Overly shy and unparticipating student...?

I would encourage the mother to have her daughter tested. It sounds like she has Aspergers. The younger she is, the better the outcome. Early intervention is important to her education and self-esteem. Speak to the school psychologist to see if they can help. I don't know why any parent would turn down help if their child needed it. You sound like a caring teacher. Good luck.