# Grading on a Curve

We all remember being students. Your first thought after turning in a test was wondering if there was going to be a curve. And I’m sure students today are no different.

What I’ve learned teaching though is that what I thought a curve was in school and what a curve can be are totally different things.

## Should you curve grades?

Let’s get this out of the way first. Is it fair, ethical, whatever to curve grades? What’s the benefit to you or your students?

Personally, I’ve never been a fan of a flat curve where the teacher adds however many points to get the highest score up to a 100%. As a teacher, it just always just felt sort of off. Never felt like the right solution. But this is what I thought a curve was when I was in school.

As far as curving, I usually save them for when grades aren’t totally the students’ fault. Maybe the test was too long. Maybe there were too many long questions. Maybe I forgot to cover something well enough. That’s when I personally see curving as a good option, knowing full well that every teacher has their own opinions on what’s a good option. And I’ll usually look through the reports in Canvas to make sure there weren’t any bad questions before making a decision.

## Flat Curve

This one is the easiest, and probably also the one that your students are asking about when they ask about curving a grade.

All you do is find the highest score and subtract it from a perfect score. Take the difference and add it to everybody’s score.

Let’s say the highest score on the test is a 92%. You’d add 8 points to every test.

It’s easy. It’s quick. And it works pretty well to take care of bad questions.

## Bell Curve

College is where I learned that a curved grade wasn’t always just adding points.

A bell curve puts the grades on a distribution where half of the students score above whatever arbitrary score the teacher thinks is fair and half below. And then apply some type of statistical math like standard deviations.

I don’t use these. It’s been a long time since I took statistics and the times I’ve tried the results just ended up feeling really arbitrary.

## Square Root Curve

A square root curve, or Texas curve, is another easy way to give students some points. Even though I don’t use this one very often, I do like it because it’s easy and helps the lower performing students more than the higher scores.

To curve you take the square root of the student’s grade and multiply by 10. Looking at the example below, let’s say a student scored a 75 on their test. We take the square root of 75, which is about 8.66, and multiply it by 10 giving the an 86.6% curved grade.

If it’s a lower score, let’s say a 25, we’ll do the same thing but the effect on the grade will be higher.

Of course, that gets pretty math heavy if you’ve got a bunch of students. We’ve got an online calculator if you’d rather go that route.

## Linear Distribution

This is the one I like the best. You select a maximum and minimum score and then all the grades are distributed between those two points using the same curve as the original scores.

The formula for calculating a score is below.

where

Now is probably a good time for an example.

Let’s say you want your scores between a minimum of 60% and a maximum of 100%. That’s $Y_0$ and $Y_1$. The actual minimum score, $X_1$ was 55 and the actual maximum score, $X_0$ was 96. Timmy scored a 72%.

After running the values through the equation Timmy now has a 77%.

This one is pretty math heavy and I would hate to run the math on 100 students. So I built another online calculator for doing linear grade distribution curves.

## Gravity Curve

This is the curve I offer when students ask for a curve.

I’ll go up to the top of the stairs, labeling each stair with a point value. From the top, I’ll throw the stack of tests. Whatever stair they land on, that’s their score.

It’s a joke, of course. But I’ve never had a student ask for a curve twice.

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