The most essential aspect of critical thinking is being honest with yourself.
Read Discourse on the Method of Rightly Conducting one’s Reason and Seeking
Truth in the Sciences, by Rene Descartes.
Write your math work out as if you were explaining it to someone else.
Establish patterns for writing out expansions, etc. For example, if you have
$(a+b)(c+d)$, always do it as
Even though you know you could just as well write
Try to preserve the order of expressions as much as possible. For example, when I produced the second example above, I copied and pasted and then edited. The original correct result was
But, in my opinion, that is bad form.
Of course, there may be good reasons for deviating from those rules from time to time. For one; the exercise of doing something the alternative way may be instructive. But having set patterns avoids a lot of mental clutter.
Read with a pencil and paper (or whiteboard, or computer, etc.), and write out the theorems and proofs in your own words and symbols. Be sure you can justify every step to yourself. But don't over do it. Sometimes it makes more sense to just read through material trying to get the gist of what is being presented. Then go back and try to get a fuller understanding.
Learn to use LyX. It's free, and it will help you post to math.stackexchange.com. https://www.lyx.org/
Consider getting a student version of Mathematica.
I dropped out of high school in the tenth grade, and was never very good at participating in academic environments. My advice comes from not doing things that way for a long time.
Edit to add:
Read the paragraph prior to the discussion of Decartes' contribution to the area of critical thinking. What I mean regarding being honest with yourself is that you should guard against believing in what Francis Bacon calls "idols".
A Brief History of the Idea of Critical Thinking
For example, if someone gives you sound advice on how to improve your problem solving techniques and improve your critical thinking, but it gets voted down. You are obligated to decide for yourself who is in error.
As an example of how I approach learning math, see my Mathematica notebook recording my study of C.H. Edwards, Jr.'s Advanced Calculus of Several Variables. They are a work in progress. My notation is non-standard. And the notes are terse and cryptic. (But I expect a seasoned mathematician could follow them.)
Notice also that I have noted where Edwards made an assertion for which I do not provide proof. That typically means I'm flagging that for later consideration. Also note that there are some errors in Edwards treatment which I discovered by attempting to rewrite his discussion in the way I understand it.