Why Students Need to Memorize Math Facts
And Why It’s Not “Rote”. It’s Foundational.
According to the NAEP (often called the Nationʼs Report Card), 61% of U.S. 4th graders scored below proficiency in mathematics in 2024. That number rises to 78% by 8th grade. As leaders, educators, and parents, we must be asking the question: What is causing this math crisis?
Over the past two decades there has been a prevalent misconception in many education circles, that memorizing math facts (those simple addition, subtraction, and multiplication facts that we want at our students’ fingertips) isn’t necessary. That students don’t need to know the multiplication table because they can always use other strategies… or just grab a calculator.
Though the solution to the math crisis is not singular, one thing is clear: this philosophy has left our students wildly unprepared. Modern education research is showing us the real story – that students who have memorized their math facts into their long-term memory learn math faster, understand it more deeply, and feel more confident doing it. Memorizing the facts isn’t frivolous busywork, it’s completely foundational to a student’s mathematical competence and long-term success.
The Power of Long-Term Memory
When students learn math (or anything for that matter), that learning starts in the working memory. This is the part of the brain that handles information that is coming from “outside” the learner and must be consciously thought about and processed. The working memory is extremely limited! Once we exceed the limits of 3-5 pieces of information, the cognitive load becomes too heavy and learning does not take place.
In contrast, long-term memory is virtually limitless. It can hold an incredible amount of information, and the more a student has stored there, the easier it is for them to learn new things without being overwhelmed. This is where we want the math facts stored! It becomes an incredible tool that the student can access instantaneously while problem solving. When math facts are stored in long-term memory and can be recalled automatically, they place no additional burden on working memory — the mental workspace where new learning and problem-solving occur — and actually free up cognitive resources, making that learning more effective.
In short, these two memories (working and long-term) work together. The things stored in long-term memory help students think critically, creatively, and effectively about the information that has entered the working memory. When students know their multiplication facts “by heart”, they have more brainpower to attend to the problems in front of them.
Knowing Math Facts Frees Working Memory (and Calculators Don’t)
So, now we know that working memory is like a student’s mental whiteboard. It only has room for a few ideas at a time.
When a student knows that 7×8 = 56 instantly, that fact takes up zero space on the whiteboard because it’s already stored in long-term memory.
But if they have to stop and figure it out (“Let’s see… 7×7 is 49, so 7×8 is 49+7…”) they’ve already used limited brainpower before even tackling the actual problem in front of them.
That’s why knowing these facts is so important. It reduces the cognitive load and frees the brain to focus on complex problem-solving and creative reasoning, the kind we want them doing in algebra, geometry, and beyond (Ding et al., 2019). Automatic recall isn’t about speed for speed’s sake; it’s about accessing higher-level thinking.
But Can’t We Just Give Kids Calculators?
A calculator can’t reduce the entire cognitive load for students. In fact, relying on one adds steps: Using the device, typing correctly, interpreting the result, and deciding whether it makes sense. Each of those eats up more working-memory space and creates new chances for error.
When facts are known, students can reason fluidly. When they’re not, even basic problems can feel like wading through mud. Take the following example: When students have to factor a number in algebra, such as 48, they need to quickly know that all of their options are 4x12, 6x8, 3x16, 2x24, and 1x48. A calculator can help a student find the factor pairs, but it will be much slower, use up a lot of working memory, and the student will not be confident that they have produced all the possible factors without first checking every single number on the calculator, which is extremely cumbersome. When students haven’t committed basic knowledge to long-term memory, their multi-step problem solving remains labored.
Math Is Hierarchical – Facts Are the Bottom Rung for Later Success
Mathematics builds like a staircase. If the lower steps aren’t sturdy, students struggle to climb.
Weak multiplication fact recall hinders students in many topics moving forward:
Fractions: finding least common denominators and simplifying fractions depend on fluent multiplication and division recall.
Algebra: factoring trinomials, expanding binomials, and balancing equations all rely on multiplication fact recall. Like the example mentioned above, students factoring 48 need to quickly know that all of their options are 4x12, 6x8, 3x16, 2x24, and 1x48.
Problem solving: estimating, checking reasonableness, and spotting errors are much harder when you don’t have access to the numbers in long term memory.
In short, multiplication facts are not the destination, they’re the bridge. Without them, higher level math becomes an uphill battle.
But Isn’t Rote Memorization Bad?
You may have heard that rote memorization is bad for learning. That is only true if “rote” means memorizing without meaning or understanding. When we talk about knowing math facts, we are talking about memorizing the facts after the students have gained understanding of what the operation is, and how it works. Once the student has that understanding, they are ready to get those facts stored in their long-term memory through consistent, repeated practice. This isn’t meaningless repetition, it is strengthening of the neural pathways and paving the way for mathematical fluency. It is similar to athletes who create muscle memory after lots of repeated practice with a physical skill.
Bringing it all together
Knowing math facts doesn’t hinder understanding, it enhances it. What used to bog the student down now lets them connect to math concepts confidently, and reason effectively. When it comes down to it, helping students memorize math facts isn’t about drilling them with mindless practice, it’s about giving them access to a powerful tool. A deep well of information they can pull from at a moment’s notice. When the facts are memorized and stored in that long-term memory, students gain the capacity to do robust, complex, mathematical problem-solving.
Citations and resources for further exploration:
Baker, A. T., & Cuevas, G. (2018). The importance of automaticity development in mathematics. Georgia Educational Researcher, 14(2). Retrieved from https://files.eric.ed.gov/fulltext/EJ1194585.pdf
Ding, Y., Li, H., Liu, M., & Zhang, Q. (2019). Effects of working memory, strategy use, and single-step mental addition skills on multi-step mental addition. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2019.00148
An introduction to cognitive load theory - THE EDUCATION HUB
Written by Janae Castro