I've detailed numerous times how I handle corrections for a standard in-class test -- basically, students earn back half the credit they missed. On AP-style tests, the half-credit-back plus the square root curve basically turns 5s into As, 4s into Bs and B+s, the 3s into B-s and Cs+s. On regular physics quizzes, (which are easier but on which the standard for success is higher), half-credit-back makes the standard 90-80-70 scale reasonable.
But what do Ido for an EXAM -- when grades for the term have already been issued, and/or when the exam is so long that the process of corrections isn't a night's assignment, but a major undertaking?
I gave a full-length, seven-question AP exam right before spring break. Since we returned from break, I've only assigned one homework problem each night, but I've assinged the correction of one exam problem each night as well. Those who did well on the exam simply have less homework. Those who didn't do so hot have the time they need to pay careful attention to the things they missed.
I count the exam corrections as a test grade for the current term. The game I play -- and everything associated with grades is, in fact, a game -- is that everyone starts with 100% on this "test." Students correct the lettered parts of the free response problems that they missed.* On each problem, a solid correction earns a "minus zero." However, small mistakes might earn "minus one" and their grade for this test is down to a 99. A major mistake might earn -5 or even in extreme cases -10. The final test grade counts on the standard 90-80-70 scale, which means that missing 10 points cumulatively will drop the grade by one letter.
* I generally ask students additional questions so that they're not just copying a friend's right answer. See this post for some examples, or search under "test corrections" on this blog.
I like this game because everyone has a reasonable opportunity to earn a high test grade with merely a solid effort. Collaboration is allowed and encouraged on test corrections (as long as no one is merely copying), so there's not reason not to get most of the answers right. Even the students who scored well on the original exam are motivated to do corrections properly so as not to lose a lot of easy points. And the students who need to pay attention to their mistakes generally do so.