A nice one-minute summary of Alfie Kohn's case against grades at www.youtube.com/watch?v=EQt-ZI58wpw

There's a great deal more Kohn has to say on the subject that is worth reading, such as at http://www.alfiekohn.org/article/case-grades/ or http://www.alfiekohn.org/article/grading/ or an interview at http://www.education.com/magazine/article/Grades_Any_Good/

From that interview, this captures the essence of the case pretty well:

"The research suggests three consistent effects of giving students grades – or leading them to focus on what grade they’ll get. First, their interest in the learning itself is diminished. Second, they come to prefer easier tasks – not because they’re lazy, but because they’re rational. After all, if the point is to get an A, your odds are better if you avoid taking intellectual risks. Third, students tend to think in a more superficial fashion – and to forget what they learned more quickly – when grades are involved.

To put it positively, students who are lucky enough to be in schools (or classrooms) where they don’t get letter or number grades are more likely to want to continue exploring whatever they’re learning, more likely to want to challenge themselves, and more likely to think deeply. The evidence on all of these effects is very clear, and it seems to apply to students of all ages.

As far as I can tell, there are absolutely no benefits of giving grades to balance against these three powerful negative consequences – except that doing so is familiar to us and doesn’t take much effort."

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