I'm not a teacher, I am a student. But in math, I am one of the best ones in my class so sometimes other people will ask me to explain stuff to them. And usually it works quite well: If I understood the topic, I am able to explain it quite well according to most of the class.
But on my way home, via train, one of my fellow students always comes to me and asks me to teach her math. She is not a good student, she is not trying to be and she is, I believe, not able to because she fails again and again at the very same things. This, of course, is not meant offensive, but just observational. But after all, she wants to be. We are all learning to get our "Abitur" (something like a "university entry exam"). She really wants to study something, so her goal is to make it.
Now to specificially the math problems. She fails again and again at the very basic things. Once, we had the expression
$63 \over 3$
and she shortened it to
$61 \over 1$
I tried to explain to her why that does not work. I told her, at first, that she cannot just take one part of the number and make it away, but she didn't remember why. So we started more basic.
$63 \over 3 $ $=$ $ 3*3*7 \over 3 $, you can make one of the three's away and replace it with 1, so you have $3*7 \over 1$ which is $21 \over 1$. She seemed to understand it as with another number, she was able to explain it to me again.
A few lines later, she did the very same mistake. We exercised it over and over again, but she didn't get it. Though she could reproduce (in her own words) why she cannot do that, she could never apply it.
And this is just one (probably bad) example. There are plenty of those.
Another problem is her self-esteem. Whenever I tell her she is wrong here and there, she tries to argue with me as if that would change anything. And she cannot take an "I don't know" as an answer from herself. Once, when she had 2.5E10 on her calculator and the teacher asked her what that means, the shrugged and told something about "emaginary numbers", of which she had no understand at all, just so the does not need to admit her not knowing what that meant. And if she does not know the answer at all, she is just guessing. In about 1% of the time she is correct and then she brags for the rest of the time how bored she is and that she is so much faster than anyone else.
I don't want to make her seem bad or something, I am just clueless and have no idea what to do anymore. I would really like to help her (though it is not my job), because she is a nice person, but as the idea that what she thinks might be wrong never enters her brain, I see barely anyway to help her.
Is there any way to bring the idea that she might sometimes be wrong and has to learn quite a lot of stuff into her brain without insulting her?