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Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area root...

Algebra is a key course in the high school mathematics sequence. Despite its prominence, large-scale examinations of algebra instruction are rare and it is not clear whether and how instruc...

Advanced math coursework can affect college and labor market outcomes, yet discretionary placement policies can lead to differential access at key points in the college preparatory pipeline. We examine a targeted approach to course assignment that uses prior test scores to identify middle school students deemed qualified for a college preparatory math sequence. Accelerated math placement of relatively low-skilled middle schoolers increases the fraction later enrolling in Precalculus by one-seventh, and by over one-third for female and non-low income students. Acceleration increases college readiness and intentions to pursue a bachelor’s degree. Course placement rules based on objective measures can identify students capable of completing rigorous coursework but whom discretionary systems might overlook.

Background For nearly three decades, policy makers and researchers in the United States have promoted more intellectually rigorous standards for mathematics teaching and learning. Yet, to date, we have limited descriptive evidence on the extent to which reform-oriented instruction has been enacted at scale. Purpose The purpose of the study is to examine the prevalence of reform-aligned mathematics instructional practices in five U.S. school districts. We also seek to describe the range of instruction students experience by presenting case studies of teachers at high, medium, and low levels of reform alignment. Participants We draw on 1,735 video-recorded lessons from 329 elementary teachers in these five U.S. urban districts. Research Design We present descriptive analyses of lesson scores on a mathematics-focused classroom observation instrument. We also draw on interviews with district personnel, rater-written lesson summaries, and lesson video to develop case studies of instructional practice. Findings We find that teachers in our sample do use reform-aligned instructional practices, but they do so within the confines of traditional lesson formats. We also find that the implementation of these instructional practices varies in quality. Furthermore, the prevalence and strength of these practices corresponds to the coherence of district efforts at instructional reform. Conclusions Our findings suggest that, unlike other studies in which reform-oriented instruction rarely occurred, reform practices do appear to some degree in study classrooms. In addition, our analyses suggest that implementation of these reform practices corresponds to the strength and coherence of district efforts to change instruction.

Education agencies are evaluating teachers using student achievement data. However, very little is known about the comparability of test-based or “value-added” metrics across districts and the extent to which they capture variability in classroom practices. Drawing on data from four urban districts, we found that teachers were categorized differently when compared within versus across districts. In addition, analyses of scores from two observation instruments, as well as qualitative viewing of lesson videos, identified stark differences in instructional practices across districts among teachers who received similar within-district value-added rankings. These patterns were not explained by observable background characteristics of teachers, suggesting that factors beyond labor market sorting likely played a key role.

In this study, we consider the implications of using mathematics-specific observation frameworks versus a synthesized list of indicators when measuring teaching quality. We compare how three mathematics-focused observation frameworks measure teaching quality across three focal lessons and consider the merits of using a synthesized list of indicators such as those presented in the MAIN-TEACH model. We find that the mathematics-specific frameworks: identify similar constructs, but assess them differently; reach similar conclusions regarding overall instructional quality, but for different reasons; and do not capture aspects of instruction that are not mathematics-specific. A synthesized framework could provide a broader set of indicators, promote a common vision of high-quality instruction, and provide a common basis for looking across studies. However, a synthesized framework may remove nuances that allow researchers to capture distinct constructs (or important differences in similar constructs), specifically at a grain size useful for instructional improvement. We also consider methodological concerns raised by the use of a synthesized framework.

Algebra is considered key to success in secondary mathematics, yet instruction remains mostly teacher-centered and procedurally oriented, with limited opportunities for students to develop algebraic understanding. This study draws on a large sample of video-recorded ninth grade U.S. algebra lessons to explore the nature of learning opportunities that may help deepen students’ algebraic understanding. I highlight aspects of opportunities to learn algebraic procedures and describe instruction that can enrich these opportunities. I posit that this holds promise as an incremental improvement approach—relatively small adjustments in teachers’ current practices that can serve as a bridge to more ambitious teaching.

Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district’s effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based on a defined prior achievement metric. This policy reduced the relationship between course assignment and student characteristics such as income and race/ethnicity, while increasing its relationship to academic skill. The policy increased the share of students on track for algebra by eighth grade. Students placed in accelerated math were exposed to higher-skilled peers but larger classes. Future work will assess impacts on subsequent achievement and course-taking outcomes.

Multiple-choice assessments are frequently used for gauging teacher quality. However, research seldom examines whether results from such assessments generalize to practice. To illuminate this issue, we compare teacher performance on a mathematics assessment, during mathematics instruction, and by student performance on a state assessment. Poor performance on the written assessment predicted poor classroom performance; likewise, strong performance on the written assessment predicted strong classroom performance. However, classroom performance of teachers in the middle of the written assessment distribution varied considerably. These results also held true using student outcomes as a criterion, leading to implications for both research and policy.

Background/Context Research on after-school programs has traditionally focused on those programs serving students in younger grades but found positive correlations between student participation in enriching after-school activities and school engagement. For older students, particularly teenagers, there tends to be lower participation. Research has also shown that students learn at different rates and need different amounts of time with the same material. School-based after-school programs have been one policy intervention to address this need. Purpose/Objective/Research Question/Focus of Study This study sought to understand better why students in one New York City high school attended after-school sessions and what kept them coming. Who does not attend, and why not? Finally, was the time after school being used in a way that most benefited students? How might the insights of those students who did attend push educators to improve after-school programming, both in terms of the teaching and in terms of how we structure these sessions? Setting This study took place in a small public New York City high school with almost all students participating in the federal free and reduced lunch program. Research Design In this action research study conducted with her own students in her own classroom, the author sought to use student perceptions to make programmatic changes that ultimately benefited the students attending the program. Through surveys, exit slips, interviews, and journal entries, the author collected student opinions and perceptions of the school's after-school program and changed the structure of her after-school sessions to maximize both attendance and student outcomes. Data Collection and Analysis The data suggest that a loosely structured and flexible program with varied types of help and, most important, individual attention is an after-school model that appears to appeal to high school students, particularly in the upper grades. Teenagers need to feel that they get something out of attending. It is critical to have the support of school administrators who understand that attendance figures alone do not reflect “success.” Students reported frustration when they were unable to get help after school because the teacher or peer tutors were overextended. The author recommends that policy makers focus on the quality of service, instead of the quantity served, to create and maintain successful interventions for all students.

To better prepare students for college-level math and the demands of the labor market, school systems have tried to increase the rigor of students’ math coursework. The failure of universal “Algebra for All” models has led recently to more targeted approaches. We study one such approach in Wake County, North Carolina, which began using prior test scores to assign middle school students to an accelerated math track culminating in eighth grade algebra. The policy has reduced the role that income and race played in course assignment. A regression discontinuity design exploiting the eligibility threshold shows that acceleration has no clear effect on test scores but lowers middle school course grades. Acceleration does, however, raise the probability of taking and passing geometry in ninth grade by over 30 percentage points, including for black and Hispanic students. Nonetheless, most students accelerated in middle school do not remain so by high school and those that do earn low grades in advanced courses. This leaky pipeline suggests that targeted math acceleration has potential to increase college readiness among disadvantaged populations but that acceleration alone is insufficient to keep most students on such a track.