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.