Making the Case for Math Fact Memorization
A guest post by Ben Harrison, developer of Big Brainz (now Imagine Math Facts)
Imagine Learning occasionally publishes guest posts about K—12 education topics. Opinions expressed herein are those of the individual author(s) and may not necessarily reflect the official opinion of Imagine Learning.
Every once in a while I encounter an educator who is opposed to memorizing math facts.
Just today I saw anl article that exclaimed "memorization can inhibit fluency" and "memorization...can be damaging."
Of course, educators are doing a wonderful job of championing number sense, comprehension, and problem-solving, but by attacking the vital skill of automaticity, they unwittingly undermine the very processes they intend to champion.
Math fact memorization done well
Before I go any further, let me jump to the punchline, because I know that if you're one of these educators, you're already getting ready to give me your very passionate point of view.
If, as an educator, you have a negative view of memorization, I would suggest that it's because you haven't seen it done well.
[It can also be that you're mostly opposed to memorized process instruction, and in your enthusiasm you lump all memorization into the mix. If so, please read on.]
When done brilliantly, core fact memorization is wildly beneficial. How? To find out, run a simple experiment with a tried and true math-fact fluency program, Imagine Math Facts.
Be sure you allow kids to go all the way through the program. Then, measure the impact on number sense over the next year. The comprehension and application of those kids will skyrocket.
How can this be?
The answer is, the program will permanently accelerate comprehension and problem-solving development by freeing up students' working memory. It will also improve number sense, reduce students' pressure, and catapult their confidence.
Kids love the experience, and you'll witness a product that actually delivers automaticity.
Oh—and kids gain that automaticity in much less time than traditional methods.
Making the case for math fact memorization
As a software developer who has spoken to teachers all over the nation, I'm familiar with most of the typical concerns math teachers face.
First, I will build a case for math-fact memorization; then, I'll address some of teachers' concerns and offer my responses to each.
Learning standards alignment
NCTM, TEKS, Common Core, and The National Mathematics Advisory Panel all agree that "curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills."
The same panel also reports that computational fluency means "automatic (i.e., quick and effortless) recall of facts." In other words—memorization!
Finally, the advisory panel views arguing over math processes as "misguided" because "(such mathematical) capabilities are mutually supportive, each facilitating learning of the others."
A tool for problem solving and comprehension
To recap so far: students need number sense, comprehension, and application.
Further, a child who enters fourth grade already automatized in core math facts has a huge advantage over students who may only know some core facts. Such a confident student can make sense of numbers and apply them in subsequent math tasks.
At Imagine Learning, our research confirms that memorization accelerates comprehension and problem-solving.
Specifically, student automaticity catapults year-end math scores--not hard to do if students really know basic facts before assessment time.
After all, if you're going to chop down trees all day, you first need a few minutes to sharpen the ax.
Pressure: the enemy to student confidence
I heard one educator lament that the pressure students feel often impedes their working memory, such that students freeze just when they need to remember something.
This concern, while well-intentioned--misses the crux of the issue: students who are automatic in math facts don't need to use working memory. For them, math facts will come effortlessly and subconsciously, even under duress.
When core facts become trusted friends rather than distant memories, their constant presence helps diminish stress and build confidence in math generally.
Rote like a Robot
I've heard some educators express concern that rote memorization creates a 'robot' effect, therefore impeding number sense. Not true.
Phrases like "robots" and "drill and kill" sound frightening, but they imply a false principle.
Mastering core skills does not in any way inhibit or undermine higher-order thinking. Quite the opposite; such mastery liberates more advanced thinking skills.
When kids don't have to devote all their concentration to basic math facts, they can focus instead on conceptual understanding and problem-solving.
At Imagine Learning, we observed students to see if they can master multiplication before learning comprehension. Unsurprisingly, kids do significantly better when they comprehend what they've been taught.
Common Core Issues
I've heard passionate educators state that Common Core raises the priority of comprehension and application while lowering the emphasis on memorization. Sorry, but—wrong again.
Common Core significantly raises the priority for memorization, not only recommending that students memorize key facts early on, but also specifying that students should then recall those facts "from memory."
And of course, CCSS also mentions the importance of comprehension and application.
Educators with a wonderful and valuable passion for number sense often express that the best way to develop automaticity is simply to use the facts regularly, combined with solid comprehension.
I really like the sound of that, and I wish it were true. But it's not. Regular math-fact use doesn't necessarily mean students have gained full automaticity.
In our experience working with thousands and thousands of students, the majority of them didn't develop automaticity of core facts simply through continued usage and exposure.
TRUE, some students will. And all students will master some facts. But at some point, most students really have to buckle down to become automatic with single-digit facts, minimum.
Programs like Imagine Math Facts are game changers because they actually guarantee automaticity in less time than teachers would normally take on methods just described.
That may be a shocking claim, but it's still true. I've seen it time and time again.
Those well-versed in CCSS and state standards may be tempted to downplay the automaticity element of math learning.
Instead, be true to the research behind such standards: "by the end of grade 3, know from memory all products of two one-digit numbers."
Don't be tempted to undermine or change this requirement. Just because it's a concise statement doesn't mean it's not important.
Remember the National Mathematics Advisory Panel recommendation I mentioned earlier?
Their plea for algebra readiness depends on whole-number fluency, the automatic and effortless recall of core facts. Without that fluency, kids won't be ready to move on to tougher math challenges.
If you're still a skeptic, don't worry--it's a sign that you care about what you teach your students.
Just remember, I wouldn't feel so passionate if I hadn't watched so many real students (including my own daughter) become fully fluent in their core math facts through our math-fluency solution.
If you're interested in knowing what I know, take a look at Imagine Math Facts. Then see if your views change.
About the Author
Ben Harrison committed himself to unlocking the massive educational potential of high-end gaming technology when his daughter started to struggle with math. In 2004, he founded Big Brainz, a company whose products dramatically impact children's core math fluency in over 200 countries. Prior to Big Brainz, Ben founded Argonaut CG films, where he developed content for Sony's PlayStation division.
In 2016, Ben sold Big Brainz to Imagine Learning in order to reach even more children and dramatically expand the company's high-end math development. Big Brainz is now called Imagine Math Facts.