Brain Game: Math Monday II (or is it III?)

Math Monday makes its return. This puzzle is worth some effort, because even when you figure out what the answer should be, you have to figure out what the answer is. I hope you find it challenging. (For what it's worth, the Roman numerals in this post's title are no hint whatsoever. Really.) Good luck!

What's the next number in this sequence?

1, 0, 11, -12,... ?

Here is the SOLUTION.