Educational Inequality Regimes amid Algebra-for-All: The Provision and Allocation of Expanding Educational Opportunities.

Schools can approach the task of sorting students to privileged learning opportunities in different ways, potentially creating distinct and durable educational inequality regimes. We test this idea by exploring variation in socioeconomic inequalities in advanced mathematics course-taking across California middle schools during a statewide algebra-for-all initiative. This case provides unique insight into local stratification processes since the state pressured schools to boost advanced course enrollments but provided little guidance about how to do so. We distinguish two critical organizational processes: the provision of different types of opportunities and the allocation of students to opportunities. The former, we argue, creates the potential for inequality; the latter determines what level of inequality is realized. Using panel data for all public middle schools in the state over a decade, we demonstrate a curvilinear association between opportunities and inequality, with disparities highest when opportunities are most differentiated. However, allocations at most schools were less unequal than would be expected under a test-based meritocratic allocation regime. Further, we find substantial school-level variation which is systematically related to organizational characteristics and consistent over time. These patterns provide evidence for local educational inequality regimes.

It matters how you start: Early numeracy mastery predicts high school math course-taking and college attendance.

Using data from the Applied Problems subtest of the Woodcock-Johnson Tests of Achievement (Woodcock & Johnson, 1989/1990, Woodcock-Johnson psycho-educational battery-revised. Allen, TX: DLM Teaching Resources) administered to 1,364 children from the National Institute of Child Health and Human Development (NICHD) Study of Early Childcare and Youth Development (SECCYD), this study measures children's mastery of three numeric competencies (counting, concrete representational arithmetic and abstract arithmetic operations) at 54 months of age. We find that, even after controlling for key demographic characteristics, the numeric competency that children master prior to school entry relates to important educational transitions in secondary and post-secondary education. Those children who showed low numeric competency prior to school entry enrolled in lower math track classes in high school and were less likely to enrol in college. Important numeracy competency differences at age 54 months related to socioeconomic inequalities were also found. These findings suggest that important indicators of long-term schooling success (i.e., advanced math courses, college enrollment) are evident prior to schooling based on the levels of numeracy mastery.

The Kids on the Bus: The Academic Consequences of Diversity-Driven School Reassignments.

Many public school diversity efforts rely on reassigning students from one school to another. While opponents of such efforts articulate concerns about the consequences of reassignments for students' educational experiences, little evidence exists regarding these effects, particularly in contemporary policy contexts. Using an event study design, we leverage data from an innovative socioeconomic school desegregation plan to estimate the effects of reassignment on reassigned students' achievement, attendance, and exposure to exclusionary discipline. Between 2000 and 2010, North Carolina's Wake County Public School System (WCPSS) reassigned approximately 25 percent of students with the goal of creating socioeconomically diverse schools. Although WCPSS's controlled school choice policy provided opportunities for reassigned students to opt out of their newly reassigned schools, our analysis indicates that reassigned students typically attended their newly reassigned schools. We find that reassignment modestly boosts reassigned students' math achievement, reduces reassigned students' rate of suspension, and has no offsetting negative consequences on other outcomes. Exploratory analyses suggest that the effects of reassignment do not meaningfully vary by student characteristics or school choice decisions. The results suggest that carefully designed school assignment policies can improve school diversity without imposing academic or disciplinary costs on reassigned students.

Teacher Effects on Student Achievement and Height: A Cautionary Tale.

We apply "value-added" models to estimate the effects of teachers on an outcome they cannot plausibly affect: student height. When fitting commonly estimated models to New York City data, we find that the standard deviation of teacher effects on height is nearly as large as that for math and reading, raising potential concerns about value-added estimates of teacher effectiveness. We consider two explanations: non-random sorting of students to teachers and idiosyncratic classroom-level variation. We cannot rule out sorting on unobservables, but find students are not sorted to teachers based on lagged height. The correlation in teacher effects estimates on height across years and the correlation between teacher effects on height and teacher effects on achievement are insignificant. The large estimated "effects" for height appear to be driven by year-to-year classroom by teacher variation that is not often separable from true effects in models commonly estimated in practice. Reassuringly for use of these models in research settings, models which disentangle persistent effects from transient classroom-level variation yield the theoretically expected effects of zero for teacher value added on height.

Heterogeneous Effects of Early Algebra across California Middle Schools.

How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th-grade test scores to place students into 8th-grade algebra courses and use a regression discontinuity design to estimate average impacts and heterogeneity across schools. Enrolling in 8th-grade algebra boosts students' enrollment in advanced math in ninth grade by 30 percentage points and eleventh grade by 16 percentage points. Math scores in tenth grade rise by 0.05 standard deviations. Women, students of color, and English-language learners benefit disproportionately from placement into early algebra. Importantly, the benefits of 8th-grade algebra are substantially larger in schools that set their eligibility threshold higher in the baseline achievement distribution. This suggests a potential tradeoff between increased access and rates of subsequent math success.

Failing at Remediation? College Remedial Coursetaking, Failure and Long-term Student Outcomes.

Colleges offer remedial coursework to help students enrolling in post-secondary education who are not adequately prepared to succeed in college-level courses. Despite the prevalence of remediation, previous research presents contradictory findings regarding its short- and long-term effects. This paper uses a doubly robust inverse probability weighting strategy to examine whether the degree completion and wage outcomes associated with remedial education vary by passing or failing remedial coursework. Using the NLSY Postsecondary Transcript-1997 data, we find that almost 30% of remedial course takers fail a remedial course. Students who took and passed their remedial coursework at both two-year and four-year colleges were more likely to graduate from college than similar students who did not take remediation. For both two-year and four-year college entrants, students who failed remedial coursework were less likely to obtain a bachelor's degree and, among degree receivers, took longer to graduate. Students who entered two-year or four-year colleges and who failed remedial coursework earned lower wages over time compared to similar students who never took remediation. Among four-year college entrants, these wage differences seem to be explained completely by degree completion. However, wage differences for two-year college entrants still remain after accounting for degree receipt. Our findings thus suggest that while many students may benefit from remedial education, a substantial number of students struggle with remedial coursework and fail to realize the intended benefits.

Civil Society Goes to School: Parent-Teacher Associations and the Equality of Educational Opportunity.

Where do parent-teacher associations (PTAs) and other similar school-linked nonprofits form? What role do PTAs play in distributing educational opportunities between and within public schools? In this paper, we link IRS data describing nonprofit organizations associated with North Carolina public schools to school- and student-level administrative data in order to answer these questions. Our analyses suggest PTAs form in a wide variety of school contexts, but high-revenue PTAs form primarily in affluent, predominantly white schools. Students in schools with active PTAs enjoy relatively strong achievement growth compared to their peers in schools without active PTAs. However, our analyses suggest that in reading, the benefits associated with PTAs flow disproportionately to nonpoor students.

Effects of state education requirements for substance use prevention.

We provide the first evidence on the effects of state laws requiring students to receive education about alcohol, tobacco, and other drugs using data on over a million youths from the 1976-2010 Monitoring the Future study. In difference-in-differences and event-study models, we find robust evidence that these laws significantly reduced recent alcohol and marijuana use among high school seniors by 1.6-2.8 percentage points, or about 8-10% of the overall decline over this period. Our results suggest that information interventions can reduce youth substance use.

Validating the SEDA Measures of District Educational Opportunities via a Common Assessment.

The Stanford Educational Data Archive (SEDA) is the first data set to allow comparisons of district academic achievement and growth from Grades 3 to 8 across the United States, shining a light on the distribution of educational opportunities. This study describes a convergent validity analysis of the SEDA growth estimates in mathematics and English Language Arts (ELA) by comparing the SEDA estimates against estimates derived from NWEA's MAP Growth assessments. We find strong precision-adjusted correlations between growth estimates from SEDA and MAP Growth in math (.90) and ELA (.82). We also find that the discrepancy between the growth estimates in ELA is slightly more pronounced in high socioeconomic districts. Our analyses indicate a high degree of congruence between the SEDA estimates and estimates derived from the vertically scaled MAP Growth assessment. However, small systematic discrepancies imply that the SEDA growth estimates are less likely to generalize to estimates obtained through MAP Growth in some states.

Boosting School Readiness: Should Preschool Teachers Target Skills or the Whole Child?

We use experimental data to estimate impacts on school readiness of different kinds of preschool curricula - a largely neglected preschool input and measure of preschool quality. We find that the widely-used "whole-child" curricula found in most Head Start and pre-K classrooms produced higher classroom process quality than did locally-developed curricula, but failed to improve children's school readiness. A curriculum focused on building mathematics skills increased both classroom math activities and children's math achievement relative to the whole-child curricula. Similarly, curricula focused on literacy skills increased literacy achievement relative to whole-child curricula, despite failing to boost measured classroom process quality.

The Links Between Youth Employment and Educational Attainment Across Racial Groups.

Research suggests that the relations between adolescent employment and youth development vary by socioeconomic status (SES) and race/ethnicity. However, it is unclear whether the links between paid work and college outcomes vary by either SES or race/ethnicity, or both. Using data from the Educational Longitudinal Study, we find that low-intensity work during high school is associated with positive college outcomes for almost all students, whereas the associations between high-intensity work and negative postsecondary outcomes are mostly limited to White students. Our results suggest that both differential selections into youth employment and differential consequences of youth employment contribute to these varying links between paid work and educational outcomes across different racial groups.

Categorical Inequality: Schools As Sorting Machines.

Despite their egalitarian ethos, schools are social sorting machines, creating categories that serve as the foundation of later life inequalities. In this review, we apply the theory of categorical inequality to education, focusing particularly on contemporary American schools. We discuss the range of categories that schools create, adopt, and reinforce, as well as the mechanisms through which these categories contribute to production of inequalities within schools and beyond. We argue that this categorical inequality frame helps to resolve a fundamental tension in the sociology of education and inequality, shedding light on how schools can-at once-be egalitarian institutions and agents of inequality. By applying the notion of categorical inequality to schools, we provide a set of conceptual tools that can help researchers understand, measure, and evaluate the ways in which schools structure social inequality.

Fadeout in an early mathematics intervention: Constraining content or preexisting differences?

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children's long-term mathematical development result more from relatively stable preexisting differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these 2 hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of posttreatment achievement and preexisting differences between these 2 groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to preexisting differences between children in treatment and control groups with the same level of achievement at posttest. These differences were fully statistically attenuated by children's prior academic achievement. (PsycINFO Database Record

`Membership Has Its Privileges': Status Incentives and Categorical Inequality in Education.

Prizes - formal systems that publicly allocate rewards for exemplary behavior - play an increasingly important role in a wide array of social settings, including education. In this paper, we evaluate a prize system designed to boost achievement at two high schools by assigning students color-coded ID cards based on a previously low stakes test. Average student achievement on this test increased in the ID card schools beyond what one would expect from contemporaneous changes in neighboring schools. However, regression discontinuity analyses indicate that the program created new inequalities between students who received low-status and high-status ID cards. These findings indicate that status-based incentives create categorical inequalities between prize winners and others even as they reorient behavior toward the goals they reward.

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

Distributional Analysis in Educational Evaluation: A Case Study from the New York City Voucher Program.

We use quantile treatment effects estimation to examine the consequences of the random-assignment New York City School Choice Scholarship Program (NYCSCSP) across the distribution of student achievement. Our analyses suggest that the program had negligible and statistically insignificant effects across the skill distribution. In addition to contributing to the literature on school choice, the paper illustrates several ways in which distributional effects estimation can enrich educational research: First, we demonstrate that moving beyond a focus on mean effects estimation makes it possible to generate and test new hypotheses about the heterogeneity of educational treatment effects that speak to the justification for many interventions. Second, we demonstrate that distributional effects can uncover issues even with well-studied datasets by forcing analysts to view their data in new ways. Finally, such estimates highlight where in the overall national achievement distribution test scores of children exposed to particular interventions lie; this is important for exploring the external validity of the intervention's effects.

Curricular policy as a collective effects problem: A distributional approach.

Current educational policies in the United States attempt to boost student achievement and promote equality by intensifying the curriculum and exposing students to more advanced coursework. This paper investigates the relationship between one such effort - California's push to enroll all 8th grade students in Algebra - and the distribution of student achievement. We suggest that this effort is an instance of a "collective effects" problem, where the population-level effects of a policy are different from its effects at the individual level. In such contexts, we argue that it is important to consider broader population effects as well as the difference between "treated" and "untreated" individuals. To do so, we present differences in inverse propensity score weighted distributions investigating how this curricular policy changed the distribution of student achievement. We find that California's attempt to intensify the curriculum did not raise test scores at the bottom of the distribution, but did lower scores at the top of the distribution. These results highlight the efficacy of inverse propensity score weighting approaches for examining distributional differences, and provide a cautionary tale for curricular intensification efforts and other policies with collective effects.

State Education Standards for Tobacco Prevention and Classroom Instruction.

OBJECTIVES: We examine whether state educational standards regarding tobacco correspond with teacher reports of classroom instruction. METHODS: We test this relation with data on tobacco use prevention standards, reports of middle and high school teachers from the 2008 and 2010 School Health Profiles study, and logistic regression models. RESULTS: State education standards are significantly related to increased likelihood of a lead health education teacher in that state reporting that the specific topic was taught in the school. These relationships are stronger for middle school teachers than for high school teachers. CONCLUSIONS: Associations between state standards and teacher reports of actual instruction are consistent with education standards influencing the teaching of these health education topics.

Raising the stakes: How students' motivation for mathematics associates with high- and low-stakes test achievement.

This study uses data from an urban school district to examine the relation between students' motivational beliefs about mathematics and high- versus low-stakes math test performance. We use ordinary least squares and quantile regression analyses and find that the association between students' motivation and test performance differs based on the stakes of the exam. Students' math self-efficacy and performance avoidance goal orientation were the strongest predictors for both exams; however, students' math self-efficacy was more strongly related to achievement on the low-stakes exam. Students' motivational beliefs had a stronger association at the low-stakes exam proficiency cutoff than they did at the high-stakes passing cutoff. Lastly, the negative association between performance avoidance goals and high-stakes performance showed a decreasing trend across the achievement distribution, suggesting that performance avoidance goals are more detrimental for lower achieving students. These findings help parse out the ways motivation influences achievement under different stakes.

The link between middle school mathematics course placement and achievement.

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness.