[Retra]

You're missing the point. Many maths students learn to dislike math because they cannot remember the rules, or they find them frustrating to use. They are often trying to appease the teacher by mimicking the process.

Meanwhile, the better students don't bother memorizing the rules, they just focus on solving the problem. Once they see how the problem is solved, those rules either come naturally, or are supplanted by some other process that also works.

This is not about parlor tricks, but about creative thinking. How do you determine whether your 'trick' works or not? How do you know if the problem is solved? Most students believe a problem is solved when they get the 'right answer' -- which often includes "doing what they were told." This is NOT how you identify a solution to a problem. The students who are left behind are the ones who never figure this out.