"Numerical Fluency" vs. Memorizing "Number Facts"

Aug 7, 2018 | Location Newton

We want to introduce the importance of “numerical fluency” and learning basic “number facts.”

Mathnasium explains the difference between Numerical Fluency and Memorization, and why Numerical Fluency is critical to mathematical thinking and problem-solving ability.Picture this scenario. A teacher asks a classroom, “If you spend 70 cents, 80 cents, and 90 cents, how much did you spend altogether?”

The teacher is thinking:

“7 + 8 + 9 = 24.  With a zero at the end, the answer would be 240 cents.”

However, our “finger counting” students, which is sadly too many of them, are thinking:

“7 + 8 = 7…8…9…10…11…12…13…14…15,” then “15 + 9 = 15…16…17…18…19…20…21…22…23…24…25 (oops).”

Many times, finger counters get the wrong answer because they either count too many or too few.

Since the process of “getting it wrong” is so uninspiring and time–consuming, not surprisingly, many students report being “bored" in math class.  In addition, the process has taken so long that the student is no longer in the flow of the lesson, which in this case, is learning about how to “add a 0 at the end.”


The term “number facts” includes all addition, subtraction, multiplication, and division problems resulting in single-digit and double-digit numbers (up to 24 for addition and subtraction, and up to 144 for multiplication and division). Examples of number facts include:

         3 + 7 = 10             13 – 5 = 8             5 x 9 = 45             120 ÷ 10 = 12 

In school, great emphasis is put on rote memorization of “number facts.”  This emphasis is misguided.

“Numerical Fluency” is the ability to “effortlessly recall—to know by heart.” Students should be able to tap into their reliable, quick, and knowable ways to answer “number facts” questions.

Many students in 2nd through 5th grade (and higher) have a limited grasp of numerical fluency. Hence, their ability to stay in the flow of new lessons is extremely limited.  This makes mathematics a frustrating and painful process for everyone involved—the kids, the teachers, and the parents!

Memorization seems to be the more understandable route initially, but it does not promote the mathematical thinking and problem-solving skills that are required for long-term success in math. Eventually, most students will forget what they memorized. 

We suggest that it is fairly easy to forget that which you have memorized, and nearly impossible to forget that which you have learned.

What students need to do is to build mental structures—frameworks for learning— so that they will know the basic number facts in a matter of a second.  Then they won’t have to worry about “forgetting.”

In a subsequent blog post, we will detail a process for teaching virtually any child how to “effortlessly recall” the number facts, paving the way for future success in the mathematics classroom.

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