[nocipher]

For me, algebra is easy, but writing out steps is very difficult, and sometimes I prefer to use a process other than the one taught in class. Should the goal of math education be to solve problems or to learn processes?

That is a false dichotomy. The goal of math education is to "learn processes" to "solve problems". You can't skip the processes and jump straight to solving. Before you can pick a proper algorithm, you have to already know a few -- that's the learning processes part in programming. This holds for any skill you choose to learn; before you can do something well, you have to be able to do it in the first place.