Comment by Aurornis
3 days ago
My controversial education hot take: Pointless rote memorization is bad and frustrating, but early education could use more directed memorization.
As you discovered: A properly structured memorization of carefully selected real world material forces you to come up with tricks and techniques to remember things. With structured information (proofs in your case) you start learning that the most efficient way to memorize is to understand, which then reduces the memorization problem into one of categorizing the proof and understanding the logical steps to get from one step to another. In doing so, you are forced to learn and understand the material.
Another controversial take (for HN, anyway) is that this is what happens when programmers study LeetCode. There’s a meme that the way to interview prep is to “memorize LeetCode”. You can tell who hasn’t done much LeetCode interviewing if they think memorizing a lot of problems is a viable way to pass interviews. People who attempt this discover that there are far too many questions to memorize and the best jobs have already written their own questions that aren’t out of LeetCode. Even if you do get a direct LeetCode problem in an interview, a good interview will expect you to explain your logic, describe how you arrived at the solution, and might introduce a change if they suspect you’re regurgitating memorized answers.
Instead, the strategy that actually works is to learn the categories of LeetCode style questions, understand the much smaller number of algorithms, and learn how to apply them to new problems. It’s far easier to memorize the dozen or so patterns used in LeetCode problems (binary search, two pointers, greedy, backtracking, and so on) and then learn how to apply those. By practicing you’re not memorizing the specific problems, you’re teaching yourself how to apply algorithms.
Side note: I’m not advocating for or against LeetCode, I’m trying to explain a viable strategy for today’s interview format.
Exactly. I agree with the leetcode part. A lot of problems in the world are composite of simpler smaller problems. Leetcode should teach you the basic patterns and how to combine them to solve real world problems. How will you ever solve a real world problem without knowing a few algorithms beforehand. For example, my brother was talking about how a Roomba would map a room. He was imagining 0 to represent free space and 1 as inaccessible points. This quickly reminded me of Number of Islands problem from leetcode. Yeah, there might be a lot of changes required to that problem but one could simple represent it as two problems.
1. Represent different objects in the room as some form of machine understandable form in a matrix 2. Find the number of Islands or find the Islands themselves.
This is the approach algomonster use. They give you a way to categorise the problem and what pattern is likely to solve it:
https://algo.monster/flowchart
Memorization of, like, multiplication tables gives us a poor view of the more interesting type of memorization. Remembering types of problems we’ve seen. Remembering landmarks and paths, vs just remembering what’s in every cell of a big grid.
I still don’t like leetcode, though.
> Memorization of, like, multiplication tables gives us a poor view of the more interesting type of memorization.
Memorizing multiplication tables is the first place many children encounter this strategy: The teacher shows you that you could try to memorize all of the combinations, or you could start learning some of the patterns and techniques. When multiplying by 5 the answer will end in 0 or 5. When multiplying by 2 the answer will be an even number, and so on.
I think there may have been a miscommunication somewhere on the chain of Mathematicians-Teachers-Students if that was the plan, when I was in elementary school.
Anecdotally (I only worked with math students as a tutor for a couple years), that math requires a lot of the boring type of memorization seems to be a really widespread misunderstanding.