How to know if you really are learning math?

[Tyrion101]

I'm doing extremely well in my math class but I worry that all I'm doing is learning how to do problem a, and not concept behind problem a. What are some signs that you are doing more than just memorizing a set of problems? I wanted to find out how many times I'd need to do something to get a certain result, and used an equation from the class from memory to find out what I needed. I got it right without having to do it again. Is that a sign? Are there others I can look for to make sure I know I really am learning?

 

[DiracPool]

What are some signs that you are doing more than just memorizing a set of problems?

The "sign" is whether or not YOU think you understand the maths and how they apply to solving the problem conceptually. Or, conversely, if YOU feel you have absolutely no clue as to why applying some equation to some problem works to get you the right answer. So, here's what you do. If you don't feel like you fully understand some problem and are just applying a solution from memory, go to your instructor and ask them to explain why the solution works. If he or she doesn't give you any more insight or "intuition" than you already had, then you probably understand the problem as well as anyone else. Just to be safe, though, run it by one of the wizards here on PF just to be sure