten through third grade; two hours for grades four through six; and two-and-a-half hours for grades seven and above. Algebra and geometry are on separate tracks starting in the sixth grade, though students may enroll in both. This paper reviews each model's methods, highlights their best practices, and shows how they complement or run parallel with mathematics taught in traditional classrooms.

This paper examines common instructional strategies in early grade mathematics interventions through a review of studies in classrooms in low- and middle-income countries. Twenty-four studies met the criteria for inclusion, and analyses reveal four sets of instructional strategies for which there is evidence from multiple contexts. Of the 24 studies, 16 involved the use of multiple representations, 10 involved the use of developmental progressions, 6 included supporting student use of explanation and justification, and 5 included integration of informal mathematics. Based on the review, we provide conclusions and recommendations for future research and policy.

We study the effects of access to high school math and science courses on postsecondary STEM enrollment and degree attainment using administrative microdata from Missouri. Our data panel includes over 140,000 students from 14 cohorts entering the 4-year public university system. The effects of high school course access are identified by exploiting plausibly exogenous variation in course offerings within high schools over time. We find that differential access to high school courses does not affect postsecondary STEM enrollment or degree attainment. Our null results are estimated precisely enough to rule out moderate impacts.

In lower- and middle-income countries, including Ghana, students in rural areas dramatically underperform their urban peers. Rural schools struggle to attract and retain professionally trained teachers (GES 2012; World Bank 2012). We explore one potential solution to the problem of teacher recruitment: distance instruction. Through a cluster randomized controlled trial, we estimate the impact of a program that broadcasts live instruction via satellite to rural primary school students. The program equipped classrooms in 70 randomly selected Ghanaian schools with the technology required to connect to a studio in Accra. An additional 77 schools served as the control. Instructors in Accra provided math and English lessons to classrooms in the treatment group. The model is interactive, and students in satellite classes could communicate in real time with their remote teachers. We estimate significant gains (p<0.05) in rural students' numeracy and foundational literacy skills. We find no impact on attendance and classroom time-on-task (as measured through unannounced classroom observations), suggesting that these gains may result from improved instructional quality rather than from increased instruction time.

PowerTeaching is an evidence-based, structured cooperative learning program. It aims to prepare students to meet the stringent demands of new state math standards, both the knowledge standards and the 21st-century skills standards, such as around communication and collaboration. Awarded a scale-up grant in 2012 by the federal government, the program expanded to more than 100 high-need middle schools to train their math teachers how to implement cooperative learning in their classrooms. The evaluation of this expansion effort found that while program teachers learned to organize their students into long-standing mixed-ability groups, which are conducive of cooperative learning, teachers did not consistently implement the instructional supports necessary to transform group work into cooperative learning. The experimental impact study found that students' math performance did not differ dramatically between program and non-program schools. A likely cause for the weak implementation was that the ongoing professional development that is an integral part of PowerTeaching mostly did not occur or was more focused on how to teach the new content required by recently adopted education standards rather than how to implement cooperative learning. The impacts were not large and significant (as earlier studies had found), in part because students in the control schools were also working in groups in response to the communication and collaboration standards embedded in the new standards. Indeed, this study is one of the first to document this shift toward group work. Given that prior studies have shown that cooperative learning teams increase the academic performance of students more than group work does, the evaluation points to the potential for increasing math performance if teachers, who are now routinely using groups, can be trained to consistently provide the supports needed to transform groups into cooperative learning teams. This type of ongoing support, missing in this trial of PowerTeaching, is likely to be key to shifting teachers' instructional practices. [This report was written with Deni Chen, Ashley Kennedy, and Joseph Quinn.]

The ongoing push to raise or eliminate the charter school cap in Massachusetts provides an opportunity to reflect upon the purpose of charter schools. When the legislature created the Commonwealth's charter school law, as a part of the 1993 Massachusetts Education Reform Act (MERA), it clearly stated a main reason for these new schools was innovation. Charters were expected to provide new curricular and pedagogical options and even experiment with existing school structures, such as grade configurations and the length of the school day and year. This paper highlights two Massachusetts charter schools that offer curricular opportunities rarely available in other public schools in Massachusetts. Both of these schools enable students to achieve exceptional results in comparison to their peers in traditional district schools. The Mystic Valley Regional Charter School (MVRCS) consistently ranks among the best schools in Massachusetts and the country. It offers two distinct but complementary curricula--the Core Knowledge Curriculum at the elementary and middle school levels and the International Baccalaureate (IB) curriculum at the high school level. At the Advanced Math and Science Academy (AMSA) in Marlborough, MA science and math are the "driving forces" behind much of the curricular content, but students are exposed to holistic and rigorous content in all subject areas. The curriculum is horizontally and vertically aligned and follows a logical, chronological sequence of content from grade to grade, enabling students to make intellectual connections not just within but also among and between content areas. In the current policy environment, understanding some of the important innovations that charter schools offer to students and families can productively inform the debate. The schools profiled in this white paper are providing high caliber educational opportunities and interesting curricular options to students and families in the communities that they serve.

In April 2000 the state of North Carolina announced an increase in the minimum number of math courses students would need to take to be considered for admission as undergraduates to any of the University of North Carolina's 15 four-year branch campuses. Previously, students had been required to take at least three math courses in high school to be eligible for admission. The new standard required at least four math courses and applied to all students graduating from high school in the 2005-06 school year or after. The state justified this increase in required math preparation by arguing that it would improve college completion rates. The purpose of this paper is to assess the effects of this increase in the mandated minimum number of math courses. This assessment entails two separate questions: (1) Did the policy affect actual course-taking among high school students; and (2) Did any such changes in high school course-taking, together with the threat of being denied admission, affect college enrollment patterns or students' choices or performance once enrolled. The study extends the existing literature in three ways. First, it sheds light on how a policy change at the university level affects the behavior of students in high school. Second, it extends the literature on the effects of math taking in high school to college enrollment and college success. Third it makes a methodological contribution by its close attention to the estimation of causal relationships that leverage the plausibly exogenous variation that arises as a result of the policy change.

The educational discourse in recent years in Australia, and in particular NSW has been on advancing the status of the teaching profession through the development of a framework of standards, and by supporting the nature of teachers' work in addition to improving student-learning outcomes. The close link between student learning outcomes and quality mathematics teaching has resulted in the call for an increase in teacher accountability and quality. This paper is an exploration of the relevant literature that focused on the professionalisation of the teaching profession in Australia and its potential impact on teaching in Australia. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

There is a growing consensus that teacher evaluation in the United States is fundamentally broken. Few would argue that a system that tells 98 percent of teachers they are "satisfactory" benefits anyone--including teachers. The nation's collective failure to invest in high-quality professional feedback to teachers is inconsistent with decades of research reporting large disparities in student learning gains in different teachers' classrooms (even within the same schools). Many states and school districts are looking to reinvent the way they do teacher evaluation and feedback, and they want better tools. With the help of nearly 3,000 teacher-volunteers, the Measures of Effective Teaching (MET) project is evaluating alternative ways to provide valid and reliable feedback to teachers for professional development and improvement. In this report, the authors focus on the value of classroom observations. They test five different approaches to classroom observations. Each observation instrument is designed to do two things: (1) focus an observer's attention on specific aspects of teaching practice and (2) establish common evidentiary standards for each level of practice. In this report, the authors investigate the properties of the following five instruments: (1) Framework for Teaching (or FFT, developed by Charlotte Danielson of the Danielson Group); (2) Classroom Assessment Scoring System (or CLASS, developed by Robert Pianta, Karen La Paro, and Bridget Hamre at the University of Virginia); (3) Protocol for Language Arts Teaching Observations (or PLATO, developed by Pam Grossman at Stanford University); (4) Mathematical Quality of Instruction (or MQI, developed by Heather Hill of Harvard University); and (5) UTeach Teacher Observation Protocol (or UTOP, developed by Michael Marder and Candace Walkington at the University of Texas-Austin). Appended are: (1) Sample Restrictions Leading to Video Sample; and (2) Regression Coefficients Used for Criterion-Based Weighting. (This report was written with the assistance of Steve Cantrell, Jeff Archer, Sarah Buhayar, Kerri Kerr, Todd Kawakita, and David Parker. Contains 10 figures, 20 tables, and 45 footnotes.) [For related reports, see "Gathering Feedback for Teaching: Combining High-Quality Observations with Student Surveys and Achievement Gains. Policy and Practice Summary. MET Project" (ED540961) and "Gathering Feedback for Teaching: Combining High-Quality Observations with Student Surveys and Achievement Gains. Policy and Practice Brief. MET Project" (ED540962).]

This paper examines the returns to math courses relative to courses in other subjects for students in community college. Using matched college transcript and earnings data on over 80,000 students entering community college during the 2000s, we find that college-level math coursework has an indirect positive effect on award completion that is stronger than that of coursework in other subjects. In terms of direct effects, we find mixed evidence on the direct effect of enhanced math skills on earnings over other college-level skills. Overall, the combined direct and indirect effect appears to be adverse: compared with other courses or college pathways, more math coursework in community college is modestly associated with relatively lower earnings in later adulthood. However, this association is sensitive to modeling, and we do find heterogeneous results by gender, race/ethnicity, and initial college ability, as well as by math field and level. Two supplementary tables are appended.

Measures of teachers' "value added" to student achievement play an increasingly central role in k-12 teacher policy and practice, in part because they have been shown to predict teachers' long-term impacts on students' life outcomes. However, little research has examined variation in the long-term effects of teachers with similar value-added performance. In this study, we investigate variation in the persistence of teachers' value-added effects on student achievement in New York City. We separate persistent effects into general effects that improve both the subject taught (math or English language arts (ELA)) and the other area of measured achievement and subject-specific effects which improve only the subject taught. Two findings emerge. First, a teacher's value-added to ELA achievement has substantial crossover effects on long-term math performance. That is, having a better ELA teacher affects both math and ELA performance in a future year. Conversely, math teachers have only minimal long-term effects on ELA performance; their effects are far more subject-specific. Second, we identify substantial heterogeneity in the persistence of English Language Arts (ELA) teachers' effects across observable student, teacher, and school characteristics. In particular, teachers in schools serving more poor, minority, and previously low-scoring students have less persistence than other teachers with the same value-added scores. Moreover, ELA teachers with stronger academic backgrounds have more persistent effects on student achievement, as do schools staffed with a higher proportion of such teachers. The results indicate that teachers' effects on students' long-term skills can vary as a function of instructional content and quality in ways that are not fully captured by value-added measures of teacher effectiveness.

This paper reviews current research on the effectiveness of interventions and reforms that seek to improve the math preparedness and success of high school students entering college. Based on gaps in the research knowledge, it also provides recommendations for further inquiry in particular areas. The studies reviewed here are selected from research conducted by the Community College Research Center (CCRC) and the National Center for Postsecondary Research (NCPR), from searches of the Education Full Text database for peer-reviewed articles, and from searches of Google Scholar for high-quality reports. The two key criteria for inclusion in the review are that (1) the study in question focuses on (a) an early assessment program in math; (b) a math bridge, boot camp, or brush-up; (c) a reform of developmental math; or (d) improvements to math instruction; and that (2) at least one of the study's outcomes is related to changes in math or college performance. To evaluate the evidence, I report on each study's design and findings. I also calculate each intervention's effect size and categorize the effect size to compare impacts across the studies under review. Overall, the evidence is limited, but some of the interventions and reforms appear promising. The evidence on early assessment is minimal. The evidence on bridges, boot camps, and brush-ups suggests that short-term programs may only have short-term impacts. The evidence on different models of developmental reform varies depending on the reform model. For dominant models, it is positive (for compression models), insignificant (for learning communities), or negative (for modularization). For less prevalent models, it is positive (for mainstreaming) or needs further research (for statistics pathways). In terms of innovations that are strictly pedagogical, the strongest positive evidence is found for using structured forms of student collaboration and for building conceptual understanding through the use of multiple representations when teaching and solving problems. The evidence on computer-mediated instruction in the developmental math classroom is very mixed, with some studies finding positive effects and others finding negative effects. Appended are: (1) Search Strategy and Inclusion Criteria; and (2) Summary of Studies. (Contains 2 tables and 11 footnotes.)

This paper examines the effects of policies that increase the number of students who take the first course in algebra in 8th grade, rather than waiting until 9th grade. Extending previous research that focused on the Charlotte-Mecklenburg school system, we use data for the 10 largest districts in North Carolina. We identify the effects of accelerating the timetable for taking algebra by using data on multiple cohorts grouped by decile of prior achievement and exploiting the fact that policy-induced shifts in the timing of algebra occur at different times in different districts to different deciles of students. The expanded data make it possible to examine heterogeneity across students in the effect of taking algebra early. We find negative effects among students in the bottom 60% of the prior achievement distribution. In addition, we find other sources of heterogeneity in effects.

In this working paper, Andrew Saultz of Michigan State University inventories the current landscape of technology programs available for middle school math. The working paper is not intended as a "consumers' guide" to technology programs, and the descriptions of some specific programs are not fully accurate or current. Readers who are interested in specific programs should consult the providers directly; web addresses are included in the working paper. The working paper also does not provide an all-inclusive list of every mathematical program available, as this is a rapidly evolving industry; rather, Saultz's report is intended to demonstrate the wide variety of existing programs. The paper makes clear that a large and growing number of options currently exist for policymakers and educators looking to incorporate technology into the teaching of middle school mathematics. The paper also notes that only few of these programs have yet been subjected to rigorous evaluation of their effectiveness with students.