The proper way is to take points off for not showing work, but still give the opportunity to pass. The point of showing your work in math is not to prove you didn't cheat, but to prove you have command of the algorithms required to solve equations AT EVERY STEP.

Now I agree her methods were excessive, but who's REALLY in the wrong here? Her for overreacting? Or you for refusing to show your mastery of the subject?

Let's think about it this way: If you're applying at my company for a job, and you say you have typing skills, the first thing I'm gonna do is assess your skills with a typing test. You refuse the assessment, and I refuse to hire you because I can't verify your skill at typing. You just lost out on a job opportunity because you didn't want to show your work. I had a friend who was a game dev and couldn't land interviews because she didn't know the vernacular of what she did for a living, and so couldn't pass assessments asking her to think about problem solving without the actual problem in front of her; she said she 'couldn't do it', but I believe it is a skill that can be learned because I'M THE EXACT SAME WAY. Once I learned to think conceptually I became WAY better at solving problems.

See where I'm headed with this? It's a lesson to children to show work, and it translates DIRECTLY into the adult world. If we were teaching our children this important but critical lesson, it'd make WAY more sense.