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One, if the "A" students aren't getting the extra credit while the "D-C" students are, you wrote the question wrong.
What does writing a question wrong or right have to do with extra credit? Why would an A student do extra credit in the first place? What is their motivating factor, unless A&M went to a 9.0 grade scale and there is now a A+ stratification?
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Two, If anything the extra credit approach will only increase the inequity in grades between the top 50% and the bottom 50%.
Maybe I'm not understanding this but please explain to me how extra credit, assignments completed to boost lower performing students to the next grade level, increases inequity? I would think it does the opposite, since you essentially tighten/skew the grade distribution towards the A-crowd.
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If extra burden on the prof is ever a consideration, that prof should not be teaching.
'Cause professors are hired to help students along with extra course work and not bring in research grants. If you just make a histogram of the grade distribution, and distribute the A's, B's, etc. accordingly, that will be it. There's always going to be A students, and D students.