It's sad one needs to reinforce the teaching of concepts rather tricks.
Even worse is when you have all the proof based and concept oriented course and are tested on trickeries on exams.
Even worse is when you have all the proof based and concept oriented course and are tested on trickeries on exams.
Disclosure: I taught college freshman math for one semester, long ago. It was a course where I was supplied with a syllabus and exams, and the students could buy a packet of exams from previous years.
The tricks are what you remember from doing problems over and over, and recognizing patterns. There is also a higher level pattern that isn't mentioned in class, but is vital to solving problems: You learn to identify each problem with a particular chapter or section in the textbook, and then solve the problem by recalling the methods in that section. This is of course a grotesque distortion of what math is, but will get you through the lower level college math courses with good grades.
The other skill is being able to perform the manipulations quickly enough that you can try one or two before hitting on one that works.
Disclosure: I taught college freshman math for one semester.
It gave me a good "visual" grasp of the concepts and made most of my higher math classes much easier.
I do agree diff eq instruction sucks. I got an A in that class and didn't understand a thing. "This equation has this form; this is the canned solution."