Thursday, February 3, 2011
How to make students love square roots
Final exam scores in my calculus class were lower than I would have liked, with a few high-scores and a lot of medium-to-low scores. Reducing the number of possible points would bump the high scores over 100%, which is undesirable. Since the scores are not normally distributed, Another teacher in my department had a better idea: adjusting each score by taking the square root of its percentage. Thus, a 0.36 becomes a 0.6, a 0.49 becomes a 0.70, etc. Students were underwhelmed when I passed back the exams with only raw scores shown. After discussing the problems they encountered, I had students "adjust" their scores. Needless to say, they now love square roots.
In a traditional grading system, below 60% is considered failing:
Here's how the square root affects grade assignments:
This idea gives rise to a discussion about the square root function itself (why is x² > x if 0 < x < 1?), and other possible functions to adjust scores. For example, if the square root (x^0.5) is too extreme, what about x^0.9? Perhaps you choose whatever power will bring the mean to 75%?