For some ring of polynomials over R, and a particular element of that ring, we define the evaluation map to be the natural thing; $P(a)$ is just what you get when you replace all the x's in the polynomial P with a's and evaluate.
Is there a consistent way of doing with when dealing with polynomials in $R[x]/I$? I imagine we need to first find a normal form for elements of $R[x]/I$, then essentially apply the same construction, but I'm not sure how to go about doing that.
consistently