Even relying on intuition, however, I need to know something. I needed to know the basic formulas. You do need to be able to remember things to be able to apply them. To give a simplistic example, memorizing your phone number without knowing how to use a phone is fairly useless. However, knowing how to use a phone without knowing any phone numbers is equally useless!

I promise I won’t let my students get away with rote memorization. They will need to remember things, but they will need to know how to apply their knowledge.

Where I studied mathematics the most, at UofT, you didn’t have much in terms of “state the XYZ theorem”. I can’t remember much, yes I’m that old, but I’m pretty sure most questions on exams were the problem-solving type. Beside, knowing the theorems well was a non-issue if you did the (very hard) homeworks: there is no way you didn’t internalized most of the important theorems if you sweated for hours over how you are supposed to use them to solve a given problem. Over time, you came to understand that knowing the statement of theorem was actually knowing very little. You had to really gain an intuition for the theorem… and once you have the intuition, the rest is easy.

In fact, a training in math., CS, Physics or Chemistry should be pretty much identical. Assuming you attend a good school. A school that has you memorize theorems and formulas to pass courses is a bad one.