In Praise of Memorization

From my personal experience, I find that schools often fail to prepare their top students because the exercises meant to teach you how to work hard for real this time are still passable with a last-minute cram session by the fastest students. By the time the assignments are actually too long to be crammed, it's often well past the safety of K–12 education.

what were the facts?

It substantially comes down to the amount of language practice those students have had over the years, starting from listening to large amounts of varied material (from conversations/books read aloud) as young children, and then from reading a wide variety of material. The kids who read, and read, and read (especially those who have someone discuss with them the meaning and structure of what they are reading, hearing, or experiencing) learn these skills to great fluency. The kids who don’t, don’t.

Some kids live in households where they listen to thousands of books by age 5 or 6, including not only stories of increasing complexity but also natural history, biography, science, technology, ..., and other kids never get that kind of attention or experience, and end up far behind in those skills.

The ability to “memorize” (i.e. learn) rests on a vast subconscious structure built up by fitting together language, starting from little bits and pieces of vocabulary, and building to subtle understandings of complicated ideas.

The way to train it is by giving the little neural net of the brain as much meaningful input as possible about the relevant parts of the world, and letting the brain fit them together in a web of connections. Not by trying to practice/drill rote trivia (say, reciting state capitals or the multiplication table).

If we're slinging anecdata around I may as well offer mine up as a long-underperforming student that also somehow took night classes at college for software when I was 11 years old.

The teachers may force the kids to memorize, but that doesn't mean it does them any good in the long run. I met tons of kids that memorized mathematics from 8 to 13 years of age in Canada. I struggled badly with fractions when I was 8 years old. The fact that there wasn't one canonical representation broke my little brain. Before in mathematics you could always "keep going until you were done" and the number looked like 1.75 and that was it. Now you could stop at 14/8 or 1 6/8 or 1 3/4 or 7/4 or even 1.75 again! And sometimes they made me round it all the way up to 175/100 instead! Madness!

But unlike the kids in my class that seemingly did better than me in grade 4 while I was wasting my time trying to make this slippery math reliable I naturally ended up memorizing little gems like 7/2 being 3 and 1/2 because I kept at doing the actual work over and over again until my brain remembered it for its own sake. I'm not fighting my brain and trying to squash stuff that I don't care about into it, I'm letting it make the tradeoff as to what to memorize and what to keep as I keep doing the work over and over again.

By grade 6 (age 11, same time I started college) I was starting to wonder why we hadn't learned anything in a couple years in math. When you understand the building blocks or "first principles" so well, what looks to be a new lesson (the area of triangles!) barely registers because it's such a basic application of what you've already learned before. By grade 8 (age 13) I was actually complaining that we'd barely made any progress in 5 years of education. I believe my exact words were "we've basically learned nothing other than maybe the Pythagorean theorem" and I still mostly believe that.

When it comes to things like science, computer science, visual (ie, non-statistical) mathematics, and probably economics, physics, optics, and some areas of statistical mathematics we could probably move 3x as fast if we would just really hammer home the first principles until we were absolutely sure they were sticking.

We don't let babies fill containers with soup because they haven't demonstrated that they understand what a hole is and does. I feel like too often we force children to remember that 3*7 is 21 without really making sure they understand multiplication. The key to getting a child to really learn something isn't by jumping to intentional memorization. Not with mathematics, anyway. The key is to get them to reason about it and to practice over and over again. Not to memorize, but to understand and though knowledge and understanding are different things, understanding always comes with some knowledge though the reverse is not necessarily the case.

Just a heads up for the author, if they are reading this thread at some point:

> Russia is a month into an invitation into Ukraine.

Probably should read 'invasion'.