To Curve or Not to Curve Revisited

Yellow traffic signs showing a bell curve and a stylized graph referencing criterion-referenced grading.The practice of normalizing grades, more popularly known as curving, was a subject of an Innovative Instructor post, To Curve or Not to Curve on May 13, 2013. That article discussed both norm-referenced grading (curving) and criterion-referenced grading (not curving). As the practice of curving has become more controversial in recent years, an op-ed piece in this past Sunday’s New York Times caught my eye. In Why We Should Stop Grading Students on a Curve (The New York Times Sunday Review, September 10, 2016), Adam Grant argues that grade deflation, which occurs when teachers use a curve, is more worrisome than grade inflation. First, by limiting the number of students who can excel, other students who may have mastered the course content are unfairly punished. Second, curving creates a “toxic” environment, a “hypercompetitive culture” where one student’s success means another’s failure.

Grant, a professor of psychology at the Wharton School at the University of Pennsylvania, cites evidence that curving is a “disincentive to study.” Taking observations from his work as an organizational psychologist and applying those in his classroom, Grant has found he could both disrupt the culture of cutthroat competition and get students to work together as a team to prepare for exams. Teamwork has numerous advantages in both the classroom and the workplace as Grant details. Another important aspect is “…that one of the best ways to learn something is to teach it.” When students study together for an exam they benefit from each other’s strengths and expertise. Grant details the methods he used in constructing the exams and how his students have leveraged teamwork to improve their scores on course assessments. One device he uses is a Who Wants to Be a Millionaire-type “lifeline” for students taking the final exam. While his particular approaches may not be suitable for your teaching, the article provides food for thought.

Because I am not advocating for one way of grading over another, but rather encouraging instructors to think about why they are taking a particular approach and whether it is the best solution, I’d like to present a counter argument. In praise of grading on a curve by Eugene Volokh appeared in The Washington Post on February 9, 2015. “Eugene Volokh teaches free speech law, religious freedom law, church-state relations law, a First Amendment Amicus Brief Clinic, and tort law, at UCLA School of Law, where he has also often taught copyright law, criminal law, and a seminar on firearms regulation policy.” He counters some of the standard arguments against curving by pointing out that students and exams will vary from year to year making it difficult to draw consistent lines between, say an A- and B+ exam. This may be even more difficult for a less experienced teacher. Volokh also believes in the value of the curve for reducing the pressure to inflate grades. He points out that competing law schools tend to align their curves, making it an accepted practice for law school faculty to curve. As well, he suggests some tweaks to curving that strengthen its application.

As was pointed out in the earlier post, curving is often used in large lecture or lab courses that may have multiple sections and graders, as it provides a way to standardize grades. However, that issue may be resolved by instructing multiple graders how to assign grades based on a rubric. See The Innovative Instructor on creating rubrics and calibrating multiple graders.

Designing effective assessments is another important skill for instructors to learn, and one that can eliminate the need to use curving to adjust grades on a poorly conceived test. A good place to start is Brown University’s Harriet W. Sheridan Center for Teaching and Learning webpages on designing assessments where you will find resources compiled from a number of Teaching and Learning Centers on designing “assessments that promote and measure student learning.”  The topics include: Classroom Assessment and Feedback, Quizzes, Tests and Exams, Homework Assignments and Problem Sets, Writing Assignments, Student Presentations, Group Projects and Presentations, Labs, and Field Work.

Macie Hall, Instructional Designer
Center for Educational Resources

Image Source: © Reid Sczerba, 2013.



To Curve or Not to Curve

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

Yellow traffic signs showing a bell curve and a stylized graph referencing criterion-referenced grading.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.

Choosing to curve grades or use a criterion referenced grading system can affect the culture of competition and/or the students’ sense of faculty fairness in a class. Curving grades provides a way to standardize grades. If a department rotates faculty responsibility for teaching a course (such as a large introductory science course), norm-referenced grading can ensure that the distribution of grades is comparable from year-to-year. A course with multiple graders, such as a science lab that uses a fleet of graduate students in the grading, may also employ a norm referencing technique to standardize grades across sections. In this case, standardization across multiple graders should begin with training the graders. Curving grades should not be a substitute for instructing multiple graders how to assign grades based on a pre-defined rubric (The Innovative Instructor: “Calibrating Multiple Graders”).

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.

Image showing a bell curve.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.

Image showing clumping.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.


Image showing quota system.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.


Image showing criterion-reference grading.IV. Criterion-reference grading

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.

Additional Resources

• Campbell, C. (2012). Learning-centered grading practices. Leadership. 41(5), 30-33

• 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.