Hmm.
Might be time for a conference with this teacher and your child-- one where you play the role of wanting to partner with the teacher to make sure that your child is getting the most out of the class, mastering the particular learning goals (what are those, again?? <-- often disorganized teachers haven't ever actually stated them for students, which is more than a little unfair if you ask me), understanding what grading is based upon and so on.
"Can you point me to that reference/document/etc?" Use that statement, and practice it in a very neutral tone, maybe even a pleasant and eager one if you can muster it.
Honestly, if the teacher CAN reach a little to help you bridge the gap, this could turn out to be a great learning experience for your child, and help her learn to adapt to a style that she doesn't innately find easy. That has a value all its own. I'd definitely bear that in mind as you try to work with this teacher. It's not about right/wrong even-- it's about bridging the apparent gap between what your child can manage and what this teacher (apparently) can. Disorganized/chaotic people are the BANE of rigid/highly structured ones everywhere. Think of it as a communications challenge.
Oh-- and good luck. My DD still struggles mightily with this type of instructor and she's in college. It was a nightmare when she was in middle school.
One tip that she probably cannot use, but which would be incredibly USEFUL if she could-- is to snap a photo of the board with a smartphone at a couple of intervals during class-- that way, at least the written info that she missed is captured. Can she record class on a voice recorder? It'd be a lot of work for you, but it would permit you to scaffold better note-taking and help her to recognize "clues" to "this information is important and I should write it down!"
Many kids are used to teachers using BOTH auditory and visual notes for the exact same information-- and when one doesn't, they miss a lot. It takes practice.
