How we think about school can limit what we get out of it.
Many students approach school like a bunch of external requirements they are being forced to meet.
This approach encourages looking for a path of minimal work.
Then long term retention of knowledge and skill is unimportant.
Consider the implications of education being preparation for life and work.
Because we don't know what we will need, we don't know what we can safely skip.
Every class becomes an opportunity to prepare.
Graduation requirements change from targets to aim for, to minimums to exceed.
More importantly, since school can never cover all necessary topics,
formal education is, at best, a foundation for ongoing learning.
This means that the student should aim at being able to learn (with minimal guidance).
Ask the right questions.
Don't ask, "What is the answer to problem #5?"
Don't ask, "What information or technique do I need to answer problem #5?"
Ask, "How could I have figured out the information or technique needed to answer problem #5?"
Then you will learn how to learn.
Be open to learning in new ways.
Don't let your preferences become limitations.
Some students prefer verbal explanations, some prefer visual examples.
The best preperation for life and work includes becoming able to learn in multiple ways.
Intuition vs. Definition
Mathematics defines its terms precisely.
Sometimes, a mathematical definition is close to the common English usage of the same words.
So, intuition may get the student through limits, slopes, and continuity.
In other cases, the mathematical definition can seem quite foreign.
A student would be unlikely to correctly intuit the meaning of "open" and "closed" sets.
At some point, it will be necessary to learn the precise definitions.
Applying Theorems vs. Proving Theorems
The focus of most classes up to the 2nd year of college is applying the results theorems.
That is, the focus is on solving problems.
When a student reaches Real Analysis or Abstract Algebra, the emphasis shifts to being able to prove the theorems.
Reading a theorom to apply its result can be different than reading the proof to understand the proof.
Experiment with different approaches to studying.
But evaluate each approach by its results.
Are you learning the material?
Is your stress level going down?
Will you retain the knowledge and techniques years into the future?