Evidence · Math achievement
How well do American children learn math?
American math scores remain below their 2013 peak, and research points to fluent basic facts and fractions as the base for later math.
The short answer
On the 2024 Nation's Report Card, 4th graders gained a little, but 8th graders showed no gain after a historic drop in 2022. Nearly 40 percent of 8th graders scored below NAEP Basic. On the TIMSS 2023 test, Singapore's 8th graders outscored American 8th graders by 117 points. A 2008 federal panel urged a focused curriculum, quick recall of basic facts, and a strong command of fractions. Federal practice guides find strong evidence for explicit, systematic teaching of children who struggle. Studies that follow children for years link early math and fraction skills to later success in algebra.
What does the Nation's Report Card show?
The National Assessment of Educational Progress, or NAEP, tests a national sample of students. In 2024, the average 4th grade math score rose 2 points from 2022. Public school 4th graders averaged 237, with 39 percent at or above Proficient. In 2019, they averaged 240, with 40 percent at or above Proficient. Nearly a quarter of 4th graders still scored below NAEP Basic.
The 8th grade picture is worse. Scores stayed flat in 2024 after a historic 8 point drop in 2022. Public school 8th graders averaged 272, the same as in 2000. In 2019, they averaged 281, with 33 percent at or above Proficient. By 2024, that share had fallen to 27 percent. Nearly 40 percent of 8th graders scored below Basic, and no state passed its 2019 8th grade score.
National math scores remain higher than in the 1990s but well below their 2013 peak. On the 2024 tests, the lowest-performing students scored about 100 points below the highest-performing students.
High school seniors also lost ground. In 2024, the average 12th grade math score fell 3 points below 2019 and 3 points below 2005. The Governing Board reports that 45 percent of seniors scored below NAEP Basic in math. NCES expects to release the 2026 math results in early 2027, under a new framework. Our page on learning loss after school closures covers the pandemic years in more detail.
What does the long-term trend show?
NAEP also runs a separate long-term trend test with a stable design. In 2023, the average math score for 13-year-olds fell 9 points from 2020 and 14 points from 2012. Lower performers lost more ground. Their scores fell 12 to 14 points, against 6 to 8 points for middle and higher performers.
Fewer 13-year-olds now take algebra. Since 2012, the share taking algebra has fallen from 34 to 24 percent, while the share in regular math rose from 28 to 42 percent. Among 13-year-olds who scored in the top quarter, 44 percent took algebra, compared with 10 percent of those in the bottom quarter.
How do American students compare with other countries?
TIMSS is an international test of 4th and 8th graders in dozens of education systems. In 2023, U.S. math scores fell 18 points in 4th grade and 27 points in 8th grade from 2019. American 4th graders averaged 517, while Singapore's averaged 615. American 8th graders averaged 488, while Singapore's averaged 605.
In 4th grade, 21 of 63 education systems scored higher than the United States. In 8th grade, 19 of 45 systems scored higher. The lowest-performing American 4th graders lost 37 points, while top performers held steady. Among 8th graders, 18 percent scored below the TIMSS Low benchmark.
PISA is an international test of 15-year-olds. In 2022, the United States scored 465 in math, against an OECD average of 472. NCES describes that gap as not measurably different. The OECD reports that U.S. results were among the lowest ever measured by PISA in math. Only 7 percent of U.S. students were top performers, compared with 9 percent across the OECD.
What did the National Mathematics Advisory Panel recommend?
In March 2008, the U.S. Department of Education released the final report of the National Mathematics Advisory Panel. The panel reviewed more than 16,000 research publications and policy reports. It called for a streamlined curriculum that stresses a short list of the most critical topics in the early grades. It warned against programs that revisit topics year after year without closure.
The panel named whole numbers, fractions, and parts of geometry and measurement as the Critical Foundations of Algebra. It called for quick and effortless recall of basic facts, built through enough practice. It found that difficulty with fractions, decimals and percents is pervasive and a major obstacle to later math.
On teaching methods, the panel found that explicit instruction for students with math difficulties has shown consistently positive effects. It recommended that struggling students receive some explicit instruction regularly. It also found that research does not support exclusive use of either student-centered or teacher-directed teaching. It advised that calculators stay off test items meant to measure computation. Our page on classroom screens looks at technology in the classroom more broadly.
What do federal practice guides say works?
The Institute of Education Sciences publishes What Works Clearinghouse practice guides that rate the research behind each recommendation. A 2021 guide on elementary math intervention gives a strong evidence rating to systematic instruction during intervention. The same guide gives a strong rating to regular timed activities to build fluency and to using the number line.
An earlier 2009 guide rated the evidence as strong for intervention that is explicit and systematic. It recommended about 10 minutes in each intervention session on fluent recall of basic arithmetic facts, with a moderate evidence rating. A 2010 guide on fractions found moderate evidence for teaching that fractions are numbers that expand the number system. It also found moderate evidence for showing students why fraction procedures make sense.
Why do early skills, facts and fractions matter?
A 2007 study in Developmental Psychology pooled six long-term data sets on young children. It found that math skills at school entry had the greatest predictive power for later achievement. Early reading skills and attention skills followed.
A 2012 study in Psychological Science used large data sets from the United States and the United Kingdom. Elementary students' knowledge of fractions and division predicted their algebra knowledge and overall math achievement in high school, 5 or 6 years later. The link held after the authors controlled for other math knowledge, general intellectual ability, working memory, and family income and education.
A smaller 2013 brain imaging study looked at fact recall. Among 33 high school students, brain activity linked to fact retrieval during simple arithmetic went with higher PSAT math scores. The authors point to the role of mental arithmetic fluency in learning higher math.
These studies show strong links, not proof of cause. They are consistent with the federal panel's advice, which treats fluent facts and fractions as foundations for algebra.
What can you ask a school about math?
Anyone who cares about a child can ask these questions of a teacher, principal or school board:
- Which math program do you use in each grade? Does it build skills in a set order and finish each topic before moving on?
- By what grade do you expect children to recall addition and multiplication facts quickly? How do you check?
- How much class time goes to practice that builds fluency?
- How do you teach fractions? Do children learn to place fractions on a number line?
- When a child falls behind, does the extra help include explicit, step-by-step teaching? How will you tell the family?
- Who takes algebra in 8th grade, and how do you decide? How do your scores compare with the state's NAEP results?
What Restore Childhood is doing
Restore Childhood is a 501(c)(3) that makes films, reporting and tools for everyone who cares about children. Its film 15 DAYS covers America's pandemic school closures. It publishes reporting on its Substack. This page is part of a series of plain evidence pages on childhood and school.
What you can do now
- Ask your school for the name of its math program, then look it up.
- Check your state's NAEP math results on The Nation's Report Card.
- Practice math facts with a child for a few minutes most days.
- Use everyday tasks like cooking and sharing to talk about fractions.
- Ask how your school helps children who fall behind in math.
- Share this page with your school board or a teacher you trust.
Related
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