In the last few years I have invested _a lot_ of time in pure, rote memorization. Over this period, I’ve changed my opinion 180 degrees from how I thought about memorization when I was in high school. Back then, I thought that any topic that was “pure memorization” wasn’t worth learning, and now I believe that memorization is a necessary condition for many types of learning, and we should re-orient the way we structure education to shift the emphasis to memorization.
First, some justification: memorization is required for fluency. It may be fluency in a language, for which you will need to memorize many thousands of vocabulary words. It may be fluency in mathematics, for which you will need to memorize many identities and relationships. In order to be fluent in a software program like Excel you’ll need to memorize many different formulas and how they work. If you want to be fluent in Python or R, you’ll need to do the same.
But what is fluency and why does it matter? In a language, it’s obvious — most people have a clear understanding of what it means to be fluent in a language and why that’s important for mastery. In mathematics, maybe less so.
When I was taking math in middle- and high-school, I remember absolutely refusing to memorize the identities and formulas we were supposed to. I’d, surely obnoxiously, ask the teachers why it was important to memorize these formulas when it was always possible to just go look them up? I really firmly believed that if I understood the concept behind the formula or the identity, then I didn’t need to memorize it. This is flat out wrong.
We can make a point clear with a simple example: the times tables — you probably have memorized that 6 x 7 = 42 (or at the very least you can get there very quickly via 36 + 6 or some other rapid shorthand that combines other smaller memorized quantities). Knowing this value cold, via pure rote memorization, is much more useful than simply understanding the concepts that underly the identity — simply knowing how multiplication relates to addition , and that 6 x 7 = 6 + 6 + 6 + 6 + 6 + 6 +6 = 7 + 7 +7 +7 + 7 +7 just doesn’t actually help you that much when you need to solve more abstracted problems.
If you were working on a complex math problem and every time you saw a multiplication symbol you had to go back to your addition rules to work out the value, this would slow you down considerably — you’d probably lose your train of thought on whatever larger procedure you were trying to work out, and you’d end up way too mired in the details — this betrays a lack of fluency. By memorizing these identities, your brain does not get “distracted” by working out the computations and you are able to focus more on the higher-level, more abstracted quantities.
And this is why memorization is so important! It allows you to gain fluency, which allows your brain to focus on other higher-level more complex problems. In mathematics, if you don’t have important identities memorized (like 6×7=42 or that sin^2 + cos^2 = 1 or whatever) then when you encounter these relationships in the wild, you will end up losing the thread of whatever problem you’re actually trying to solve while you work out the details of these values from first-principles.
Mastery of a subject can only be acquired through great fluency — you have to allow your brain to work with higher-order abstract concepts and not get bogged down in the details, and that means being able to use higher-level abstractions (which have been memorized) in order to solve much more complex problems. If you never do the memorization (i.e., you don’t have the higher-level abstractions to work with) then it will be much more challenging to solve these complex problems and at some point you won’t be able to solve them at all.
When I’m encountering a new topic that I want to gain mastery of, I actually invest in memorization even before I invest in understanding — knowing the identities and being able to use them is more important than understanding where they come from or why they work the way they do. I know that I can always come back to learn about the why, but I’ve found that going to memorization first tends to help me gain a better working knowledge of whatever topic I’m interested in which in turn helps me understand the system as a whole.