## What Rote Learning Is, And What It Isn’t

**Online learning pioneer Salman Khan, interviewed on Jonathan Wai’s blog, takes on the notion that Khan Academy is all about “rote” learning:**

“Sometimes I think people confuse rote learning with conceptual instruction. A good traditional conceptual instruction is what I got from my better professors at MIT. They would be at a chalkboard, and they would literally be explaining something and working through a problem, but it wasn’t rote. They were explaining the underlying theory and processes and intuition behind it. And some people just assume that if you have an equation on the board or you are working through mathematical symbols that it is somehow rote, which is not the case.

We do also have a lot of worked examples on the site, in fact probably six or seven hundred. And perhaps this is where people come up with the perception that these are just a bunch of step by step problems, but I personally think it’s valuable to see worked examples because this is how I liked to learn as a kid, but at the same time the worked examples are very seldom memorized. There are the rare instances where I have to give a formula without proving it but I say ‘I hate memorizing things and you should not have to memorize things, but every now and then it might be helpful.’

And we do have exercises that I wouldn’t call ‘rote’ but would call “deliberate practice.” The difference is rote means just memorizing the formulas. Deliberate practice is when we say ‘Look, we’re going to have you solve a bunch of equations. And solving these questions will help you get into the rhythm and logic.’ I personally believe that most of the time if you’ve worked yourself enough, your brain starts to draw connections. Sometimes the connections happen before the problem solving, sometimes the problem solving happens before the connections.

There are basic rote things that people do have to know, such as the multiplication tables and basic addition and subtraction. And even once you get into higher mathematics, you’re more likely to be able to engage at a more fluent level if you do have some key things that are in rapid access memory. But my main thing is to make sure that students really deeply understand the conceptual underpinnings.” (Read more here.)

**There’s a lot here, but let me sum up the takeaways:**

**1) Instruction that involves explaining and working through the conceptual structure of a problem is not rote.**

**2) Research shows that studying worked examples, along with solving similar problems yourself, is a very effective way to enhance learning.**

**3) Repeated practice at solving problems is essential to mastery.**

**4) Some math facts, like multiplication tables, must be memorized to automaticity in order to allow fluent problem-solving in more advanced problems.**

**Often the word “rote” gets thrown around inaccurately or gratuitously to describe a form of instruction that the speaker doesn’t like. Let’s save the word “rote” for when it’s really justified, and not use it as an all-purpose term of derogation.**

Worked examples are helpful but I wonder how people ever get to true understanding by simply doing things over and over? I learned a constructivist approach that has been very useful — hands on, letting people discover where possible the concepts and see for themselves with guided experiences how it works. This seems to me to be a far better way to learn than watching worked problems and then doing a million just like it.

That being said, I do think your videos can be helpful to some for sure. Also certainly practice is important once a person understands a concept.

What do you think about this?

It’s my understanding that constructivist approaches can take a long time to get students to the point where they understand and internalize the procedure, especially in math and statistics. Pragmatically, when one is under pressure to complete X material in Y time, so that the students can go on to the next semester having some mastery of the material, this can be a problem, especially if you have an unstable position and have a chair or superior who doesn’t believe in the benefits of constructivist pedagogy.

I’m not even sure if rote learning in its true form is always bad. If it weren’t for rote memorization, which can lead to automaticity and reduced cognitive load, I’d never have leaned a few hundred regular and irregular German verbs in the present, past and past perfect. What helped me retain them was continuing to drill. That’s also how I learned my multiplication tables. Granted, it didn’t make sense until later that 7 times 7 was 49 precisely because it was seven sevens, but as a third or fourth grader, I suspect the magic of that would have been lost on me anyway.

In all things moderation is good.

The issue isn’t whether rote learning is bad or good, but what it comprises. You can’t memorize a concept. You can’t drill a concept into anyone’s head. Math being a matter of thinking, you can drill facts and procedures all you want, but you won’t teach math that way: only facts and procedures.

As long as Americans continue to swallow the empty idea that mathematics is computation and nothing more, they will believe that rote learning is a great idea in mathematics education. And they will remain deeply suspicious of any approach that is focused on anything else. That is a tragedy for our children.

I struggle to understand my son’s first grade math homework which takes an overly conceptual approach. They are learning how to divide shapes into equal pieces and break large numbers down into groups and do tallies, but they are not learning their addition facts, which is so essential to doing well in math in the upper grades. It is hard to figure out what is being asked of the students much of the time. I wonder how second language learners and their parents are managing the assignments. I’ve heard repeatedly from parents, some of whom have graduate degrees in math that they can’t figure out what their kids’ homework is asking. That’s not right.

When I was teaching 4/5th grade, I noticed that the students who had recently emigrated from Taiwan were head and shoulders above their American peers. They breezed through their long division. For the American students who had not mastered their addition and subtraction and multiplication facts it was extremely difficult. We’re not helping students by pulling back on the rote memorization of basic math. We’re hobbling them.