Here is what Richard Feynman advised CALTECH students regarding mathematics (section 1-3 of Feynman Lectures Physics):
So, this guy comes into my office and asks me to try to make everything straight that I taught him, and this is the best I can do. The problem is to try to explain the stuff that was being taught. So I start, now, with the review. I would tell this guy, “The first thing you must learn is the mathematics. And that involves, first, calculus. And in calculus, differentiation.”
Now, mathematics is a beautiful subject, and has its ins and outs, too, but we’re trying to figure out what the minimum amount we have to learn for physics purposes are. So the attitude that’s taken here is a “disrespectful” one towards the mathematics, for sheer efficiency only; I’m not trying to undo mathematics.
What we have to do is to learn to differentiate like we know how much is 3 and 5, or how much is 5 times 7, because that kind of work is involved so often that it’s good not to be confounded by it. When you write something down, you should be able to immediately differentiate it without even thinking about it, and without making any mistakes. You’ll find you need to do this operation all the time—not only in physics, but in all the sciences. Therefore differentiation is like the arithmetic you had to learn before you could learn algebra.
Incidentally, the same goes for algebra: there’s a lot of algebra. We are assuming that you can do algebra in your sleep, upside down, without making a mistake. We know it isn’t true, so you should also practice algebra: write yourself a lot of expressions, practice them, and don’t make any errors. Errors in algebra, differentiation, and integration are only nonsense; they’re things that just annoy the physics, and annoy your mind while you’re trying to analyze something. You should be able to do calculations as quickly as possible, and with a minimum of errors. That requires nothing but rote practice—that’s the only way to do it. It’s like making yourself a multiplication table, like you did in elementary school: they’d put a bunch of numbers on the board, and you’d go: “This times that, this times that,” and so on—Bing! Bing! Bing!
P.s. Having some rote skills makes it easier to work on other aspects of problems. That is not same as saying having no intuitions is helpful either. Especially for things you don't grind into muscle memory. But for others better to have almost iconic recall, like "bsq-4ac"; do you really want to be completing the square because you don't remember the quadratic as you go through all of upper math, chemical equilibrium problems, physics everywhere, or EE or control systems (characteristic equation of harmonic oscillator ODE).
P.s.s. I actually find that some ideas come to me AS I DRILL, about the substance of what I am working on.
P.s.s.s. When working a homework set (on a new concept), it can be useful to have some easier, drill type problems for the new equation. Then progress to harder problems with proofs or word problems or combining concepts. Because you have a little more feel for things than just reading the text would give you, before you dive into the nutcracker questions. This is actually a major failing of harder classes, graduate school etc. in that the easier running start problems are omitted. Than again these classes seem to have a very cavalier attitude towards actually training people.