First of all, I would like to thank you for replying so soon. That was more replies than I had hoped for and I will try to fill in some missing information which you ask for.
It is a matter to catch his attention because that the lack of attention is one of his problems. Another is to make something on request. For these two problems, we schedule his days using many pictures which we have on a wall at home and this is a very common way to help autistic people to bring some order in daily routines. as an example, before he wakes up, we have 5 pictures (not really pictures but drawn character which we make ourselves together with professional personnel). First when he goes to the toilet, second taking pyjamas off, clothes on, eat breakfast and then brush his teeth. Without these pictures, he can become confused and not know what to do or in what order to do things. It sounds strange for us normal people but the most natural things for us are the most unnatural things for him. And some things that comes very natural for him like remember a certain combination of figures is very difficult for us. That is because their brain does not know how to differ useless information from important. Also, he becomes, like many with Asperger's syndrom and HFA (High Functional Autism), very interested and skilled within a very small area. Like when he was 1 1/2 years old and could do for his age difficult puzzles. But well, he maybe laid 50 puzzles every day so of course he becomes skilled No normal kid would have the patience for that. He is also extremely good in computer games. For him they are very simple, you should usually do a certain stage and it is just to try all possible combinations of the stage and finally you make it. He can easily sit 8 hours playing if we do not have rules.
Now this is a long introduction and perhaps useless for the subject but it might give you a hint on his character.
One of you said that perhaps it is best to not do anything and just let him have fun at the piano and I agree to that. It is perhaps the best thing to do as I see him making progress every day when imitating pianists (today he had fun imitating Richter and laughed at him and said "he is angry with the piano"). Richter does look angry from time to time

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We have a great deal with help from the Swedish government and get treatments for free. Next meeting where we will schedule his autumn is tomorrow so I will bring this issue up and see if they know about some organisation specialised on educating autistic kids in music.
When it comes to what I refer to as basics, I more or less mean my old book from when I begin to play which is created to introduce people in piano playing with the auther Carl Bertil Agnestig. Anyone studying piano in Sweden known this author. The book has several series with different difficulties and contain a clever designed combination of well-known melodies transcribed for piano and in most cases simplified. All from Bach, Mozart, Joplin, Swedish hymns and children's songs etc. They focus on a certain technical issue and always show the scale the piece is in etc. I think it is a good start for the ordinary piano kid, however, I know I got bored pretty fast with them (and just to show the teach played the last piece of the book and suggested we should skip it). I am not sure I can describe better than this without scanning some sheets from it.
He has not yet made the connection from a note written on a page to a certain key and I am even not sure if it is important in his case. I am pretty certain I can teach him that later on if necessary.
As already suggested by you, imitating is a fun game but only when I sit at my grand and he at his piano and only when it fits him. This does not happen often so it seems impractical. When I want to show him something on his piano, he bang on my hands and want me to remove them every time. I have tried to name these games but without success. One thing that comes to my mind is that I perhaps should draw pictures of fingers playing certain keys or even better film my hands when I play a certain melody and also himself so that he can see what he is doing. Too bad the camera broke down some time ago but I guess I have to buy a new one

. I have also tried by putting colors on the keys but that just made him angry with me.
Of course I want to learn to think like him. If I did that, I would hold the key to his mind and most like to his future. This is what the special kindergarten, me and my wife and the special clinic try to do all the time. It is just so difficult to understand him as he speak very poor. Or rather does not understand the importance of speaking which for us normal persons are extremely important. But for him, it is enough with "toilet, sleepy, hungry, angry, happy, ball, out, in, rain, cold, warm" and some other words. So he cannot describe what he thinks or what he feels. But at least we know that he thinks in terms of pictures as he is very picture oriented and remember much details as he cannot sort them out. Also, he likes structures and logical patterns. So by combining pictures with logics, we can communicate rather good with him and so can his older sister who is very patient and kind to him. Perhaps I now gave you a better insight in my son and his behavior.
I hope I don't bore you

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