So I discovered halfway through my first year university math term that my foundation of mathematics is very poor. I would memorize stuff rather than understand it and still get 95+ in high school so that's what I did. I quickly realized that doesn't work at all in university. It's embarrassing but I didn't really even know what a derivative really meant and I'm in University Math!
Anyways, I passed my math courses barely with 60-70, and did way better on the finals than I did on my midterms which is a sign that I'm heading in the right direction (I went back and looked at a whole bunch of khan academy high school math concepts) but it was hard to juggle doing that and keeping up with current stuff in class.
So now the term is over and I want to prepare for next term. My question is, should I go back and review basically all the high school stuff I memorized (and forgot), or should I just start studying the new material by reading the textbook ahead and actually understanding the concepts through practice this time?
(The 2 math classes I had this previous term was Calculus 1 and Algebra/Proofs, and my next 2 classes are Linear Algebra and Calculus 2)
Thanks!
As I'm sure is the situation with many other people, I've had friends who did well in math earlier on in school, but then got behind, mostly due to having a poor teacher. They usually never got back on track and continued having difficulty with math. More than most other topics, I believe, later math is built on understanding and using concepts learned earlier, which is an important reason why those friends weren't able to continue doing well in later years. If you don't understand those earlier topics, it will make it difficult to understand many later ones, especially those which directly use or expand on the earlier concepts. As such, instead of first trying to study ahead, I think it's best to first ensure you fully understand your high school math concepts. After that, if you have the time and interest, it would then be useful to examine the material for next year ahead of time.
Good luck in your future studies.