I've noticed that I have a really hard time getting my leg to look straight when I'm doing grand battements or things like that...I seem to have very hypo-extended knees (is that a word?) and I was wondering if this is a flexibility issue with the muscles in the backs of my knees, or just something I'm born with and will have to deal with? The reason I ask is because even when I'm sitting on the floor with one leg bent and the other extended, I still can't get the extended leg flat on the floor, and that doesn't seem like something that would be related to flexibility. Anyone have any ideas?

It may just be the way your leg is constructed. When doing battments make sure that your muscles are engaged and pulled up.

You don't know me, because I'm new here, but I can help you. I have hyperextensive knees, which basically means that if I don't control my knees properly they slide through my unusually loose knee ligaments and bend backwards. I too have a hard time straightening my knees completely. However, over a period of 11 years, during which I have danced for 9 years (I haven't danced for two years, but I'm going back) I have learned how to strengthing my muscles enough to pull my knee cap up.
People with strong knees don't realise the complexity of the "simple" movement of pulling up the knee cap. When you're straightening your knee what actually happens is you are lifting your knee cap up and then tucking it between muscles. Just thinking about lifting your knee cap should help when you're doing things. However, I have gotten quite a few exercises from doctors and dance teachers over the years that I would like to share with you.
Sit on a chair or bed with your feet on the floor. Lift one leg from the knee down and flex your foot reaching your toes for your knee. Eventually you will be able to straighten your knee completely while doing this. After you can completely straighten your knees on both legs one at a time, lift them at the same time.
Another exercise is to stand with one foot pointed forward and just lift and release the knee cap. This feels weird for a while, but it works wonders.
The main thing is to do everything you can to strengthen your quads (the muscle on the front of your thigh).
Hope this helped and good luck

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A dancer is not made by technique, but rather by the passsion that burns in her heart.