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The road to math proficiency is paved with basic facts mastery

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With mathematics, it is not enough that students simply “learn” their number facts—they must be committed to memory, just as letter sounds must be memorized in development of phonics automaticity (Willingham, 2009). Automatic retrieval of basic math facts is necessary for students to develop computational fluency, which in turn allows students to spend mental energy on more complex math problems.

The key to automaticity is practice, and lots of it (Willingham, 2009), but as Burns, Ysseldyke, Nelson, and Kanive (in press) note, “few projects have sought to empirically determine which math facts require more time and practice” (p. 2). To this end, in a recent study, Burns et al. examined the differential difficulty of single-digit multiplication math facts by analyzing the number of repetitions students require to master these facts.

It is not enough that students simply “learn” their number facts—they must be committed to memory.

(Willingham, 2009)

Using the national database for the Accelerated Math Fluency software (previously called MathFacts in a Flash) the researchers studied math facts practice records for 15,402 students in grades 3–5. Burns et al. (in press) found that students from all three grade levels studied needed the fewest attempts to master single-digit multiplication facts for digits 2 and 3 and 8 and 9, while digits 4, 5, 6, and 7 required significantly more repetition. This finding held true regardless of proficiency level. The researchers also found an inverse relationship between students' grade levels and prior math achievement and the number of repetitions required by students for mastery. As grade level and proficiency level increased, students needed fewer attempts to master single-digit multiplication skills (see figure).

The researchers noted these results followed a somewhat predictable trajectory, but that the breadth of the database studied provided an unprecedented view into single-digit math fact difficulty for students in elementary grades, spanning all skill levels. These results may prove helpful to teachers with instructional planning, such as in understanding which math facts require more instruction and independent practice time to develop computational fluency.


Burns, M. K., Ysseldyke, J., Nelson, P., & Kanive, R. (in press). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology Quarterly.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. Retrieved from http://ies.ed.gov/ncee/wwc/pdf/practice_guides/rti_math_pg_042109.pdf

Willingham, D. T. (2009). Why don't students like school? A cognitive scientist answers questions about how the mind works and what it means for the classroom. San Francisco: Jossey-Bass.