It's a really stressful situation. I can achieve but not retain expertise in maths problems.
6 months back, I studied integration in Calculus at college. I learnt it all by myself as I was didn't attended college for days on end. I learnt it with great level of comprehension. In the beginning I solved all the exercises one by one, dealing with all kinds of varied techniques required by the various questions.
Over 6 months, I then progressed to the point that I could manage to do 85% of all the questions in a minute. Rarely did I take 1.5-2 minutes (on the really difficult ones). This mastery was achieved by reviewing and re-solving the exercises once a month for 5 months.
I used to do all this timed practice like a race-against-time using a 1-minute hourglass.
Now, there came a Gap of 3 months between my college ending and university starting. Now I can't do any of the questions of integration except the simplest ones and even they would take me well over a minute.
This proves the point that "practice" and "understanding" is not all to learning maths. There must be something else too that teachers and students are overlooking.
Now, unlike college, there will be 80 exercises instead of 8 at the university-level. What do I do, I cannot just practice maths-problems again and again and again every month & then fall & then go from prince to pauper after a couple of months gap in review (in terms of exam preparation).There are a lot of twisted techniques, a lot of rules and methods in solving problems just like a toolbox.
My question is this: Why does this happen to me & What can I do ?
Any help in this regard is highly appreciated. Moreover, I believe I have come to the right place as the people here can surely help with their knowledge of mathematics, learning , education and pedagogy.
A Note on Problem-Solving
"Understanding" means "knowing what specific techniques or some combinations of them have to be applied in a specific orderly manner to solve the integrals".
Mathematical problem-solving is akin to programming, what really matters is proper, orderly application of logic and procedural operations.
It's not so much about "conceptual enlightenment" & "intuition" & "deep-learning".
Since we are humans, we cannot store all these rules of if X, then Y, else Z. Neither can we analyse all multiple possible approaches (brute-force method) without expending considerable time and effort. That, my friends, is The Problem.