I've been tutoring a new student for a couple weeks now. I have a decent amount of experience tutoring, but this has been difficult. She taking an introductory class in real analysis. I took the same class with the same professor and got an A. I have experience tutoring, usually with a lot of success. This student though has been hard. She came to me a few days before the first midterm and wasn't getting very basic concepts. For example, the epsilon-N definition of a limit. She didn't know what it was. We worked together a bit, and she was able to get a C on the first midterm. Since then though it's been getting harder and harder. She never really grasped the original ideas, so adding onto it makes it worse. It seems like I have a few hours a week to teach her how to think like a mathematician AND the old material AND the new material. I've learned one thing though, is don't always trust someone when they say they understand something. I'm not sure what it is, but I can explain something. She'll say she gets it, so I move on. But I've learned that you can't always trust that. I can explain a theorem or idea, then use it 10 minutes later, and she'll be lost. So I have to go back and explain the theorem again. I think it's more about experience. Unless you have experience working with the theorem, it's just meaningless words. We ARE making progress, but it's slow. Very slow. When I usually tutor, I help with homework or clarify ideas. It seems like I've stepped out of the realm of tutor and into the realm of teacher. Rather than helping with homework, clarifying things, I'm having to teach the core ideas. We spent like an hour one time on me just explaining the epsilon-N definition of limit (of course not just me talking for an hour. It was a dialogue and problems). It helped, I think she grasped it better, but it's just that by that time in the course, she should have known it because everything is piling on top of it. She's been out of school for awhile, and hasn't taken a math class in I think she said 5 years. She comes back and the first class she takes is real analysis, so of course it's going to be hard. I'm just asking for advice, stories, etc. I'm always sympathetic and willing to help. I really want to see her succeed, it's just been hard.