So I'm currently a calculus student, next semester I'll take calculus 2. I'm wondering if I should go to a book like the one by Spivak which is entirely different from the book used for my course, and learn or in a way re-learn it the way it's presented in that book?
Reason I ask this is, I know how to carry out the different steps for the calculus problems I've thus far been exposed and how to apply them to different problems but I don't really understand what I'm doing, if that's the appropriate way to word it.
Would a more proof based approach help me in this understanding? Will I always lack some aspect of understanding if I don't know how to prove these problems?
To quote one of the comments on this question, the question can also be put
"will studying calculus in a proof based manner help in understanding the techniques I've already learned"