Okay, beating on a student isn’t training, it’s sadism. You see this out of popular media a lot. The idea is, that it somehow makes your characters more badass when they come out the other side. The reality is, you don’t learn anything except what getting hurt feels like.
You will see some physically demanding calisthenics in martial arts training, but that’s more about building physical fitness and conditioning. It’s not about beating on the student. That said, a lot of disciplines will also use it to push the student to learn to expand their limits, and try to teach them philosophical clarity through adversity. At the risk of offending some martial artists who follow this blog, it’s not critical for teaching self defense. Also, I’ll stress, I’m talking about exercise. Strenuous, exhausting, exercise. Not beating on the student.
Good training involves showing the student what to do, explaining how to do it, walking them through the techniques. Correcting their form. Practicing. Correcting their form. Practicing. Repeating until they can do it right. Move to a new technique. Repeat. Teaching them to connect what they just learned to a previous technique. Correcting the transition. Practicing. Repeat. Repeat. Repeat.
You train techniques starting with the foundation of the style, and then branching out into more advanced techniques. Usually this means starting with simple strikes, before moving on to holds, ground fighting, kicks, throws, advanced strikes, and weapon forms. Though the exact order varies based on the master’s preferences.
Depending on the master, training may include a detailed explanation for how techniques function (not how to perform them, but when and why they are used). Complex discussions on combat psychology. Or it may simply involve cryptic comments designed to provoke the student into philosophical enlightenment. Generally speaking, practical martial artists are far more prone to talking about why, but this really is about who the master is, and what their perceptions of “proper training” are.
Second, martial arts are built around the idea that you’re going to be dealing with opponents who are physically more powerful than you are. You learn to fight so that you don’t need a raw strength advantage.
I don’t know what your character would emphasize in training. Self defense is about situational awareness and creating avenues of escape; not being the better fighter. That said, there there are strands of self defense that focus on using the minimum possible force, while others advocate using lethal force to protect your life. Your character could easily end up in either camp, based on their background and outlook.