Improvement depends not entirely on the teacher. It’s on the parents, to make sure the kids practice and it’s on the child. Perhaps you should counter….parents need to provide a practice schedule for their child. Also a guarantee that the child will play & practice what they are told, perfectly. After all, perfect practice makes perfect. Also have them agree that the kid needs to play it three times in succession for progression. Unless these are met your price is higher than what you originally stated. After all, you are the one taking the risk. They will be representing you and your teaching ability.