I started tutoring people this year, and its really really hard to not have it devolve into just doing their work for them. I don't really mind that much but I have no idea what to do about it.

The only thing I've figure out is that apparently its helpful to talk about proof methods rather than problems and to have a good grasp on set theoretical foundations. Oh, and also that its generally good to ask lots of questions, and check pretty often that what you're saying and how you figured it out is clear.

I don't know if there really is anything to explain about x^2 though. It's just the notation, there isn't really much to do but memorize it.

I've devoted a good portion of my life to teaching math and only recently have I started my career as a professional tutor. However, because I've been doing this for a very long time, I must say I haven't run into the same troubles OP has gone through.

It's very common for people to memorize mathematical rules rather than understand what they are and how they work. Eventually there comes a time where this practice comes back to bite them in the rear, like when they mix up their mental rules of adding coefficients versus adding exponents. You have to be prepared to explain everything you do step by step whenever you show them an example or show how they should work a problem. Remember the power of normal numbers. Even in college some people are captured by the idea that variables have this magical property that makes them behave differently than 'normal' numbers. Whenever you see someone struggling to follow your work from step A to step B, simplify every aspect of the step with its arithmetical equivalent until they understand. If that means you have to prove that x^4 is different from 4x using arithmetic, then so be it.

The whole 'further point' idea is very good. It's always nice to provide some motivation for a student to succeed in their studies, but tread cautiously with it. I know some people that would mentally shut down if I ever strayed from the path of what was relevant to their set of problems. The person was sharp, don't get me wrong, but they simply couldn't handle too much information at once.

One of my major worries is helping people too much with their homework. I'm afraid of being used as a crutch to help someone hobble through a class without their complete understanding of the material. At the very least I shoot for their being able to competently take tests and answer questions even if they're forced by time or circumstance to memorize a formula or process.

I'm surprised at the amount of tutors here. If I may ask, what do you request for your pay?

I'm dirt cheap, about 10 dollars an hour. The school I work for pays me less, though.

>>70
I charge $15 Canadian. or equivalent trees.
I've seen people advertise for up to like 35, 40 dollars, which seems kind of crazy. I'd feel bad charging that much, which maybe sounds dumb

SAGE has been used.

>>70
OP here, only done it once, so I haven't charged anything. I think there's a benefit to charging for both people, which is that everyone takes it more seriously. I'd be more inclined to prepare ahead of time on what they're working on, if I were being paid. Otherwise I'm happy to help, but I'm probably not going much further than answering questions that come up while we're together. Likewise, they probably won't mind if we quit early or get sidetracked.

After I get some volunteer experience in, I plan to charge 10-20 USD, depending on who it is, their level, and transportation.