Chaotic Math

Miki's worse subject is probably math. I feel like because math comes so naturally to me, I probably shouldn't be teaching it. I mean, what could I possibly teach them? I've never struggled with things like fractions, so I'm a bit at a loss when Miki demonstrates a repeated and baffling inability to understand basic concepts like these. (She is about 13 years old or so, by the way, so she should have these basics covered.)

Her problem seems to stem from a lack of organization. She can't organize her work and as a result, her math is just chaotic. She either tries to do it all in her head or she scribbles down messy and illogical things on paper.

I will teach her how to set up a problem and solve it, step by step, and ask her to copy this method when she solves a problem on her own. She doesn't seem to have trouble understanding the method I teach her, but then when she is solving on her own again, she reverts back to her chaotic system.

Don't get me wrong - I would totally support someone making their own system of solving if it worked for them. But it doesn't work for Miki. She mixes up multiplication, division, addition, and subtraction so often that it becomes clear she's not really thinking about the problem; she's just trying to race through it. For example, if presented with the problem 3X=9, she would most likely subtract 3 from each side, coming up with the answer X=6, even though if she followed my method she would see that the last step is to divide by the number in front of X.

What can I do for someone who simply refuses to follow the given method and make up their own (incorrect) one? I try to be strict with her, telling her to use my method every time and write down her work, but she just keeps lapsing.

This summer, I am planning to go over math basics extensively and try to reteach her everything in a much cleaner, more organized way. I'm really, really hoping she will absorb some of it.