Repetition Is Pushed In Math And Physics But There’s An Intuition You (ought To) Develop As Time Passes.

Repetition is pushed in math and physics but there’s an intuition you (ought to) develop as time passes. Physics is intuitive but it might be possible to do well in beginner level classes without having a strong conceptual or intuitive understanding of what systems you’re looking at (it might even be possible to go through undergrad without a strong intuitive understanding as stated by some physics grad students who didn’t have this until after their undergraduate years). As an engineering student I see my engineering peers move through introductory physics but when they try to explain things or solve a problem they haven’t seen before, they have no clue. This is because they trained themselves to do problems. They didn’t train themselves to think. They also rely on equations but don’t have any regard for the derivation. Memorizing equations can get you places but not very far, after a while.

I wish I could think like a physicist. I want to make the right assumptions. I want a grasp on the system without needing numbers. I want to make solid predictions on what will happen in a system even if I’m not familiar with it. I’m not equipped with it now but this is something I hope will be developed as time passes. It’s not a one day development, of course.

I notice mathematical intuition is also something that’s lacking in students because it’s not taught to be a priority. I’m not sure if this intuition can even be directly taught, I don’t think it can be.

I see what you mean when you say practice is encouraged in order to do better at problems and how this idea of developing an intuition, which will be your greatest asset in physics or mathematics, isn’t prioritized.

I think something that was underemphasized in my education was the framing of learning as a process that occurs over time.

I mean, to some extent and more so in certain subjects, you are just looking to accumulate some static information in your brain*. but I think most professors would say they are ideally looking to impart a more nebulous sort of skill in "how to think". like, if you are studying mathematics, you need to know the content, and be able to prove theorems, but you also want to be developing a sort of intuition for thinking mathematically.

[*I said this originally in the draft, but in fact even static information seems to be best acquired through spaced repetition!]

they will tell you to practice problems, of course. but it is framed as a way of getting better at doing the problems, not as a generalisable skill. not like in: you have to move the material through your brain repeatedly in different ways to get its value. not like in: you are trying to forge adaptations, not much differently to building muscle. often like: "it might take some time to understand this [because it is hard and you will struggle with it]" (read: if I'm clever enough I could totally pull it off quickly, skill issue), but not like: time is an actual ingredient in this recipe.