Sunday, March 18, 2007

Grading Tip

If you ever find yourself needing to curve grades on a 100 point scale sometime, try this method:

Take the square root of the original grade and then multiply it by 10.

It's a wonderfully elegant curve. It's simple and fast to do. It adds the most the lowest scores. It adds a modest bump to high scores. No grade ever goes above 100. And the rank ordering of the grades never changes, that is, a lower grade never gets curved above a higher grade. Plus, if you still don't like the average, you can repeat the curve as many times as you like until you get the average you like. Try it.


  1. I hope you like it. Family lore attributes this curve to "Square Root Jackson," a much feared engineering professor at Texas A&M many years ago.

  2. It is not too fearful! Square root of 60, typically a D-, brings the person all the way to a high C. In order to use this and not be too easy, I have to take off more points. I am so used to no curve, and lowest A being 90 or even 93, that I am an expert in not taking out too *many* points ... with this curve I must go the opposite way ... it is very interesting.

  3. I am in disagreement with the way a high school physics teacher has curved grades.
    I need you to weigh in on this issue that we will debate very soon.

    Background Info
    The high school teacher was not recording the raw score on tests and quizzes. The kids were in total darkness and was only privy to their curved scores. This would be OK if my student was receiving high scores. I would not have questioned the teacher at all.
    The teacher refused to disclose this information because she said it would cause students and parents to have heart failure.
    I told her that curved scores don’t tell me how my son performed and I insist on knowing raw scores. So I appealed to the principal.

    The principal said the teacher did the following: 10*SQRT of Original Grade.
    I rejected this curve because I told them that by definition of this curve no kid can score over 100. I told them I knew of a kid who had more than 100 points so this is not the curve being used.

    The Asst Principal came back with another curve: 11*SQRT of Original Grade.
    I told them that I would believe this if I can compute my son’s score using this data. I was not able to arrive at his score. So I rejected this curve formula as bogus too.

    Finally, the teacher stated that she was using 11*SQRT of Original Grade with a cap of 20.
    I told her that capping the curve would cause the kids that scored less than the average on the test to receive less than the full benefit.
    The kids that score above average received the full benefit of the curve. This causes a greater disparity among the kids who scored below the average.
    I need to know your opinion

    I would like an expert opinion on what putting a cap on a square root curve does to students. I think it is extremely unfair. If she is going to use this curve she must not use a cap; otherwise, the curve is not doing what is was designed to do. It would be better just to add points to a raw score and give all the students the same amount of points.

    Fulton County has disallowed the bell shape curve but allows a cap on a square root curve? This makes no sense to me.

    I am seeking an opinion on square root curving with a cap. Is this a fair and objective way to curve?

  4. My advice would be to relax. It's almost Christmas and you and the teacher and your son probably all need some time to enjoy the holidays.

    If you insist on keeping at it, I know of no test of fairness about curves other than that whatever rule is decided on it applies to all the students. Keep in mind that actual curving often lowers some grades at the bottom end of the curve.

    If you want more opinions from stray academic bloggers, I suggest you try Angry Prof over at A Gentleman's C. She loves questions like this.

  5. Agreed about relaxing.

    When I was at UCSD, a very serious science school, in intro chemistry classes the curve was used to turn scores in the thirties out of a hundred into A's. Curves are not absolute. They are relative to standards, just like all grading systems.

    No matter how curves are calculated, they never alter the relative positions of the students. Do better on the test, do better on the curve - more or less, but rank does not change. Any parent interested in what curves mean, or whether they are fair, should stop right here. Your kid is near the top, near the middle, or near the bottom. That's plenty of information about performance for most purposes, including all of the life-chance ones.

    Any decent teacher can rank student work bad, fair, good, better, best. If you don't trust a teacher to be minimally competent in this way, 'fairness' is the least of your worries. Numbers and curves are just a way to deflect responsibility for these elementary judgments.