I've had dreams where I (myself in the dream) know I'm dreaming, but I (my conscious self) don't know I'm dreaming.

I had a dream once where I thought, "This is a dream. Do I want to become lucid?" I decided the answer was yes and then there's a definite switch to being aware of the fact that I was dreaming.

I think just knowing your dreaming isn't enough. You have to be aware of that fact and what it means.