Comment by HankStallone 3 days ago
Probably. I hated memorization when I was a student too, because it was boring. But as soon as I did some teaching, my attitude changed to, "Just memorize it, it'll make your life so much easier." It's rough watching kids try to multiply when they don't have their times tables memorized, or translate a language when they haven't memorized the vocabulary words in the lesson so they have to look up each one.
I think the problem is that in spots where the concepts build on one another, you need to memorize the lower level concepts or else it'll be too hard to make progress on the higher level concepts.
If you're trying to expand polynomials and you constantly have to re-derive multiplication from first principles, you're never going to make any progress on expanding polynomials.
I never memorized multiplication tables and was always one of those "good in math" kids. An attempt to memorize that stuff ended with me confusing results and being unable to guess when I did something wrong. Knowing "tricks" and understanding how multiplication works makes life easier.
> "Just memorize it, it'll make your life so much easier."
That is because you evaluate cost of memorization to 0, because someone else is paying it. And you evaluate the cost of making mistakes due to constantly forgetting and being unable to correct to 0, because simply the kid gets blamed for not having perfect memory.
> or translate a language when they haven't memorized the vocabulary words in the lesson so they have to look up each one
Teaching language by having people translate a lot is an outdated pedagogy - it simply did not produced people capable to understand and produce the language. If the kids are translating sentences word by word, there was something going on wrongly before.
> It's rough watching kids try to multiply when they don't have their times tables memorized
As someone who never learned my multiplication tables – it’s fine. I have a few cached lookups and my brain is fast at factoring.
8*6? Oh that’s just 4*2*6= 4*12 = 48. Easy :)
It's a lot easier to memorize things when it's your job i find.
maybe they pay hits a reward centre in my brain.
There's things that you need to know (2*2 = 4) and there are things that you need to understand (multiplication rules). Both can happen with practice, but they're not that related.
Memorization is more like a shortcut. You don't need to go through the problem solving process to know the result. But with understanding, you master the heuristic factors needed to know when to take the shortcut and when to go through the problem solving route.
The Dreyfus Skill Model [0] is a good explanation. Novice typically have to memorize, then as they master the subject, their decision making becomes more heuristic based.
LLMs don't do well with heuristics, and by the times you've nailed down all the problems data, you could have been done. What they excels at is memorization, but all the formulaic stuff have been extracted into frameworks and libraries for the most popular languages.
[0]: https://en.wikipedia.org/wiki/Dreyfus_model_of_skill_acquisi...