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Common Core-Aligned Math Measures for Elementary Students — August 2021


Could you provide research on measures for student math progress or achievement in grades 3–5 that are aligned to the Common Core State Standards?


Following an established REL West research protocol, we conducted a search for research reports and resources on Common Core-aligned math measures for elementary students, with special attention to those in grades 3–5. 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

Arieli-Attali, M., & Cayton-Hodges, G. (2014). Expanding the “CBAL” mathematics assessments to elementary grades: The development of a competency model and a rational number learning progression (ETS RR-14-08, ETS Research Report Series). Educational Testing Service (ETS). Full text available from

From the abstract: “Prior work on the ‘CBAL’ mathematics competency model resulted in an initial competency model for middle school grades with several learning progressions (LPs) that elaborate central ideas in the competency model and provide a basis for connecting summative and formative assessment. In the current project, we created a competency model for Grades 3–5 that is based on both the middle school competency model and the Common Core State Standards (CCSS). We also developed an LP for rational numbers based on an extensive literature review, consultations with members of the CBAL mathematics team and other related research staff at Educational Testing Service, input from an advisory panel of external experts in mathematics education and cognitive psychology, and the use of small-scale cognitive interviews with students and teachers. Elementary mathematical understanding, specifically that of rational numbers, is viewed as fundamental and critical to developing future knowledge and skill in middle and high school mathematics and therefore essential for success in the 21st century world. The competency model and the rational number LP serve as the conceptual basis for developing and connecting summative and formative assessment as well as professional support materials for Grades 3–5. We report here on the development process of these models and future implications for task development.”

Northwest Evaluation Association. (2013). RIT stability through the transition to Common Core-aligned MAP tests. How using MAP to measure student learning growth is reliable now and in 2014. Author. Full text available from

From the abstract: “While many educators expect the Common Core State Standards (CCSS) to be more rigorous than previous state standards, some wonder if the transition to CCSS and to a Common Core aligned MAP test will have an impact on their students’ RIT scores or the NWEA norms. MAP assessments use a proprietary scale known as the RIT (Rasch unit) scale to measure student achievement and growth. The RIT scale, based on item response theory (IRT), has been used since the late 1970s by NWEA and is a proven, stable scale for educational assessment. The principle behind the RIT scale is simple: Test questions vary in difficulty and can be given a score on the RIT scale. A student’s achievement level can then be measured on the same scale by referencing the questions they were able to answer correctly. Every item in MAP tests is calibrated against one of the stable RIT scales: Reading, Language, Math or Science. Student responses on these items are used to generate a final RIT score for each student. An individual item with its associated RIT value may appear in tests aligned to various learning standards, such as state standards and the Common Core State Standards. Regardless of the standards alignment of a particular test, a given item has a single RIT value associated with it. This RIT value is obtained using a rigorous calibration process in which each item is field tested with thousands of students across the nation. The purpose of MAP tests is to measure growth by examining RIT scores over time. If two different MAP tests are on the same scale (e.g., Math) and measure similar constructs, then scores for these two tests can be compared directly. MAP tests aligned to CCSS, as well as other state standards (state-aligned) on a given scale, measure similar constructs due to the high degree of content overlap among learning standards. This underlying design of MAP tests is critical to ensuring that RIT scores carry the same meaning, in terms of student ability, regardless of which test was used to obtain them. Because the RIT scales are independent of standards alignment, transitioning between two tests is not anticipated to have a significant impact, however, States that are transitioning (or who have already transitioned) to teaching the CCSS, and are working to understand the gap between their state standards and what’s required by the CCSS, are seeing some key shifts. Those shifts are detailed in this report, and questions and answers are provided.”

Park, B. J., Irvin, P. S., Alonzo, J., & Tindal, G. (2012). The alignment of the easyCBM grades 3-5 math measures to the Common Core Standards (Technical report #1229). Behavioral Research and Teaching. Full text available from

From the abstract: “Within a response to intervention system of teaching and learning, important instructional decision-making (e.g., implementation of targeted intervention) is regularly tied to the results of formative assessments administered to students throughout the academic year. The validity of these instructional decisions depends to an extent on the alignment between formative measures and the content standards on which classroom instruction is based. Specifically, formative assessments must be aligned to adopted content standards in order for teachers to make valid instructional decisions around individual student learning needs. In this technical report, we report on the alignment between easyCBM® grades 3-5 seasonal mathematics benchmark items and the Common Core State Standards (CCSS). Results suggest reasonable alignment to the standards overall, with areas of relatively stronger and weaker alignment across grade level domains and standards. These results serve as the basis for assessment development in school year 2012-2013 to address gaps in alignment between easyCBM® and the CCSS. The following are appended: (1) Participants; (2) Alignment by Item; and (3) Alignment by Standard.”

Additional Organizations to Consult

Education First –

From the website: “Education First (EF) provides life-changing education for global citizens. For over 50 years, our mission has been to give confidence and freedom to people of all ages, nationalities and backgrounds. With the desire to define your own path in life, and a little courage, EF opens up a world of possibilities.”

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

Education First. (2013). A primer on Common Core-aligned assessments. Author. Full text available from

Mathematics Assessment Project –

From the website: “The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students’ mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students’ understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems.”

REL West note: Some assessment tools listed on this website may be relevant to your request.

Smarter Balanced –

From the website: “The Smarter Balanced assessment system provides educators with standards-aligned tools and resources to support their teaching and improve student learning.”

REL West note: Some assessment tools (either interim or summative assessments) listed on this website, may be relevant to your request in addition to the following resource:

Smarter Balanced. (2021). Interim assessments overview. Author. Full text available from


Keywords and Search Strings

The following keywords and search strings were used:

[(“common core state standards/CCSS”) AND (aligned OR alignment) AND (measure OR assessment) AND (math OR mathematics) AND (“elementary school” OR “3rd grade/grade 3” OR “4th grade/grade 4” OR “5th grade/grade 5” OR “grades 3–5”)]

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.