I think his problem (or perhaps your problem) is that he does not like to fail - not that he wants to be first. When he realizes that he is going to have a problem, he shuts down. If this is true - this is a learned response.
He needs to relearn that it is ok to try and fail. That he will not be penalized if he does not know all his letters or numbers, etc. Kids with ADHD have trouble memorizing because their attention wanders. If the letters, numbers, etc. can be made into a fun game it will be more helpful. In my last post to you, I said the school needs to know about him and they need to reduce the pressure on him.
Here are two links that may help you. The first is just basic parenting ideas. The second is aimed at teachers, but a number of the ideas also apply.
Hope this helps. Please ask if you need more info. Best wishes.