# To Curve or Not to Curve

A version of this post appeared in the print series of The Innovative Instructor.

Instructors choose grading schemes for a variety of reasons. Some may select a method that reflects the way they were assessed as students; others may follow the lead of a mentor or senior faculty member in their department. To curve or not to curve is a big question. Understanding the motivations behind and reasons for curving or not curving grades can help instructors select the most appropriate grading schemes for their courses.

Curving defines grades according to the distribution of student scores. Grades are determined after all student scores for the assignment or test are assigned. Often called norm-referenced grading, curving assigns grades to students based on their performance relative to the class as a whole. Criterion-referenced grading (i.e., not curving) assigns grades without this reference. The instructor determines the threshold for grades before the assignment is submitted or the test is taken. For example, a 92 could be defined as the base threshold for an A, regardless of how many students score above or below the threshold.

In addition to standardizing grades, norm-referenced grading can enable faculty to design more challenging assignments that differentiate top performers who score significantly above the mean. More challenging assignments can skew the grade distribution; norm-referenced grading can then minimize the impact on the majority of students whose scores will likely be lower.

A critique of curving grades is that some students, no matter how well they perform, will be assigned a lower grade than they feel they deserve. Shouldn’t all students have an equal chance to earn an A? For this reason, some instructors do not pre-determine the distribution of grades. The benefit of using a criterion-referenced grading scheme is that it minimizes the sense of competition among students because they are not competing for a limited number of A’s or B’s. Their absolute score, not relative performance, determines their grade.

There are multiple ways to curve grades.

I. The Bell Curve

Normalizes scores using a statistical technique to reshape the distribution into a bell curve. An instructor then assigns a grade (e.g., C+) to the middle (median) score and determines grade thresholds based on the distance of scores from this reference point. A spreadsheet application like Excel can be used to normalize scores. CER staff can assist instructors in normalizing scores.

II. Clumping

The instructor creates a distribution of the scores and identifies clusters of scores separated by breaks in the distribution, then uses these gaps as a threshold for assigning grades.

III. Quota Systems

Often used in law schools, the instructor pre-determines the number of students who can earn each grade. The instructor applies these quotas after rank ordering student scores.

Using a pre-determined scale, assessments are based on clearly defined learning objectives and grading rubrics so students know the instructor’s expectations for an A, B, C, etc.

During the 2011 Robert Resnick Lecture at Johns Hopkins, Carl Wieman, Nobel Laureate and Associate Director for Science at the President’s Office of Science and Technology, argued that most instructors are not trained to create valid assessments of student learning. Curving can be used as a tool to adjust grades on a poorly designed test, but consistent use of curving should not be a substitute for designing assessments that accurately assess what the instructor wants students to learn by the end of the course. CER staff are happy to talk to faculty about defining learning objectives and/or strategies for designing challenging and accurate student assessment instruments.

• Jacobson, N. (2001). A method for normalizing students’ scores when employing multiple gradersACM SIGCSE Bulletin. 33(4), 35-38.

Joe Champion’s Grading Transformation Spreadsheet. This spreadsheet automatically curves students’ scores after the instructor copies the scores into the spreadsheet and sets a variable defining the amount of curve.

Michael J. Reese, Associate Director
Center for Educational Resources

Image Sources: © Reid Sczerba, 2013.

## 4 thoughts on “To Curve or Not to Curve”

1. Pingback: To Curve or Not to Curve | jhublogs

2. While criterion-reference grading does let the students know the expectations, it seems to assume that all of the variation from year to year or section to section is due to students. I am not so presumptuous that a examination I write this year will be of the same difficulty as it was last year for the same course, especially for questions at higher Bloom levels. Consequently, setting some number ahead of time as a certain grade also seems to me to be problematic and justifies some component of curving to adjust for instructor imperfections..

• Hal,

Thanks for your comments. Curving grades definitely has a place. We aren’t advocating for one method or another. Our purpose in publishing this article was to encourage instructors to reflect on how they structure their grading system in their class.

In the spirit of pushing our thinking on this topic, however, there are ways of creating project-based assignments that can be reused year-to-year. If a clearly defined rubric is also included then the variability in assignment difficulty can be minimized. I recognize that these assignments can be challenging to create for introductory science courses that focus on problem solving. Another option in these situations is to offer students extra credit assignments if the class appears to be struggling…. or curve grades. Either way the decision should be purposeful.

Mike