Over the course of my teaching career I have come across a number of younger students who do not know how to handle frustration. Learning how to help them and adjust my teaching style to meet their needs has become a challenge in piano lessons but is well worth the effort. Keep in mind that every student is different and one approach that is successful with one student may only make matters worse for another. Continue trying new and different methods until you find what works with each student.
One of the hardest cases I had was with a student who wanted to come into the lesson play the song and once and be done with it. If I tried to correct any rhythm or note problems there would be a battle to hold back tears and the rest of the lesson would be useless. The student was afraid of being in trouble with me and at home if the song wasnt perfect the first time. Clearly no teacher expects this and the parents didnt expect it either. I tried to explain to the student that he did not need to play it perfectly the first time but things did not improve. I realized after trying several approaches that he simply did not yet know how to handle frustration and work through it. This one of the reasons I suggest learning an instrument, it teaches diligence and other character qualities early on. Finally I found an excellent solution that has worked for me ever since. Before he began working on a song in lessons I explained that even if the song was perfect we were still going to work on it for a total of 10 minutes. This totally took the pressure off of him and has worked ever since. I also made a point of asking him what he thought he did well and what he thought he could do better. This was also super helpful because he was becoming his own teacher. Instead of me being critical and finding mistakes he was correcting himself which motivated him to fix the problems more than if I had pointed them out.
Another younger student I had would get frustrated and give up on things much faster than I would have like. If she did not understand something right away she would get frustrated and not be able to accomplish anything at all. I found that she was just young and like my other student did not handle frustration well. With this student I had to keep things fast paced and do a LOT of review. Its not that she was incapable of learning she was just young. I would go as far as we could get in her piano book and when she stopped progressing we would go back to the beginning and do all the pages again. Each time we would get further before she stopped progressing and eventually we did get through the book. I think a lot of teacher feel that to go back is not giving the student their monies worth and that they should always be moving forward. It has taken me a while to learn that for some students the best thing you can do is backtrack or move to the beginning of a new series. This student also had a very short attention span so I would try and not stay on one thing longer than five minutes. I would have her find notes on the piano, review flash cards, open the piano and explain how it worked anything to keep her engaged and from getting frustrated.