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Math Proficiency
March 2021


"What does the research say about the relationship between mathematics proficiency by the end of third grade and future educational success?"

Ask A REL Response

Thank you for your request to our Regional Educational Laboratory (REL) Reference Desk. Ask A REL is a collaborative reference desk service provided by the 10 RELs that, by design, functions much in the same way as a technical reference library. Ask A REL provides references, referrals, and brief responses in the form of citations in response to questions about available education research.

Following an established REL Northwest research protocol, we conducted a search for evidence- based research. The sources included ERIC and other federally funded databases and organizations, research institutions, academic research databases, Google Scholar, and general Internet search engines. For more details, please see the methods section at the end of this document.

The research team has not evaluated the quality of the references and resources provided in this response; we offer them only for your reference. The search included the most commonly used research databases and search engines to produce the references presented here. References are listed in alphabetical order, not necessarily in order of relevance. The research references are not necessarily comprehensive and other relevant research references may exist. In addition to evidence-based, peer-reviewed research references, we have also included other resources that you may find useful. We provide only publicly available resources, unless there is a lack of such resources or an article is considered seminal in the topic area.


Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1-29.

From the Abstract:
"Background: Children's early skills are essential for their later success in school. Recent evidence highlights the importance of early mathematics, relative to reading and socioemotional skills, for elementary school achievement. Key advocacy groups for both early childhood and mathematics education have issued position statements on the importance of early mathematics, arguing that mathematics education for 3- to 6- year-olds is essential to promoting future mathematics achievement. Focus of Study: Despite the fact that advocates and researchers are focusing on early math skills, we are still learning about the mathematics knowledge and skills young children typically have and how these early skills affect later academic achievement and school success. This study aims to address these gaps in the extant research by investigating how early math skills predict later school success. We explore how early math skills relate to achievement, from kindergarten through eighth grade, across reading, math, and science test score outcomes, as well as grade retention and teacher-reported academic achievement. We also explore whether there is variation in the relationship between early math skills and later outcomes for children who enter school with limited math skills. Research Design: We conduct secondary analysis with data from the Early Childhood Longitudinal Study-Kindergarten Cohort, a longitudinal, nationally representative sample of children who were in kindergarten in 1998-1999 and were followed through eighth grade. Results: We find that early math skills predict reading, math, and science achievement as well as grade retention from kindergarten through eighth grade. Results show that kindergarten math skills in pattern recognition, measurement, and advanced number are most predictive of eighth-grade outcomes overall and for subgroups including students who enter school with low math skills. The importance of these math skills for subsequent achievement increases or is maintained over time. Conclusions: The results reported here have implications for education policy regarding mathematics instruction in the earliest years of schooling. The fact that early mathematics knowledge and skills are the most important predictors not only for later math achievement but also for achievement in other content areas and grade retention supports a greater emphasis on mathematics than is currently the case in many kindergarten classrooms. It also suggests the possibility that focusing more on advanced number, pattern recognition, and measurement might develop skills that will benefit students in the later years of schooling."

Dragoset, L., Baxter, C., Dotter, D., & Walsh, E. (2019). Measuring school performance for early elementary grades in Maryland. Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Mid-Atlantic.

From the Abstract:
"The purpose of this report is to investigate the feasibility of constructing a school-level measure of students' academic growth from kindergarten to grade 3, and to assess the validity and precision of that measure. The study measured schoolwide student growth for reading and math using student growth percentiles based on Maryland's 2014/15 Kindergarten Readiness Assessment (KRA) and the 2017/18 grade 3 Partnership for Assessment of Readiness for College and Careers (PARCC) assessment. To assess validity, the study calculated correlations between student scores on the two assessments and compared those correlations with correlations between scores on tests in later years. To assess precision, the study constructed 95 percent confidence intervals around schools' growth estimates. Schools' K-3 growth estimates are likely less valid than schools' grade 3-4 growth estimates but have a similar level of precision. Schools' K-3 growth estimates are much less precise for smaller schools than for larger schools. Similarly, they are much less precise when they include only random samples of students as compared to all students in a school's relevant cohort. The study offers lessons to other states interested in constructing early grade growth measures using two different assessments that are administered multiple years apart. The following are appended: (1) a description of methods and (2) supporting analyses."

Goldhaber, D., Wolff, M., & Daly, T. (2020). Assessing the accuracy of elementary school test scores as predictors of students' high school outcomes. (CALDER Working Paper No. 235-0520). Washington, DC: National Center for Analysis of Longitudinal Data in Education Research (CALDER).

From the Abstract:
"Testing students and using test information to hold schools and, in some cases, teachers accountable for student achievement has arguably been the primary national strategy for school improvement over the past decade and a half. Tests are also intended to be used as a diagnostic tool to identify individual student needs, so that students can be set on a trajectory for long-term academic success. We use panel data from three states -- North Carolina, Massachusetts and Washington State -- to investigate how accurate early measures of achievement are in predicting later high school outcomes. We contribute to the literature in three distinct ways. First, the long panels we employ allow us to quantify the accuracy of models predicting how early (3rd and 4th grade) measures of student background and achievement predict several later schooling outcomes: 8th grade test achievement, high school course-taking, and high school graduation. Second, we test the extent to which predictions based on distinct segments of student data (e.g., grades 3 to 8, then 8 to 12) sacrifice forecast accuracy; this is of particular policy relevance for states or localities that do not yet have long administrative data panels. Finally, we test the degree to which the use of parameter estimates from models predicting schooling outcomes derived from one state diminish the accuracy of predicting outcomes in other states."

Herrera, S., Zhou, C., & Petscher, Y. (2017). Examining school-level reading and math proficiency trends and changes in achievement gaps for grades 3-8 in Florida, Mississippi, and North Carolina (REL 2017-235). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southeast.

From the Abstract:
"The 2001 authorization of the No Child Left Behind Act and its standards and accountability requirements generated interest among state education agencies in Florida, Mississippi, and North Carolina, which are served by the Regional Educational Laboratory Southeast, in monitoring changes in student reading and math proficiency at the school level. This study was requested by governing board members representing North Carolina, members of the Improving Literacy Research Alliance (which includes representatives from Florida) and, members of the Improving Schools in Mississippi Research Alliance. All three of these states monitor and report changes in performance for schools. However, this study goes beyond reporting averages to examine school-level academic performance using a growth curve modeling approach. This approach can provide stakeholders with a deeper understanding of trends in student proficiency at the school level, by grade at the school level, and among key demographic groups to allow for more accurate policy responses. This study uses growth curve modeling to investigate trends in student reading and math proficiency on state accountability assessments for grades 3-8. Growth curve modeling makes it possible to determine if growth rates in reading and math proficiency are statistically significant and if the differences in proficiency growth rates between grades and subgroups differ in statistically significant ways. Using four to six years of publicly available school-level data between school years 2007/08 and 2013/14 from each state department of education, this study assessed trends in three areas. First, it estimated trends in average school-level student growth rates in reading and math proficiency on the statewide assessment and examined whether these growth rates varied across grades 3 through 8. Second, it calculated average school-level student growth rates in reading and math proficiency for racial/ethnic subgroups and economic subgroups (eligibility for the federal school lunch program, a proxy for economic disadvantage) in grades 3-8. Third, it examined whether there were any statistically significant decreases in achievement gaps by grade between White and Black students, between White and Hispanic students, and between economic subgroups. This information was then used to estimate reading and math proficiency gaps that remained at the end of the period studied."

Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88. Retrieved from

From the Abstract:
"Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions."

Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45-58.

From the Abstract:
"Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each contributed uniquely to later conceptual understanding of fractions. Number line estimation, attentive behavior, calculation fluency, and working memory made unique contributions to acquisition of fraction arithmetic procedures. Notably, number line estimation made the largest independent contribution in both models. The results suggest that although there is considerable shared variance among the predictors, both general and number-related competencies are uniquely important for explaining why some children struggle with fractions."

Schenke, K., Rutherford, T., Lam, A. C., & Bailey, D. H. (2016). Construct confounding among predictors of mathematics achievement. AERA Open, 2(2), 1-16.

From the Abstract:
"Identifying which early mathematics skills have the largest effects on later mathematics achievement has important implications. However, regression-based estimates often rely on untested assumptions: (a) Scores on different mathematics skills reflect unique constructs, and (b) other factors affecting early and later mathematics achievement are fully controlled. We illustrate a process to test these assumptions with a sample of third and fourth graders who completed measures of mathematics skills, working memory and motivation, and standardized mathematics and English language arts tests. Factor analyses indicated that mathematics skills largely reflect the same underlying construct. The skills that loaded highest on the general factor most predicted both later mathematics and English language arts, even after adjusting for working memory and motivation. Findings suggest that relations between earlier mathematics and later achievement largely reflected more general factors that contribute to children's learning. We discuss the importance of establishing construct validity in correlational studies."

Schwerdt, G., West, M. R., & Winters, M. A. (2017). The effects of test-based retention on student outcomes over time: Regression discontinuity evidence from Florida. NBER Working Paper No. 21509. National Bureau of Economic Research.

From the Abstract:
"Many American states require that students lacking basic reading proficiency after third grade be retained and remediated. We exploit a discontinuity in retention probabilities under Florida's test-based promotion policy to study its effects on student outcomes through high school. We find large positive effects on achievement that fade out entirely when retained students are compared to their same-age peers, but remain substantial through grade 10 when compared to students in the same grade. Being retained in third grade due to missing the promotion standard increases students' grade point averages and leads them to take fewer remedial courses in high school but has no effect on their probability of graduating."

Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., & Engel, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691-697.

From the Abstract:
"Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed."

Stevens, J. J., Schulte, A. C., Elliott, S. N., Nese, J. F., & Tindal, G. (2015). Growth and gaps in mathematics achievement of students with and without disabilities on a statewide achievement test. Journal of School Psychology, 53(1), 45-62. Retrieved from

From the Abstract:
"This study estimated mathematics achievement growth trajectories in a statewide sample of 92,045 students with and without disabilities over Grades 3 to 7. Students with disabilities (SWDs) were identified in seven exceptionality categories. Students without disabilities (SWoDs) were categorized as General Education (GE) or Academically/Intellectually Gifted (AIG). Students in all groups showed significant growth that decelerated over grades as well as significant variability in achievement by student group, both at the initial assessment in Grade 3 and in rates of growth over time. Race/ethnicity, gender, parental education, free/reduced lunch status, and English language proficiency were also significant predictors of achievement. Effect size estimates showed substantial year-to-year growth that decreased over grades. Sizeable achievement gaps that were relatively stable over grades were observed between SWoDs and students in specific exceptionality categories. Our study also demonstrated the importance of statistically controlling for variation related to student demographic characteristics. Additional research is needed that expands on these results with the same and additional exceptionality groups."


Keywords and Search Strings: The following keywords, subject headings, and search strings were used to search reference databases and other sources: (Math or mathematics or mathematical), ("Third grade" OR "3rd grade"), (Proficiency OR proficient), ("Student outcomes" OR "academic outcomes" OR achievement), ("High school OR "middle school"), Predictor

Databases and Resources: We searched ERIC for relevant resources. ERIC is a free online library of more than 1.6 million citations of education research sponsored by the Institute of Education Sciences (IES). Additionally, we searched Google Scholar and EBSCO databases (Academic Search Premier, Education Research Complete, and Professional Development Collection).

Reference Search and Selection Criteria

When we were searching and reviewing resources, we considered the following criteria:

Date of publications: This search and review included references and resources published in the last 10 years.

Search priorities of reference sources: Search priority was given to study reports, briefs, and other documents that are published and/or reviewed by IES and other federal or federally funded organizations, as well as academic databases, including ERIC, EBSCO databases, and Google Scholar.

Methodology: The following methodological priorities/considerations were given in the review and selection of the references:

  • Study types: randomized control trials, quasi experiments, surveys, descriptive data analyses, literature reviews, and policy briefs, generally in this order
  • Target population and samples: representativeness of the target population, sample size, and whether participants volunteered or were randomly selected
  • Study duration
  • Limitations and generalizability of the findings and conclusions

This memorandum is one in a series of quick-turnaround responses to specific questions posed by stakeholders in Alaska, Idaho, Montana, Oregon, and Washington, which is served by the Regional Educational Laboratory (REL) Northwest. It was prepared under Contract ED-IES-17-C-0009 by REL Northwest, administered by Education Northwest. The 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.