Friday, March 13, 2009

On grades and inflation

Recently, another article on grade inflation appeared at the Chronicle for Higher Education. Entitled "Grade Inflation Continues at Varying Pace in Colleges, Says Researcher," the article refers to studies by Stuart Rojstaczer, which can be found at

Most articles on grade inflation, including the ones above, make some positive statements about grade inflation, comparing the average GPA of students "way back when" to the average GPA of students "these days". Discussions of this grade inflation usually fall into two camps.

The traditional educators argue that our expectations of students have been lowered, that we are taking the easy way out to please our students, that students are no more (and perhaps less) deserving of A's today than they were 10, 20, or 50 years ago. They argue that inflated assessments have rendered grades meaningless, and that the system of educational assessment has been unduly influenced by concerns over student self-esteem.

The progressive educators argue that students are more intelligent these days, their efforts more impressive, and they deserve these grades. Sometimes it is argued that giving A's for less-than-stellar work can be justified for pedagogical reasons, since A's can be used as a "carrot" to encourage effort on the part of ill-prepared students. It could be argued that, given student expectations now -- in an era where an A represents good effort -- it would be disingenuous to give a student a low grade based on performance if their effort was extraordinary.

Why is it that the phenomenon of grade inflation leads directly to the old divisions among educators? Are we unable to study such a phenomenon without aligning with one of the two stereotypes outlined above?

I suggest looking at some different questions, related to grades and grade inflation.

At the most basic level, let us consider the situation that there is a student and a teacher. The student enrolls in a course given by the teacher, and the teacher is asked to assign a letter grade, between F and A. As educators, we identify with the teacher, and ask the normative question: "How should the teacher assign the grade?".

The first answer to this question, one which all teachers should agree upon, is "honestly". In other words, a syllabus should be given at the beginning of the class, and it should serve as a binding agreement between the student and teacher, describing the grading process used by the teacher. Regardless of this process (even if it is "grades will be assigned based upon the teacher's whim"), it should be communicated clearly to the student. Honesty does not guarantee "fairness", but I would assume that honesty is a prerequisite for healthy student-teacher interaction.

Given that the teacher creates this binding agreement, the teacher must consider the meaning of each grade. Consider for example, the grade "A". What does it mean for the teacher to give the student an "A"?

Like any written statement, there are many parties to consider. What does the teacher intend with the letter "A"? How does the student interpret the letter "A"? How does the administration interpret the letter "A"? How does a potential employer interpret the letter "A"? Given that the teacher decides whether to give the student an "A", all of these questions should be considered by the teacher.

So, addressing this post to a teacher, here are some possible and somewhat tongue-in-cheek prescriptions.

Is pedagogy your first concern? Are you trying to maximize student growth in your course? Then perhaps, you should use grades as pedagogical carrots and sticks to reward effort and growth, and punish sloth and ignorance. Perhaps you should strategically consider the psychological impact of your grades -- giving low grades early might scare your students into working harder. But then again, giving low grades to many students early might scare them away or discourage them.

Is student satisfaction your first concern? Are students the customers at your university or department, whose happiness is your top priority? Maybe you should give students very high grades. But, given that students like to think that they have worked hard for these high grades, perhaps you should give them grades which start low and grow higher to convince them that they are earning their final high marks.

Is public assessment your first concern? Are you trying to give grades, which will tell future employers exactly how well the students perform? Are you teaching a course for future public servants, safety engineers, or doctors, a filtering course to guarantee a qualified workforce? If so, your intended audience should be those future employers. Your grade should clearly separate those who are qualified from those who are not. Perhaps you should not give "middle-of-the-road" grades, if it might confuse the potential employer.

Whether or not you agree with the above rationales for grading, one point is clear; a letter or number -- a one-dimensional metric -- cannot express your opinions adequately. Without more information on a transcript, an employer can never know whether the "A" means that a student put in a lot of effort, whether they were given an "A" for encouragement, or whether the "A" demonstrates a high degree of practical competence.

I have no desire to prescribe one rationale for grading over another. Rather, I claim that grades are so inadequate as a method of communication that they are nearly useless. One-dimensional assessment has led to a broken market. Rather than assigning blame or bemoaning grade inflation, I propose the following scenario for study:

Consider an economic market, in which there is a product and method of assessment; producers assess their product and their assessment is meant to aid the consumer in valuation. There is an obvious incentive for the producer to assess their product highly, so that their product is highly valued. However, there is also an incentive for the producer's assessment to yield high variance, because the consumer does not trust uniformity (we are not talking about genetically engineered, perfect and uniform vegetables, for example). What regulations should the producer choose, to maintain honesty (for ethical reasons) and keep the consumer's trust. Does assessment in more than one dimension (rather than a simple A-F style quality rating) lead to more honesty and trust, in such economic scenarios?

To attempt a pragmatic solution, in the context of grading, I would recommend numerical assessment in multiple dimensions. I do not recommend the current "narrative evaluation" system used by UC Santa Cruz, since it takes the other extreme and does not recommend any dimensions for grading. UCSC asks teachers to assign a letter grade (a one-dimensional assessment with all of the problems outlined above) as well as a narrative evaluation (which does not specify metrics and cannot be effectively aggregated).

I would recommend the following methods of assessment, to clearly communicate to the student, the employer, and the administration. In each course, the teacher should assign multiple numerical (1-5) grades, in an attempt to measure the following:
1. How much effort did the student put into the course? (relative to teacher expectations)
2. How much growth did the student demonstrate? (as evidenced by periodic assessment)
3. At the end of the course, how competent was the student? (as evidenced by a final examination)

More dimensions would be possible of course, but these three seem like a good baseline. Perhaps by grading in these three dimensions, employers and graduate schools would not be frustrated by the "uniformly excellent" student body. On the other hand, students could be rewarded, after observing how their efforts led to growth, encouraging them to work hard and achieve. By measuring these dimensions numerically (rather than with narratives), the administration could still aggregrate data, and study the student body with statistical methods.

Of course, these suggestions raise more questions - how should growth, effort, and competence be measured. But these questions are the subject for another post.


I will attempt, in my blog posts, to be pragmatic.

As a math professor, I care about issues such as education, mathematics and technology, and these related topics will probably dominate this blog. I will attempt to approach topics in a pragmatic way. The following are some goals that I set for myself:

1. Ask good questions. Sometimes the same old questions recirculate, eliciting stale responses. I will attempt to cut through and find the questions that have not, but should be asked.

2. Use firsthand knowledge, and occasionally admit ignorance. I will attempt to apply the same degree of critical thought to my writing here that I apply in my scholarly work. I will not make things up. When I do not know something, I will (following goal #1) try to formulate a good question. I will never falsify data. When discussing scholarly results, I will never depend upon other media to present these results; I will always attempt to track down original citations.

3. Focus on topics with high potential impact. I am not using this blog to advance theory; my work in mathematics is theoretical enough. I will focus on questions and studies that could be implemented, and could impact large groups of people in a positive way.