Two or three of my honors students have barely skated upward into final grades they probably shouldn't have gotten, due to an extra-credit option I gave everyone early in the semester. I calculate the extra credit as simply another daily work grade, but I don't increase the total number of daily work points when I calculate final grades--so it's possible for 1) a student with a poor daily work score to bring it up a bit; 2) a student with a close-to-perfect or perfect daily work score to have more than the maximum. One student who should have had a D got a C, barely; two who should have had C's got B's, barely.
Several different factors play into the final grades, of course; I maintain one never passes or fails my courses because of one thing only. But I will admit it is possible to hover close to the borderline for the whole semester and have a daily work grade in the form of extra credit bump you over.
So philosophically, I think I'm done with it. It's rather high-schoolish, isn't it? And it probably distorts a student's overall grade profile. I've had the option more often than not in all my teaching semesters, but as the estimable Dean Dad says, it rewards the wrong things. Extra credit may reduce the value of the other grades, too. What does it reward? I would say motivation, mostly; less writing or thinking skills.
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