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Seems to me the rhymes makes it a more complex problem creating the need to focus on it more. That is a great way to recall information.
Sohcatoa was an Indian maid whose slope was only on one side. A way to recall the laws of a right angle triangle for trigonometry. Teachers have set these tools aside many years ago and they worked.
Nine times table little John leaves home and steps one to nine (write it on the left side) On the way home he walks again one to nine (right on the right side) You now have the times table for nine from one to nine.
There has to be a site with these tricks of the trade. Also could the student be nervous and just freezing up? If so could the teacher just take time and set it aside and say to the student come for a moment would like to do some questions with you. The just give a few different questions say one of each type one at a time so the student only sees the one question and is put more at ease?
I am really stretching here I know but if the teacher cares then I bet they are willing to try. Show them the work you have done with them and if you test the student show that to the teacher after all it could be a trust issue as well.
If you do not stand for the student with the parents who will. Sound to me like you care a lot and as such I bet you will try.