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High School Interim Math Assessments — July 2021


Could you provide research on benchmark, interim, or formative math assessments at the high school level?


Following an established REL West research protocol, we conducted a search for research reports and resources on benchmark, interim, or formative math assessments at the high school level. 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

Herman, J. L., Matrundola, D. L. T., Epstein, S., Leon, S., Dai, Y., Reber, S., & Choi, K. (2015). The implementation and effects of the mathematics design collaborative (MDC): Early findings from Kentucky ninth-grade Algebra 1 courses. National Center for Research on Evaluation, Standards, and Student Testing (CRESST). Full text available from

From the abstract: “With support from the Bill and Melinda Gates Foundation, researchers and experts in mathematics education developed the Mathematics Design Collaborative (MDC) as a strategy to support the transition to Common Core State Standards in math. MDC provides short formative assessment lessons known as Classroom Challenges for use in middle and high school math classrooms. UCLA CRESST’s study of ninth-grade Algebra 1 classrooms in Kentucky implementing MDC showed strong support from teachers for the intervention and a statistically significant positive impact on student scores on the PLAN Algebra assessment, as compared to similar students statewide in Kentucky.”

Lawrence, N., Sanders, F., Christman, J. B., & Duffy, M. (2011). Establishing a strong foundation: District and school supports for classroom implementation of the MDC framework. Research for Action. Full text available from

From the abstract: “The Bill and Melinda Gates Foundation has invested in the development and dissemination of high-quality formative assessment tools to support teachers’ incorporation of the Core Common State Standards (CCSS) into their classroom instruction. Lessons from the first generation of standards-based reforms suggest that intense attention to high quality instructional tasks, use of formative assessments embedded in those tasks, and professional development (PD) that attends to both content knowledge and instruction are essential considerations if teachers are to meet the demands of the CCSS. Experts from the Shell Centre have developed a set of formative assessment lessons (FALs) for high school mathematics teachers to facilitate CCSS-based student mathematics learning and provide teachers with feedback about student understanding and mastery. The tools are designed to target the ‘instructional core’ by: (1) Raising the level of content; (2) Enhancing teachers’ skill and knowledge about instruction, content and formative assessment; and (3) Catalyzing student engagement in their learning so that they will achieve at high levels. In 2010–2011, the Mathematics Design Collaborative (MDC) was piloted in four districts and two networks of schools. In most cases, school districts applied for and received grants to implement MDC; in others, national networks were the grantee and the organizer. It is important to note that during the MDC pilot year, the use of FALs was limited in most sites. Many districts received the beta versions of the FALs towards the end of the school year and teachers did not have the opportunity to use them, as they were preparing students for state tests and end-of-course exams. Most teachers have only used the FALs as part of PD sessions. In this report, which draws largely on data from three school districts and one school network, Research for Action (RFA) identifies the conditions and contexts for successful use of the tools, and examines the actions that district and school-based leaders can take to support teachers’ adoption and effective implementation of the math tools. It provides specific recommendations to guide local leaders as they gear up to help year one teachers deepen their use of the MDC tools and teachers who are just joining the initiative to efficiently gain the expertise and skills they need to successfully implement the tools.”

Lee, H., Chung, H. Q., Zhang, Y., Abedi, J., & Warschauer, M. (2020). The effectiveness and features of formative assessment in US K-12 education: A systematic review. Applied Measurement in Education, 33(2), 124–140. Abstract available from and full text available for a fee from

From the abstract: “In the present article, we present a systematical review of previous empirical studies that conducted formative assessment interventions to improve student learning. Previous meta-analysis research on the overall effects of formative assessment on student learning has been conclusive, but little has been studied on important features of formative assessment interventions and their differential impacts on student learning in the United States’ K–12 education system. Analysis of the identified 126 effect sizes from the selected 33 studies representing 25 research projects that met the inclusion criteria (e.g., included a control condition) revealed an overall small-sized positive effect of formative assessment on student learning (d = 0.29) with benefits for mathematics (d = 0.34), literacy (d = 0.33), and arts (d = 0.29). Further investigation with meta-regression analyses indicated that supporting student-initiated self-assessment (d = 0.61) and providing formal formative assessment evidence (e.g., written feedback on quizzes; d = 0.40) via a medium-cycle length (within or between instructional units; d = 0.52) were found to enhance the effectiveness of formative assessments.”

Lyon, C. J., Nabors Oláh, L., & Caroline Wylie, E. (2019). Working toward integrated practice: Understanding the interaction among formative assessment strategies. Journal of Educational Research, 112(3), 301–314. Abstract available from and full text available for a fee from

From the abstract: “The purpose of this study was to directly observe and investigate the factors that support or hinder the implementation of an integrated approach to formative assessment and to understand how the implementation of formative assessment strategies interact. The authors present findings from a collective case study that included the observation of six teachers (three mathematics and three English language arts) who were purposefully sampled from a large, public, suburban high school in the northeast United States. The analysis of the case studies resulted in the identification of different patterns in teachers’ formative assessment practice. These patterns illustrate how the complex interaction between formative assessment practices can either support or hinder the implementation of an integrated approach to formative assessment and suggests classroom observations as a potential mechanism for identifying challenges and informing just-in-time professional development.”

Makkonen, R., & Jaquet, K. (2020). The association between teachers’ use of formative assessment practices and students’ use of self-regulated learning strategies (REL 2021-041). Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory West. Full text available from

From the abstract: “Three Arizona school districts surveyed teachers and students in grades 3–12 in spring 2019 to better understand the association between teachers’ use of formative assessment practices and students’ use of self-regulated learning strategies and to help shape related teacher development efforts moving forward. Formative assessment is a set of practices that enable teachers and students to examine how learning is progressing throughout a lesson or related series of lessons, so that teaching and learning activities can be adjusted as needed. Self-regulated learning is a proactive process in which students select an appropriate learning strategy to advance their learning goals. The survey results indicated that responding teachers frequently gave students feedback but less frequently provided occasions for students to provide feedback to one another, while responding students frequently tracked their own progress but less frequently solicited feedback from their teacher or peers. Only a small positive association was found between the frequency of teachers’ formative assessment practices and the average number of self-regulated learning strategies that their students used. The correlation was stronger in elementary school than in secondary school and stronger in science, technology, engineering, and math (STEM) classrooms than in non-STEM classrooms. Some of teachers’ least frequently used formative assessment practices—facilitating student peer feedback and self-assessment—had stronger positive associations with the average number of self-regulated learning strategies that their students used than other, more frequently used practices. The more frequently that teachers reported using these practices, the more self-regulated learning strategies their students reported using.”

Pinger, P., Rakoczy, K., Besser, M., & Klieme, E. (2018). Interplay of formative assessment and instructional quality—Interactive effects on students’ mathematics achievement. Learning Environments Research, 21(1), 61–79. Abstract available from and full text available for a fee from

From the abstract: “Formative assessment is considered to be a promising teaching practice for promoting teaching and learning processes. The implementation of teaching practices into instruction involves intervening with a learning environment that is characterized by certain features of instructional quality. Our study aims to contribute to the understanding of formative assessment by analyzing the interplay between a formative assessment intervention and aspects of general instructional quality. In a quasi-experimental study design, 15 teachers participated in a control group (n = 361 students) and 20 teachers in the intervention classes (n = 498 students) implemented a curriculum-embedded formative assessment tool in their ninth-grade mathematics classes. No effects were found for the intervention on the assessed aspects of general instructional quality (process-oriented instruction, teacher-student relationship, effective use of instructional time). However, multilevel regression analyses revealed an interaction effect between the intervention and process-orientation and the effective use of instruction time. Our findings suggest that implementing formative assessment tools do not seem to suffice regarding changes in general instructional quality, but that an intervention with detailed material and guidelines can counterbalance effects of instructional quality, fostering students’ achievement in classes with lower degrees of process orientation and a less effective use of instructional time.”

Southern Regional Education Board. (2015). Literacy and math strategies that prepare students for college and career. Best Practices Newsletter. Author. Abstract available from and full text available from

From the abstract: “The Literacy Design Collaborative (LDC) incorporates challenging literacy standards into middle grades and high school content areas within a variety of academic disciplines, not just English/language arts courses. The Mathematics Design Collaborative (MDC) provides schools with instructional tools needed to help teachers understand and implement the college- and career-readiness math standards effectively while allowing them the flexibility to select topics and adapt assignments to their specific instructional plans. MDC is about formative assessment, allowing students to engage in ‘productive struggle’ to make sense of math concepts. Teachers are able to identify misconceptions, learn from what students do or do not know and build on that to determine how to change instructional strategies to help all students master rigorous standards. This newsletter explores how schools are raising student achievement and teacher self-efficacy through implementation of the LDC and MDC frameworks.”

Wylie, E. C. (2017). Winsight™ assessment system: Preliminary theory of action. ETS Research Reports Series, 2017(1), 1–17. Full text available from

From the abstract: “The ‘Winsight’™Assessment System integrates summative, interim (including both benchmark assessments and testlets), and formative assessment components initially focused on mathematics and English language arts (ELA) in Grades 3-8 and high school. This report provides a preliminary theory of action for the Winsight Assessment System. A theory of action illustrates the claims made about a program through a logic model (a diagram that links program components to intermediate and long-term outcomes for various stakeholders) and a review of supporting literature for those claims. We first briefly describe the assessment and professional support components of the system, and then we identify 5 principles that undergird the theory of action and the logic model. We then present the logic model diagram and set of claims in the logic model that are ultimately intended to lead to improved student outcomes in the educational system. The report ends with a summary of logical, theoretical, and empirical evidence that supports these claims.”

Other Resources

Joyner, J. M., & Bright, G. W. (2017). INFORMative assessment: Formative assessment practices to improve mathematics achievement. Middle and high school. Math Solutions. Full text available for a fee from

Book description: “INFORMative Assessment should be intertwined with instruction. As we teach, we assess; and as we assess, we teach. With this in mind, INFORMative Assessment goes inside more than 30 classrooms to take ‘A Closer Look’ at how to: create learning targets from instructional standards; design and use probing questions, intentional listening, and follow-up tasks to reveal students’ thinking; use mathematically rich tasks to gather evidence about students’ thinking; identify students’ ‘logic’ that leads to correct, incomplete, or incorrect responses; provide actionable feedback to students; and plan with colleagues to implement INFORMative Assessment in instruction.”

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

Spencer-Waterman, S. (2012). Assessing middle and high school mathematics and science: Differentiating formative assessment. Routledge. Abstract available from full text available for a fee from

Book description: “For middle and high school teachers of mathematics and science, this book is filled with examples of instructional strategies that address students’ readiness levels, interests, and learning preferences. It shows teachers how to formatively assess their students by addressing differentiated learning targets. Included are detailed examples of differentiated formative assessment schedules, plus tips on how to collaborate with others to improve assessment processes. Teachers will learn how to adjust instruction for the whole class, for small groups, and for individuals. They will also uncover step-by-step procedures for creating their own lessons infused with opportunities to formatively assess students who participate in differentiated learning activities.”

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


Keywords and Search Strings

The following keywords and search strings were used:

[(“interim assessment” OR “benchmark assessment” OR “formative assessment”) AND (math OR mathematics) AND (“high school” OR secondary)]

[(“interim math assessment” OR “benchmark math assessment” OR “formative math assessment” ) AND (“high school” OR secondary)]  

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.
  • 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.