Does the use of formula collections facilitate the study of math?

Question

This maybe a silly question but I have always wondered what is the best approach to understand math. I always tried to understand concepts and limited my formula collections to things like formulas which are hard to remember or some "tricks" you need to know in order to solve a problem. However I have encountered several students who rely on vast collections of handwritten formula collections which include everything from exercises to formulas, to graphs. I'm not studying math but a related topic (computer science). So does extensive use of formula collections facilitate or hinder understanding of math?

Answer 1

I always tried to take your approach, and am baffled by people who write down all possible formulas.

The first time I noticed this was in high school physics, when dealing with "fall curves".

I just had 1 formula, perhaps 2 (horizontal and vertical position) and was able to work out anything I needed from that. Other people had entire lists of formulas for range, velocity, time until the projectile hits the ground, ... for all settings going from "release object from a height, from stationary" to "shoot projectile at angle $\alpha$ and so on.

I would spend a bit more time during the test to reconstruct a formula, but I was less likely to get confused.

The same happened when dealing with combinatorics. There's a lot of formulas you can try to memorize, but when you need them, how do you know you're using the correct one? I much prefer reconstructing the appropriate formula.

Memorization is dangerous. If you misremember, how would you ever find out? If you try to reconstruct, you won't have this problem.