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Characteristics of High-Performing Districts in Elementary Math — June 2020


What does research say about characteristics of high-performing districts in elementary math in the U.S.?


Following an established REL West research protocol, we conducted a search for research reports and resources on characteristics of high-performing districts in elementary mathematics. The sources included ERIC, Google Scholar, and PsychInfo. (For details, please see the methods section at the end of this memo.)

We have not evaluated the quality of references and the resources provided in this response. We offer them only for your reference. Also, we searched for references through the most commonly used sources of research, but the list is not comprehensive and other relevant references and resources may exist. References are listed in alphabetical order, not necessarily in order of relevance. Access to the full articles is free unless indicated otherwise.

Research References

Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6–33. Full text available from

From the abstract: “Our purpose in this article is to propose a comprehensive, empirically grounded theory of action for improving the quality of mathematics teaching at scale. In doing so, we summarize current research findings that can inform efforts to improve the quality of mathematics instruction on a large scale, and identify questions that are yet to be addressed. We draw on an ongoing collaboration with mathematics teachers, school leaders, and district leaders in four urban school districts in the US. The provisional theory of action that we report encompasses a coherent system of supports for ambitious instruction that includes both formal and job-embedded teacher professional development, teacher networks, mathematics coaches’ practices in providing job-embedded support for teachers’ learning, school leaders’ practices as instructional leaders in mathematics, and district leaders’ practices in supporting the development of school-level capacity for instructional improvement.”

Cobb, P., Jackson, K., Henrick, E., & Smith, T. M. (2018). Systems for instructional improvement: Creating coherence from the classroom to the district office. Cambridge, MA: Harvard Education Press. Abstract available from and full text available for a fee from

Book description: “In ‘Systems for Instructional Improvement,’ Paul Cobb and his colleagues draw on their extensive research to propose a series of specific, empirically grounded recommendations that together constitute a theory of action for advancing instruction at scale. The authors outline the elements of a coherent instructional system; describe productive practices for school leaders in supporting teachers’ growth; and discuss the role of district leaders in developing school-level capacity for instructional improvement. Based on the findings of an eight-year research-practice partnership with four large urban districts investigating their efforts to enhance middle school math instruction, the authors seek to bridge the gap between the literature on improving teaching and learning and the literature on policy and leadership. They look at the entire education system and make recommendations on improvement efforts with a focus on student learning and teachers’ instructional vision. In particular, the authors offer insights on the interplay among various supports for teacher learning, including pullout professional development, coaching, collaborative inquiry, the most instructionally productive uses of principals’ time, and the tensions that tend to emerge at the district level. They provide a guide for district-level leaders in organizing their work to support significant teacher learning. ‘Systems for Instructional Improvement’ provides an invaluable resource for school and district leaders, while outlining a clearly focused agenda for future research.”

Cobb, P., & Smith, T. (2008). The challenge of scale: Designing schools and districts as learning organizations for instructional improvement in mathematics. In K. Krainer & T. Wood (Eds.), International handbook of mathematics teacher education: Vol. 3. Participants in mathematics teacher education: Individuals, teams, communities and networks (pp. 231–254). Rotterdam, The Netherlands: Sense. Full text available from

From the abstract: “This paper focuses on research that can inform the improvement of mathematics teaching and learning at scale. We first argue that such research should view mathematics teachers’ instructional practices as situated in the institutional settings of the schools and districts in which they work. We then discuss a series of hypotheses about school and district structures that might support teachers’ ongoing improvement of their classroom practices. In the latter part of the paper, we outline an analytic approach for documenting the institutional settings of mathematics teaching established in particular schools and districts that can feed back to inform the instructional improvement effort.”

Gates, S. M., Baird, M. D., Master, B. K., & Chavez-Herrerias, E. R. (2019). Principal pipelines: A feasible, affordable, and effective way for districts to improve schools. Santa Monica, CA: RAND Corporation. Full text available from

From the abstract: “Research across the decades has confirmed that effective school leadership is associated with better outcomes for students and schools. A high-quality school leader affects dozens of teachers and hundreds or thousands of students. It is a pivotal role. From 2011 to 2016, The Wallace Foundation, through its Principal Pipeline Initiative (PPI), provided funding and technical assistance to support six large school districts in their efforts to put in place systematic processes for the strategic management of school leaders. The purpose was to examine whether a comprehensive principal pipeline would be more effective than business-as-usual approaches to the preparation and management of school leaders. The term principal pipeline is shorthand for the range of talent management activities that fall within a school district’s scope of responsibility when it comes to school leaders, including leader standards, preservice preparation opportunities for assistant principals and principals, selective hiring and placement, and on-the-job induction, evaluation, and support. This report documents what the PPI districts were able to accomplish, describing the implementation of the PPI and its effects on student achievement, other school outcomes, and principal retention. The authors found that all six PPI districts were able to implement comprehensive pipelines, and they did so in different ways. The PPI had positive effects on a wide range of outcomes that school districts care about, and evidence of these positive effects was widespread. The authors also found that the work is affordable: It cost a PPI district about $42 per pupil per year, or less than 0.5 percent of the district’s budget in each school year, to operate and enhance its principal pipeline. The authors conclude that districts looking for ways to enhance school outcomes and improve the retention of newly placed principals should be encouraged by the experiences of PPI districts. The findings of this study suggest that when districts focused attention on activities related to principal pipelines, then principals, schools, and students benefited.”

Hemelt, S. W., & Lenard, M. A. (2020). Math acceleration in elementary school: Access and effects on student outcomes. Economics of Education Review, 74, 1–21. Full text available from

From the abstract: “This paper examines curricular acceleration in mathematics during elementary school using administrative data from a large, diverse school district that recently implemented a targeted, test-based acceleration policy. We first characterize access to advanced math and then estimate effects of acceleration in math on measures of short-run academic achievement as well as non-test-score measures of grit, engagement with schoolwork, future plans, and continued participation in the accelerated track. Experiences and effects of math acceleration differ markedly for girls and boys. Girls are less likely to be nominated for math acceleration and perform worse on the qualifying test, relative to boys with equivalent baseline performance. We find negative effects of acceleration on short-run retention of math knowledge for girls, but no such performance decay for boys. After initial exposure to accelerated math, girls are less likely than boys to appear in the accelerated track during late elementary school and at the start of middle school.”

Leithwood, K., & Azah, V. N. (2017). Characteristics of high-performing school districts. Leadership and Policy in Schools, 16(1), 27–53. Abstract available from and full text available for a fee from

From the abstract: “This mixed-methods study inquired about characteristics of districts which influence changes in student achievement and how those characteristics are developed. Staff in 49 Ontario districts were surveyed to estimate the status of nine district characteristics on changes in provincial tests of math and language achievement over five years. A cross-case analysis of interview data collected in three high-performing districts provided in-depth descriptions of each of the nine district characteristics. Results indicated that most of the nine district characteristics had significant effects on student achievement. Implications for policy and practice are suggested.”

Maass, K., Cobb, P., Krainer, K., & Potari, D. (2019). Different ways to implement innovative teaching approaches at scale. Educational Studies in Mathematics, 102(3), 303–318. Full text available from

From the abstract: “The article examines ways to implement innovative teaching approaches at scale. It mentions that research and experience reveal that innovative teaching approaches promoted by mathematics education researchers differ significantly from the day-to-day practices of teachers in many countries; and suggests that investigations of scaling up should be broad in scope and attend not only to the practices of teachers and researchers.”

McCommons, D. P. (2014). Aim higher: Lofty goals and an aligned system keep a high performer on top. Journal of Staff Development, 35(1), 12–14. Abstract available from and full text available from

From the abstract: “Every school district is feeling the pressure to ensure higher academic achievement for all students. A focus on professional learning for an administrative team not only improves student learning and achievement, but also assists in developing a systemic approach for continued success. This is how the Fox Chapel Area School District in Pennsylvania propels the high-performing district forward. Fox Chapel Area School District is a nationally recognized, award-winning public school district with high student achievement. Located in a suburban community about 11 miles northeast of Pittsburgh, the district encompasses an area of 36 square miles with 30,000 residents. Six municipalities (the boroughs of Aspinwall, Blawnox, Fox Chapel, and Sharpsburg, and the townships of Indiana and O’Hara) comprise the district and represent a wide range of social, economic, cultural, and religious backgrounds. The district operates six schools: four elementary K–5 schools, one grades 6–8 middle school and one grades 9–12 high school. The schools provide a comprehensive array of educational opportunities to serve the needs of its 4,200 students and meet the high expectations of area residents. The district has consistently exceeded state assessment targets. Over the last three years, state assessment results continue to improve. However, annual gains have gotten smaller. This trend is attributed to the nearness of the district’s scores to the ceiling score, which is 100% of students demonstrating proficiency. In 2011, 89% of students in grades 3–8 and 11 were proficient or advanced in math and 90% in reading. The district’s high level of achievement is attributed to the alignment of systems such as curriculum, instruction, assessment, professional learning, supervision, and resources with the vision, mission, core values, and beliefs outlined in the strategic plan. The administrative team and teacher leaders work collaboratively to assure that goals, action plans, and strategies among these systems are cohesive. This article provides a look at how the district aligned the content and processes of professional learning and supervision to foster organizational change.”

Rigby, J. G., Larbi-Cherif, A., Rosenquist, B. A., Sharpe, C. J., Cobb, P., & Smith, T. (2017). Administrator observation and feedback: Does it lead toward improvement in inquiry-oriented math instruction? Educational Administration Quarterly, 53(3), 475–516. Abstract available from and full text available from

From the abstract: “This study examines the content and efficacy of instructional leaders’ expectations and feedback (press) in relation to the improvement of middle school mathematics teachers’ instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in four large urban school districts across the United States. We used transcripts of interview data, surveys, and video recordings of instruction of 271 cases, over 4 years, to determine the content of administrator press, as reported by teachers, and the relationship between the content and change (if any) in instruction. To do so we used qualitative coding of interview transcripts, and ran a series of statistical models to examine the nature of the variance in and impact of administrative press. Findings: Most of the administrators’ press, as reported by teachers, was not targeted toward specific teachers’ mathematics instruction in ways that would likely lead toward improvement in those practices. Rather, the press focused on content-neutral instructional practices or classroom management and organization. Implications for Research and Practice: The instructional leadership practice of administrator observation and feedback is widespread, yet understudied as it relates to changes in teacher practice. Our findings indicate that current policies that mandate principals to spend substantial time in classrooms are unlikely to result in significant improvements in the quality of instruction unless meaningful resources are invested to support administrator learning.”

Spillane, J. P., Hopkins, M., & Sweet, T. M. (2018). School district educational infrastructure and change at scale: Teacher peer ineractions and their beliefs about mathematics instruction. American Educational Research Journal, 55(3), 532–571. Abstract available from and full text available from

From the abstract: “While current reform efforts press for ambitious changes to teachers’ instructional practice, teachers’ instructional beliefs are also consequential in such efforts as beliefs shape teachers’ instructional practice and their responses to instructional reforms. This article examines the relationship between teachers’ instructional ties and their beliefs about mathematics instruction in one school district working to transform its approach to elementary mathematics education. Quantitative results show that while teachers’ beliefs did not predict with whom they interacted about mathematics instruction, teachers’ interactions with peers about mathematics instruction were associated with changes in their beliefs over time. Qualitative analysis confirms and extends these findings, revealing how system-level changes in the district’s educational infrastructure facilitated change in teachers’ beliefs about mathematics instruction at scale.”

Takanishi, S. M. (2012). Implementation of school instructional improvement and student growth in math: Testing a multilevel longitudinal model. Journal on Educational Psychology, 6(2), 41–49. Full text available from

From the abstract:NCLB policies in the United States focus schools’ efforts on implementing effective instructional processes to improve student outcomes. This study looks more specifically at how schools are perceived to be implementing state required curricula and benchmarks and developing teaching and learning processes that support the teaching of state standards and influence student learning. This longitudinal, multilevel study focuses on how the implementation of standards-based learning and monitoring of student progress affects students’ likelihood to attain proficiency in math over time. All 5th-grade students enrolled in a western United States public school district who attended the same school in both 3rd- and 5th-grades and had complete 3rd- and 5th-grade test results for mathematics (11,345 students, 79% of all Grade 5 students, in 172 schools). A multilevel value-added model (hierarchical logistic regression) was used to estimate the extent to which school processes influenced math outcomes at single and at multiple points in time. The results of this study identify effective schools and practices and illustrate the relationship between schools’ academic organization and students’ growth; they show that organizational processes do impact student learning over schools’ contextual features. The quality of schools’ implementation of the required Standards Based Learning curriculum is strongly related to students’ likelihood to be proficient in math. Implications for practice: Build human and social capital by focusing on school process variables for school improvement. Because school leaders have relatively greater control over organizational processes, they can proactively focus on identifying needs, providing staff professional development and follow-up support, and implementing and evaluating changes. Growth models and case studies may provide more information about learner outcomes in math over time.”

Additional Organization to Consult

Education Week –

From the website: “Education Week is an independent news organization that provides comprehensive coverage on K–12 education news, analysis, and opinion. We believe that an excellent education is possible for all students and our mission is to inspire and empower our readers to continue advancing the field every day.”

REL West note: Education Week has one resource that is relevant to this request:

Samuels, C. A. (2020). How one district is raising math rigor and achievement for students of color. In the Long Beach, Calif., school district, educators deploy a multifaceted strategy to raise math rigor and achievement. Bethesda, MD: Education Week. Full text available from


<Keywords and Search Strings

The following keywords and search strings were used:

[(math OR mathematics) AND (elementary or “K-5” OR “K-6”) AND (characteristics) AND (“high-performing districts”)]

[(math OR mathematics) AND (elementary or “K-5” OR “K-6”) AND (district) AND (“effective schools” OR “systemic improvement” OR “educational improvement” OR scale OR scaling)]

Databases and Resources

We searched Google Scholar and ERIC for relevant resources. ERIC is a free online library of over 1.6 million citations of education research sponsored by the Institute of Education Sciences.

Reference Search and Selection Criteria

When searching and selecting resources to include, we consider the criteria listed below.

  • Date of the Publication: References and resources published within the last 15 years, from 2005 to present, were included in the search and review.
  • Search Priorities of Reference Sources: Search priority is given to study reports, briefs, and other documents that are published and/or reviewed by IES and other federal or federally funded organizations and academic databases. Priority is also given to sources that provide free access to the full article.
  • Methodology: Priority is given to the most rigorous study designs, such as randomized controlled trials and quasi-experimental designs, and we may also include descriptive data analyses, survey results, mixed-methods studies, literature reviews, or meta-analyses. Other considerations include the target population and sample, including their relevance to the question, generalizability, and general quality. Priority is given to publications that are peer-reviewed journal articles or reports reviewed by IES and other federal or federally funded organizations. If there are many research reports available, we select those with the strongest methodology, or the most recent of similar reports. When there are fewer resources available, we may include a broader range of information. References are listed in alphabetical order, not necessarily in order of relevance.

This memorandum is one in a series of quick-turnaround responses to specific questions posed by educational stakeholders in the West Region (Arizona, California, Nevada, Utah), which is served by the Regional Educational Laboratory West at WestEd. This memorandum was prepared by REL West under a contract with the U.S. Department of Education’s Institute of Education Sciences (IES), Contract ED-IES-17-C-0012, administered by WestEd. Its content does not necessarily reflect the views or policies of IES or the U.S. Department of Education nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.