My former colleague Steven Taylor and his current cross-campus colleague Scott Nokes reflect on the strange fact that “students who wouldn’t scratch their bottoms to get a final exam grade will do anything for extra credit.”
My guess is that it’s mostly a function of perceived costs and benefits. Studying for an exam is difficult and mysterious, with students having to both grapple with the material and try to fathom what the prof is looking for. Extra credit, generally, involves some sort of rote assignment where mere completion brings rewards. Moreover, extra credit is usually offered toward the end of the semester when students realize that they are about to fall short of their desired grades and are therefore desperate to bring them up.
Granted, one would think that would be true of final exams, too. Then again, students doing poorly in one class are often doing likewise in others and are having to manage their time in preparing for multiple exams in close proximity.