Neatness and accuracy

I was teaching a class of children fractions. They had got the idea and were doing well with the questions I had set them. There was one girl who had got the first 4 questions correct, but who had made a mistake in the fifth one, before going on to get the sixth correct...
I pointed out her error to her, and suggested that she cross out the wrong calculation and do it again. She was reluctant to do so. The correction would only have required her to cross out a couple of numbers and replace them with others, but she declined to do so. Her problem was that she thought that that would make her work look untidy. She would rather have her sum wrong and her page neat than have the correct answers and minor crossing out on her page.
This is a problem, especially with girls, they have been praised for the neatness of their work early in their school career, and they elevate this criterion above that of getting the correct answer.
Although neatness in layout is a requirement of mathematics, it should not be put above getting the correct answers. A compromise is required.