Strengthening Math Fluency Through Cognitive Science
Strengthening Math Fluency Through Cognitive Science
Arithmetic fluency, the efficient, accurate, and relatively effortless recall of basic addition, subtraction, multiplication, and division facts, is one of the strongest predictors of long-term math achievement and overall academic success. However, its role in math education has been widely misunderstood. Some argue that memorizing math facts is harmful or outdated, while others insist on a return to traditional drills. But all concur that the nation’s persistent math underperformance underscores the urgent need to strengthen foundational fluency.
The Status Quo
School Level - Match proficiency
At Grade 4:
performed at or above NAEP Proficient in math (2024).
At Grade 8:
performed at or above NAEP Proficient in math (2024).
At Grade 12:
of twelfth-graders were at or above NAEP Proficient (2024)
scored below NAEP Basic (2024). This is the highest share below Basic ever reported for Grade 12. The Grade-12 average math score is the lowest since NAEP began reporting in 2005.
“Students still haven’t caught up to where they were before COVID-19… Five years after classrooms first shut down, student achievement remains below pre-pandemic levels, especially in math.”
College Readiness
Benchmark Unmet
of graduates met all four ACT college-readiness benchmarks (English, Reading, Math, Science) in 2023.
of students met the ACT STEM College Readiness Benchmark in 2023, down from 20 percent in 2018-19
Failing Remediation
of students entering college need remedial coursework and outcomes are poor:
of students who start in remediation ever complete a degree (20% of low-income students) (Center for American Progress; FutureEd, 2024).
Misconceptions about teaching and learning based on intuition have led to an epidemic of disengagement in schools (Evans, 2023), higher education (Chronicle of Higher Ed, 2022; NY Times, 2022), and the workplace (Society for HR Management, 2023).
What the Science of Learning Teaches Us About Arithmetic Fluency
Insights from White Paper by Nicole M. McNeil, Nancy C. Jordan, Alexandria A. Viegut, and Daniel Ansari published by Association for Psychological Science (2025)
Some argue that memorizing math facts is harmful or outdated, while others insist on a return to traditional drills. McNeil et al. (2025) present a more accurate and science-based view: fluency must be built through both meaningful understanding and structured practice. It is not a choice between memorization or thinking strategies; both are essential and work together. Fluency is not simply fast answers. It relies on deep number sense, strategic flexibility, and automaticity that frees cognitive resources for higher-level reasoning. When students lack fluency, their working memory becomes overloaded during problem solving, making complex math unnecessarily difficult. The authors conclude that building fluency is not optional—it is a foundation for later mathematical success and equity in education.
