Fear of Failure

Half way though our first day back at home education. Sam, of course is away to real school. Jude has been quietly getting on with her reading. Today she has a piano lesson. She hasn't practiced all summer long. I don't mind really, she's been having fun. But today she sat at the piano and couldn't remember how the piece went. I played it to her on the flute, but explained that I didn't know how the piece went either, but I was reading the notes and playing what I read. I tried to get her to do the same. Jude has an immense fear of failure. Reading the book, How Children Fail, I now understand and see this more. She will not have a go at playing a piece by sight reading it. Instead, she memorizes each line of the music, and plays it from memory without looking at the book at all. What a difficult way to play the piano. I tried to encourage her to try to sight read it. I said to her, it doesn't matter how bad it sounds, how many mistakes you make, it can sound really dreadful, but at least try to look at the music and play what you read. Instead, she burst into tears and ran off to her room. Her fear of failing is so immense that she won't even try. I am at a loss as to what to do about it. Other than encouraging her to try, what else can I do? She can't complete all her grades in piano by memory. And she does love to play the piano, she is not forced to do it. I notice she is the same in maths. If you try to explain something, and she doesn't understand it, she cries and gets so terribly upset. No matter how much I explain to her that it doesn't matter if she can't do it, if she doesn't understand or if she makes a mistake, it doesn't change her behaviour. At school the teachers told me she was very bright, but she took so much longer than everyone else to complete her work, because she was so afraid of making a mistake. Ah, what am I to do?