If you're like me, you find this very wasteful.
So, what should you do with all that discarded dough? Here's my answer: fry it up!
All you need to do is take your mature and active starter, which will now be doubling ever 12 hours, and pour it into a pre-heated frying pan (medium-high heat) with olive oil. I've made them about the size of a large pancake. Once it's in the pan. feel free to sprinkle something delicious into the wet part of the dough. I used some garlic seasoning, but something like chopped green onions, or even ham (or all three!) would be delicious.
After it's about 1/2 way cooked, flip it over (like a pancake). Once it's cooked through, flip it onto a plate. I dipped it into olive oil. But butter, or even soy sauce, would work too (depending upon what flavors you're trying for.)