First he tried doing what all her other teachers did. He showed her how to do Algebra using some simple examples. And she was able to do them immediately after his instruction. But when she tried a little while later, she could not remember what to do.
He knew this student was doing well in her other classes. He knew she was intelligent. So what was keeping her from learning Algebra?
Eventually he realized she didn't know know one basic concept about math. The root of her problem was that she didn't know that the equal sign meant that the value on both sides of an equation is the same.
Once he showed her how the equal sign worked it was like a light went on in her head. "Oh. I get it."
He then showed her how to apply this principle to Algebra: Whatever you do to one side of an equation must be done to the other to keep it equal.
She was then able to solve the problems he presented to her and eventually she was able to solve more and more complex problems.
At that point she really understood Algebra for the first time. Most importantly she was able to remember how to do the problems later.
A few years later my friend got a call from this woman. She was excited to tell him that she had the highest grade in her math class at the University of Alabama and that she was studying to be an accountant.
What an incredible turnaround for her. And it's all because she had a patient teacher who assumed she had the ability to succeed even when she had her doubts.