My wife (who teaches - I just play) has just signed up a new pupil who is quite seriously autistic. She's had no experience teaching autistic kids: I've worked with one or two in passing but none quite this severe. We wondered if anyone has experiences and/or tips they could pass on. The girl in question is delightful and has a natural talent for piano but is otherwise quite strange to deal with, and has many classic autistic traits - for example in her first lesson today she played some Beethoven and Bach very well but could only start each piece prefaced by a crudely harmonised nursery rhyme.
I am not an expert or specialist in teaching people with autism but have taught 3 for a period of time. One thing I picked up on all of them is that structure, that is a constant familiar subjects and/or order of events, must be respected. One of these student could do nothing else but Bach, everything else was just not in the question. He also needed to plot difficult sections on paper and draw lines highlighting the coordination and even went so far as to write algebraic maths to represent things like syncopation. I worked with higher functioning autistics, I know that the intensity of autism varies a great deal to teach someone with severe autism seems to me a monumental task that could only work with a trained music/medical therapist.
You already have picked up that your student needs to start each lesson in a particular way, you must use that and find how you can teach different ideas through that medium. I had this same experience, they would simply break into mucking around with the sound improvising, I didn't stop them and let them carry on correcting their fingering as they went along and explaining why it was better when they stopped and where interested in that particular fingering challenge. I would continue this process every time he broke into improv and over time I noticed a change in his decision making and finger he used. We would do similar with pieces we studied, it is very hard to get the autistic student to stop when they don't want to, with normal students you can focus their attention to small parts and ask them to repeat but it is a different matter with the autistic student.
You cannot direct their attention with as much ease as you do with the non-autistic, sometimes they get trapped in a circle and cannot leave a particular section and you end up playing one phrase for the whole lesson! He would say to me he needs to get this done, it's the order he can't stand leaving it unsolved and moving on it doesn't work that way, he can't stop thinking about why he can't master that small part, please let him do that small part until he is confident to move on! This was the cycle that was impressed on me a lot of the times and often it would get us playing small passages for extended periods of time. You simply cannot force them to move on, I did that a couple of times and noticed that from then on I lost their attention and they started feeling very negative.
You must learn how to direct their attention to issues, often it must come packaged in a way that is familiar to them and not introducing too many new concepts. You must always build upon what they know and relate everything back to that, where non-autistics can more readily create newly learned habits and discipline themselves to develop it.
To say the least teaching people with autism was a great joy. It taught me a huge amount of teaching music through the perspectives of the student. All teachers do it with their students no matter who they are or what challenges they have. We must look at music through our students eyes before we know how to make the most effective changes to their approach.
I must also add that the students I had with autism needed constant reassurance that what they where doing was appreciated by me and acceptable. This need for approval is quite intense and they can get quite depressed if you set them work that they fail at completing. You must always give them that extra compliment and confidence boost. They also need to know that you are like a friend to them, autistics find it very difficult to understand peoples emotions so even if you smile they might not understand that you are happy, they can find it difficult to look at peoples face so what you say needs to be very carefully considered and you need to pick up on reactions in them when they are in a positive or negative frame of mind.