Why is it her fault that she is bored? We are now homeschooling our son, who is doing wonderfully during school time. He was getting in trouble at school (Kindergarten) and not completing his work. We thought he had behavior issues, because that's what they described to us, but we really don't feel that was it. He has recently been diagnosed with ADHD, which explains some things. But he is excelling in school. He is doing addition and subtraction problems here at home. I'm sure it was that he was bored. They were learning their colors, numbers, letters, and so forth, which he already knows.
Why is it our fault or our kids' faults they are intelligent? Why should we punish them for wanting to be intellectually challenged and stimulated? Perhaps there is another class/teacher that would work out better. I wouldn't be so quick to lay the blame on her for being disobedient. Now, I don't know what she does or doesn't know, compared to what they are learning, but she is probably bored if she already knows it. And her lying to you is a sign of her fear of getting in trouble. Don't adults sometimes tell lies (even "little white lies") to get out of trouble? Well, children are smart, too, and can figure that out.
Follow your gut feeling. YOU know what's best for your daughter. Don't let the system tell you what's right for her. YOU are her most important teacher, and SHE is your most important student...ever! So, just be there for her and let her open up to you about the work on her own. Let her know that you love her and know that she knows a lot of things but that her teacher doesn't know if she knows those things. Maybe you could offer the more challenging work at home with enrichment workbooks or something that picks her brain. Does she like word find puzzles? Maybe get her interested in some simple ones or mazes or something. Would her teacher allow her to take the challenging work to school to work on after she's completed her school work? There's got to be a way to help her. Best wishes to you, R.. Remember, she's already got the teacher on her case. She needs a comforter and someone that understands her.