Every once in a while I encounter a savvy educator who is opposed to memorizing math facts–or at least they appear to be. Just today I saw a fearful article that exclaimed “Memorization Can Inhibit Fluency” and “Memorization . . . can be damaging.” Such educators are doing a wonderful job of championing critical math skills such as number sense, comprehension, and problem-solving, but by attacking the vital skill of automaticity, they’re unwittingly undermining the very processes they intend to champion.
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. So . . . if as an educator you have a negativity towards 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 in all memorization. If so, please read on.]
When done brilliantly, core fact memorization is wildly beneficial. So my call to action is this–run a simple experiment with Big Brainz. Run some kids through our program. All the way through our program. Then measure the impact on number sense over the next year. I can guarantee the comprehension and application of those kids will skyrocket because I see it happen every single day with every student who runs through our program.
It permanently accelerates comprehension and problem-solving development by freeing up working memory. It improves number sense! It reduces pressure and catapults confidence. The kids love it. Oh, and it actually delivers automaticity–every time.
Again, until you put us to the test it’s likely you will be defensive and won’t really see anything I’m saying. So seriously, please put us to the test.
Now getting back to how negativity towards memorization undermines overall math success. Imagine a basketball coach telling his team, “To win games you need great defense and shooting–so stop learning how to dribble and pass.” That would make no sense. Great ball-handling only helps everything else you want to do in basketball, and automaticity only helps comprehension and problem-solving.
Sidenote: Just like in math, a basketball player absolutely needs to progress as quickly as possible from static dribbling drills to dynamic dribbling drills. And even static dribbling drills should be motivational and productive. But showering players with negativity towards drilling in general is going to undermine the overall skill, handicapping all their future success because they’ll constantly have to be thinking and looking at the ball, rather than their teammates or the hoop.
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,” further clarifying that computational fluency means “automatic (i.e., quick and effortless) recall of facts.” That’s memorization.
Furthermore, that same Final Report specifies that arguing about the relative merits of these different facets of math is “misguided” because “these capabilities are mutually supportive, each facilitating learning of the others.”
Memorization Accelerates Comprehension and Problem-Solving
Students need number sense, comprehension, and application, and a child who enters fourth grade already automatic with core math facts is going to be able to develop these math concepts FASTER than a student who doesn’t. They will be more confident, but they will also have more available working memory.
Our own research confirms that memorization accelerates comprehension and problem-solving. Specifically, giving student populations the gift of automaticity catapults their year-end math scores. Fluency accelerates overall math learning because once they’re fluent, students permanently have more available working memory with which to learn new concepts and applications. If you’re going to chop down trees all day, please take a few minutes to sharpen the ax.
I heard one educator lament that pressure can impede working memory so when a student most needs to recall a fact, they can’t and then they’re stuck. This misses the point. If the fact had been actually memorized, it wouldn’t have needed working memory. It would be effortless and automatic, even under duress. When core facts become trusted friends rather than distant memories, they are always available to help diminish stress AND free up precious working memory.
Of course they still need comprehension and application skills as well. They need all three.
I’ve heard some educators express concern that rote memorization is creating robots and therefore impeding the development of number sense. Not true. Phrases like “robots” and “drill and kill” have a nice, scary ring to them, but they imply a false principle. Mastering core skills does not in any way inhibit or undermine higher-order thinking. Quite the opposite, it liberates it. Freeing up working memory absolutely helps students be more successful at conceptual understanding and problem-solving. We’ve run tests where students master multiplication before learning ANY comprehension, and they still do significantly better when they are taught the comprehension.
I’ve heard some educators complain that the pressure of memorization can give students a bad experience. So stop doing it badly and start doing it well! It’s not memorization that creates bad experiences any more than math instruction in general creates bad experiences. It’s bad instruction and bad memorization that create bad experiences. And be very aware that the frustration kids feel when they have to stop and think about every single basic calculation they encounter is always significant. You don’t remove that frustration simply by telling them it’s OK.
Common Core Emphasis
I’ve heard passionate educators exclaim that Common Core raises the priority of comprehension and application while lowering the emphasis on memorization. Absolutely false. Common Core significantly raised the priority of memorization, bumping it an entire grade earlier AND increasing the specificity of recalling facts “from memory.” Now, they ALSO raised and clarified the priority of comprehension and application . . . because all three are necessary and mutually beneficial.
Once again, successful math students “must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills.” “Debates regarding the relative importance of these aspects of mathematical knowledge are misguided” because “these capabilities are mutually supportive, each facilitating learning of the others.” [Final Report, 2008 emphasis added]
Educators with a wonderful and valuable passion for number sense often express that the best way to develop automaticity is to simply use the facts regularly, combined with solid comprehension. I really like the sound of that, and I really wish it were true. But it’s not. It doesn’t work.
We’ve worked with millions of students, and the majority of them will never develop automaticity with their core facts simply through continued usage and exposure. Some students will. And all students will master some. But most students at some point will need to buckle down and focus to become automatic with just their single digit facts.
However, they CAN acquire this precious skill in a matter of hours–at least with Big Brainz they can. EVERY student on earth should be given the precious few hours needed to acquire this precious skill and permanently expand their mathematical working memory.
Wrapping up, let me also point out that it CAN be perfectly accurate to rant and rave against memorization IF you get just a bit more specific. Rant and rave against ineffective memorization–techniques that generate a negative experience and/or don’t actually generate fluency (which is most of them). Blast these traditional methods out of the water.
You’re also welcome to rail against step-by-step process instruction that less effective teachers often fall into.
Don’t Change or Undermine Common Core or TEKS Requirement
But at the same time be very careful not to undermine the critical skill of automaticity. Be true to all the research behind the very specific common core requirement: “by the end of Grade 3, know from memory all products of two one-digit numbers.” Don’t undermine or change this requirement. And don’t think it’s importance is small just because it can be written concisely. The best scientific research in the world found that the #1 “Critical Foundation for Algebra” is whole-number fluency, the automatic and effortless recall of core facts, because it frees up working memory to focus on higher-order concepts and application. Give this precious gift to every single student.
Sharpen the Saw
Your students are going to be chopping away at comprehension and problem-solving 180 hours a year, every year. Give them the few hours needed (and a sufficiently powerful fluency program) to permanently sharpen their saw.