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Aligning Math Assessments with Curricula — February 2021


Can you provide research on aligning math assessments with curricula in schools and across schools within districts?


Following an established REL West research protocol, we conducted a search for research reports and resources on aligning math assessments with curriculum in schools, and across schools within districts. The sources we searched 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

Detweiler, R. J. (2012). In pursuit of a balanced system of educational assessment: An evaluation of the pre-kindergarten through 8th grade math assessment system in one Massachusetts regional school district. Open Access Dissertations, 542. Abstract available from from and full text available from from

From the abstract: “School leaders in the United States live in an educational era characterized by a desire for and expectation that all students attain high levels of academic proficiency. There is an increased reliance on all types of educational assessment as a key component to help school leaders attain that goal. The purpose of this study is to understand how school administrators can foster a balanced system of assessment at the local level to genuinely harness the power of assessment to enhance student learning. The significance of the study rests in the fact that there is a general failure of states and school districts to conceive of educational assessment as a system that operates at all levels of the educational system from the classroom up to the district and state level. The findings of this study support the efforts of a group of administrators to develop a balanced system of math assessments in their school district.”

REL West note: This article is a dissertation. We include it here because of its relevance to the request.

Elmore, R. F., & Rothman, R. (1999). Testing, teaching, and learning: A guide for states and school districts. National Academy of Sciences. Full text available from from

From the abstract: “The purpose of this document is to help states and districts meet the challenges posed by the 1994 reauthorization of Title I. The goal in developing this document was to produce a practical guide for states and districts to use in developing the systems they were creating under the Title I law. Following an introduction to Title I, chapter 2 considers and critiques the theory of action behind the Title I law and various attempts at standards-based reform. The theory of action is expanded to reflect an analysis of effective reform. Chapter 3 examines the issue of standards, and chapter 4 discusses assessments, including assessments for young children and for special populations, and reporting and disaggregating assessment results. Chapter 5 considers systems for monitoring the conditions of instruction at the school level and professional development at the district level. In chapter 6, ways to measure adequate progress of schools toward standards are provided, and chapter 7 discusses accountability.”

REL West note: Although this article was published in 1999, we include it here because of its relevance to the request.

Flaherty, J., Jr., Sobolew-Shubin, A., Heredia, A., Chen-Gaddini, M., Klarin, B., & Finkelstein, N. D. (2014). Under construction: Benchmark assessments and Common Core math implementation in grades K–8. WestEd. Full text available from from

From the abstract: “Math in Common® (MiC) is a five-year initiative that supports a formal network of 10 California school districts as they implement the Common Core State Standards in mathematics (CCSS-M) across grades K–8. As the MiC initiative moves into its second year, one of the central activities that each of the districts is undergoing to support CCSS implementation involves putting in place new or revised student assessment processes or systems to better align with the new standards. This report examines the MiC districts’ strategies and initial implementation efforts related to benchmark assessments used throughout the school year to assess student mastery of the CCSS-M and signal districts’ progress. The report also highlights the range of approaches to developing and implementing benchmark assessments used across the MiC district community, in order to illuminate the challenges and headway that many districts in California, and perhaps beyond, are facing as they work to implement CCSS-M, specifically across grades K–8.”

La Marca, P. M. (2001). Alignment of standards and assessments as an accountability criterion. ERIC Clearinghouse on Assessment and Evaluation. Full text available from from

From the abstract: “This digest provides an overview of the concept of alignment and the role it plays in assessment and accountability systems. It also discusses methodological issues affecting the study of alignment and explores the relationship between alignment and test score interpretation. Alignment refers to the degree of match between test content and subject area content identified through state academic standards. It is highly unlikely that a single test can achieve a desirable degree of match, and this fact provides the rationale for using multiple accountability measures and points to the need for studying the degree of match at the test level and the system level. The two overarching dimensions of alignment are content match and depth match. Alignment can best be achieved through sound standards and assessment development activities. The analysis of alignment requires a systematic review of standards and a systematic review of test items/tasks. Alignment is not only a methodological requirement, but also an ethical requirement, as it would be a disservice to students and schools to judge academic achievement based on a poorly aligned system of assessment. The systematic study of alignment is time consuming and can be costly, but the benefits outweigh the costs.”

REL West note: Although this article was published in 2001, we include it here because of its relevance to the request.

La Marca, P. M., Redfield, D., & Winter, P. C. (2000). State standards and state assessment systems: A guide to alignment. Council of Chief State School Officers. Full text available from from

From the abstract: “Alignment of content standards, performance standards, and assessments is crucial. This guide contains information to assist states and districts in aligning their assessment systems to their content and performance standards. It includes a review of current literature, both published and fugitive. The research is woven together with a few basic assumptions, best practice, and practical reality to produce a resource for planning and achieving a comprehensive aligned system of standards and assessments. The guide rests on six general assumptions about the foundations of an aligned system and draws on relevant research in discussing critical aspects of alignment: (1) content match; (2) depth match; (3) emphasis; (4) performance match; (5) accessibility; and (6) reporting. It also discusses alignment in the context of other components of the educational system, including accountability, teacher involvement and professional development, policy development, textbook adoption and use, and K–16 connections. An appendix contains an annotated checklist that states and localities can use to evaluate the degree of alignment of their assessments and standards or to develop an aligned assessment system.”

REL West note: Although this article was published in 2000, we include it here because of its relevance to the request.

Martone, A., & Sireci, S. G. (2009). Evaluating alignment between curriculum, assessment, and instruction. Review of Educational Research, 79(4), 1332–1361. Abstract available from from and full text available from from

From the abstract: “The authors (a) discuss the importance of alignment for facilitating proper assessment and instruction, (b) describe the three most common methods for evaluating the alignment between state content standards and assessments, (c) discuss the relative strengths and limitations of these methods, and (d) discuss examples of applications of each method. They conclude that choice of alignment method depends on the specific goals of a state or district and that alignment research is critical for ensuring the standards-assessment-instruction cycle facilitates student learning. Additional potential benefits of alignment research include valuable professional development for teachers and better understanding of the results from standardized assessments.”

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 from and full text available for a fee from 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.”

McGehee, J. J., & Griffith, L. K. (2001). Large-scale assessments combined with curriculum alignment: Agents of change. Theory Into Practice, 40(2), 137–144. Abstract available from from and full text available for a fee from from

From the abstract: “Examines the high stakes of large-scale mathematics assessment practices and ways in which they are agents of change, focusing on: types of instruments used; how test design informs instructional practice; how dissemination of test information informs instructional practice; and who is responsible or accountable for results.”

REL West note: Although this article was published in 2001, we include it here because of its relevance to the request.

McMahon, K. A., & Whyte, K. (2020). What does math curriculum tell us about continuity for PreK-3? Curriculum Journal, 31(1), 48–76. Abstract available from from and full text available for a fee from from

From the abstract: “Increasingly school districts are attempting to align curricula, assessments, and standards, in an effort to eliminate inequities. Some approaches like prek–3 initiatives call for coordination of instruction between preschool and later elementary grades that would resemble a coherent instructional system with clear learning goals for students aligned to supports for teachers to help them to teach in, possibly new, ways that would realize such goals. Central to these efforts are instructional materials like curricula that specify learning goals used to teach the students and the guide teachers. Districts seeking to coordinate prek with elementary must create novel solutions for coordinating supports for teaching that is connected across prek and elementary classrooms. In this study, we consider the mandated math curricula that two school districts in California used to establish district-wide prek–3 programs. What emerged from our analyses of curricula were distinct designs for continuity of instruction across grades: one district’s curricula offered consistently challenging tasks across grades, while the other emphasized easy tasks for younger students followed by increasing levels of challenge for advanced grades. We argue that prek–3 initiatives present a unique opportunity to recognize why continuity of instruction specified by curricula matters as much, if not more, than coherence or alignment when districts seek to coordinate and connect instruction in preschool and elementary classrooms.”

Nichols, T. P., & Plummer, E. (2017). Year 1 state report: Massachusetts. Center on Standards, Alignment, Instruction, and Learning. Full text available from from

From the abstract: “The Center on Standards, Alignment, Instruction, and Learning (C-SAIL) examines how college- and career-readiness (CCR) standards are implemented, whether they improve student learning, and what instructional tools measure and support their implementation. Established in July 2015 and funded by the Institute of Education Sciences (IES) of the U.S. Department of Education, C-SAIL has partnered with California, Kentucky, Massachusetts, Ohio, and Texas to explore their experiences with CCR standards-based reform, particularly with regard to students with disabilities (SWDs) and English language learners (ELLs). This report examines how the state of Massachusetts is approaching CCR standards implementation during a time of transition, as it develops the Next-Generation Massachusetts Comprehensive Assessment System, or the ‘Next-Gen MCAS,’ in 2015–2016. The transition will take place in 2016–2017, with full implementation of the next-generation assessment by the spring of 2017. For the purposes of this report and in keeping with C-SAIL’s focus, the authors concentrate on implementation of Massachusetts’ English language arts (ELA) and math standards. Drawing on interviews with four key state officials across various offices of the Massachusetts Department of Education, the report synthesizes and analyzes those responses using the ‘policy attributes theory’ (Porter, Floden, Freeman, Schmidt, & Schwille, 1988), a theoretical framework positing five attributes related to successful policy implementation (specificity, authority, consistency, power, and stability). The report focuses on five focal areas—standards and curriculum, assessment, professional development (PD), English language learners (ELLs), and students with disabilities (SWDs). The authors report on each focal area through the lens of the policy attributes to help readers see how state officials identified areas of strengths and challenges related to standards implementation in Massachusetts.”

Roach, A. T., Niebling, B. C., & Kurz, A. (2008). Evaluating the alignment among curriculum, instruction, and assessments: Implications and applications for research and practice. Psychology in the Schools, 45(2), 158–176. Abstract available from from and full text available from from

From the abstract: “Alignment has been defined as the extent to which curricular expectations and assessments are in agreement and work together to provide guidance for educators’ efforts to facilitate students’ progress toward desire academic outcomes. The Council of Chief State School Officers has identified three preferred models as frameworks for evaluating alignment: Webb’s alignment model, the Surveys of Enacted Curriculum model, and the Achieve model. Each model consists of a series of indices that summarize or describe the general match or coherence between state standards, large-scale assessments, and, in some cases, classroom instruction. This article provides an overview of these frameworks for evaluating alignment and their applications in educational practice and the research literature. After providing an introduction to the use of alignment to evaluate large-scale accountability systems, the article presents potential extensions of alignment for use with vulnerable populations (e.g., students with disabilities, preschoolers), individual students, and classroom teachers. These proposed applications can provide information for facilitating efforts to improve teachers’ classroom instruction and students’ educational achievement.”

Rothman, R., Slattery, J. B., Vranek, J. L., & Resnick, L. B. (2002). Benchmarking and alignment of standards and testing (CSE Technical Report). National Center for Research on Evaluation. Full text available from from

From the abstract: “The success of standards-based education systems depends on two elements: strong standards and assessments that measure what the standards expect. States that have, or adopt, test-based accountability programs claim that their tests are aligned to their standards. But there has been, up to now, no independent methodology for checking alignment. This paper describes and illustrates such a methodology and reports results on a sample of state tests. The protocol reviewers use to analyze alignment considers four dimensions to be central in determining the degree of alignment between an assessment and standards: (1) content centrality; (2) performance centrality; (3) challenge; and (4) balance and range. This Achieve alignment protocol has been applied to the tests of more than 10 states, but for this study, data from 5 states are used. In general, individual test items are reasonably well-matched to the standards they are meant to assess. However, the collection of such items in a test tend to measure only a few of the less challenging standards and objectives. As a result, few state tests can be said to be well-aligned assessments of challenging standards.”

REL West note: Although this article was published in 2002, we include it here because of its relevance to the request.

Webb, N. L. (1997). Criteria for alignment of expectations and assessments in mathematics and science education (Research Monograph No. 6). Council of Chief State School Officers. Full text available from from

From the abstract: “This monograph discusses criteria for judging the alignment between expectations of student achievement and assessment. Alignment is central to current efforts of systemic and standards-based education reforms in mathematics and science. More than four-fifths of the states have content frameworks in place in mathematics and science, and a large number of these have some form of statewide assessment to measure student attainment of expectations given in the frameworks. Various approaches to alignment have been attempted, but they have generally lacked specific criteria for judging the alignment. Twelve criteria for judging alignment grouped into five categories are described, along with examples and levels of agreement. The five general categories are: (1) content focus; (2) articulation across grades and ages; (3) equity and fairness; (4) pedagogical implications; and (5) system applicability. These criteria were developed by an expert panel formed as a cooperative effort of the Council of Chief State School Officers and the National Institute for Science Education provide guidance to educators trying to develop a coherent system of expectations and assessments. An appendix lists the task force participants.”

REL West note: Although this article was published in 1997, we include it here because of its relevance to the request.

Webb, N. L. (1999). Alignment of science and mathematics standards and assessments in four states (Research Monograph No. 18). Council of Chief State School Officers. Full text available from from

From the abstract: “Reviewers analyzed the alignment of assessments and standards in mathematics and science from four states at a four-day institute conducted June 29 through July 2, 1998. Six reviewers compared the match between assessment items and standards in mathematics and seven compared the match in science. Data from these analyses were processed and used to judge the degree of alignment on four criteria: categorical concurrence, depth-of-knowledge consistency, range-of-knowledge correspondence, and balance of representation. The analyses indicated that the standards of the four states varied in what content students were expected to know, the level of specificity at which expectations were expressed, and organization. Nearly all of the sixteen assessment instruments reviewed incorporated some constructed-response items. Only one mathematics assessment for grade 10 from one state consisted solely of multiple-choice items. The items in three science and two mathematics assessments analyzed from one state were evenly divided between multiple-choice and constructed-response items. Assessments from the other three states included from 80% to 90% multiple-choice items. Alignment between assessments and standards varied across grade levels, content areas, and states without any discernable pattern. Assessments and standards of three of the four states satisfied the categorical concurrence criterion. This criterion, the most common conception of alignment, required the assessment and standards to include the same content topics. Alignment was found to be the weakest on the depth-of-knowledge consistency and range-of-knowledge correspondence criteria. Generally, assessment items required a lower level of knowledge and did not span the full spectrum of knowledge as expressed in the standards. However, for the knowledge and skills identified in the standards and addressed by the assessments, generally the assessment items were evenly distributed. A major goal of this study was to develop a valid and reliable process for analyzing the alignment among standards and assessments. The process did produce credible results that distinguished among the different attributes of alignment and detected specific ways that alignment could be improved. Issues that did arise from an analysis of the process indicated that reviewers could benefit from more training at the beginning of the institute. Reviewers also needed more clarification of the four depth-of-knowledge levels and more explicit rules for assigning an assessment item to more than one statement of expectation.”

REL West note: Although this article was published in 1999, we include it here because of its relevance to the request.

Webb, N. L. (2007). Issues related to judging the alignment of curriculum standards and assessments. Applied Measurement in Education, 20(1), 7–25. Abstract available from from and full text available from from

From the abstract: “A process for judging the alignment between curriculum standards and assessments developed by the author is presented. This process produces information on the relationship of standards and assessments on four alignment criteria: Categorical Concurrence, Depth of Knowledge Consistency, Range of Knowledge Correspondence, and Balance of Representation. Five issues are identified—but not resolved—that have arisen from conducting alignment studies. All of these issues relate to making a decision about what alignment is good enough. Pragmatic decisions have been made to specify acceptable levels for each of the alignment criteria. The assumptions are described. The issues discussed arise from a change in the underlying assumptions and from considering variations in the purpose for an assessment. The existence of such issues reinforces that alignment judgments have an element of subjectivity.”

Additional Organizations to Consult

Achieve the Core – from

From the website: “Achieve the Core dedicates to high-quality instructional materials and their use in classrooms. Teachers need high-quality materials in order to serve students well. They also need information, strategies, and ideas on how to use these materials to help ALL their students meet their learning goals. This blog provides information for those looking to make the most of the instructional materials they have through effective instructional practice techniques, adaptation/supplementation, and content-focused professional learning. This blog also features information for those reviewing and selecting new materials. ”

REL West note: Achieve the Core has one resource that is relevant to this request:

Cole, S., & Paillé, A. S. (2017). The connection between math materials and assessment. What happens when curricula and summative assessments don’t match? Achieve the Core. Full text available from from

Center for American Progress – from

From the website: “The Center for American Progress is an independent nonpartisan policy institute that is dedicated to improving the lives of all Americans, through bold, progressive ideas, as well as strong leadership and concerted action. Our aim is not just to change the conversation, but to change the country.”

REL West note: The Center for American Progress has one resource that is relevant to this request:

Brown, C., Boser, U., Sargrad, S., & Marchitello, M. (2016). Implementing the Every Student Succeeds Act: Toward a coherent, aligned assessment system. Center for American Progress. Full text available from from

Center on Education Policy – from

From the website: “The Center on Education Policy is a national, independent source for research and information about public education. The Center helps Americans better understand the role of public education in a democracy and the need to improve the academic quality of public schools. We do not represent any special interests. Instead, we try to help citizens make sense of the conflicting opinions and perceptions about public education and create the conditions that will lead to better public schools.”

REL West note: The Center on Education Policy has one resource that is relevant to this request:

Rentner, D. S., & Kober, N. (2014). Common Core State Standards in 2014: District implementation of consortia-developed assessments. Center on Education Policy. Full text available from from

The Standards Aligned System – from

From the website: “The Standards Aligned System (SAS), developed by the Pennsylvania Department of Education, is a comprehensive, researched-based resource to improve student achievement. SAS identifies six elements that impact student achievement: Standards, Assessments, Curriculum Framework, Instruction, Materials & Resources, and Safe and Supportive Schools. Schools and educators across Pennsylvania are supported in their efforts to implement SAS by the development of a state-of-the-art portal.”

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

Standards Aligned System. (2011). Teachers’ desk reference: Pennsylvania’s standards aligned. Author. Full text available from


Keywords and Search Strings

The following keywords and search strings were used:

[(Math OR Mathematics) AND (“aligned assessment with curriculum” OR “curriculum assessment alignment” OR “assessment curriculum alignment” OR “aligned assessment systems” OR “assessment alignment”) AND (state OR district OR school) AND (research OR “best practice”)]

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 2006 to present, were included in the search and review. However, seven studies that were published before that date were included because of their relevance to the request.
  • 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.