I hate to say it, but in this case, you mother wasn't right: it is better to avoid rinsing the pasta whenever possible. As pasta cooks and the outer surface softens, it becomes more absorbent, which means the flavor of your sauce will better permeate each and every strand, curl or tube. If you run the pasta under cold water, you wash off that absorbent outer surface, and the sauce doesn't have anything to grab on to.
When you are using the pasta in a cold dish (such as a pasta salad) and you want to stop it from continuing to cook, drain the pasta in a colander and plunge the colander, pasta and all, in a bowl of ice water.
See our collection of pasta recipes for both hot and cold pasta dishes.
Recipe: Fusilli with Pistachio Pesto