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%?


  1. That's one path to success, just lower the bar for everybody.

  2. I should have clarified that this is to be used on a summative assessment that cannot be retaken. My students ordinarily have the opportunity to retake assessments to demonstrate proficiency, and I don't use this method on those. If the grades on a summative assessment are below what you expected, then (A) your assessment was misaligned, or (B) you were not aware of your students' understanding (or possibly both). Since you use frequent formative assessments, then (B) cannot be the case. You should reexamine why (A) has occurred, but in the meantime you need to adjust scores to fairly reflect understanding. Hence this formula, humbly offered for consideration.

  3. I'm a high school student taking a college level (AP) physics class. My teacher uses this curve because that's the way the end year credit test grades. Even getting 50% of the questions right is enough to pass. He does this in conjunction with tests equal in challenge to the "AP Test" so we know what the conditions will be like, and so that the big scary test is so big and scary.

  4. Another good idea. Exposing students to more difficult questions without penalizing them for those misses. Reminds me of what I read on the collegeboard web site today about the AP Calc test: "Since the exams are designed for full coverage of the subject matter, it is not expected that all students will be able to answer all the questions."

  5. I wish some of my professors would curve like this...
    However, when taking AP Calc in high school, my teacher used a different method: He would use a formula of the form e^x, adjusting the coefficient for x, and x being our grade. I'm not sure if he was just having fun with it, but thought you'd enjoy hearing of that.

  6. Cool! You'd probably want it to go between (0,0) and (1,1) and be concave down, though - maybe ln(x+1)/ln(2). But the beauty might be lost on the students...