# My Math Education Blog

"There is no one way"

## Sunday, May 22, 2016

### The Assessment Trap, Part 3: The Meaning of Grades

(This is a slightly edited version of a post from 2011)

Previous posts [Part 1, Part 2] have focused on the uses of assessment. For many students, parents, teachers, and administrators the key purpose of assessment is to assign grades. Before going any further, we need to think about the meaning of grades.

Grades have no intrinsic, absolute meaning. An A at an elite private school does not mean the same thing as an A at a public school that serves a poor neighborhood. An A at my own school today does not mean the same thing as an A meant 20 years ago. An A in Science does not mean the same thing as an A in History. And on it goes. The one feature of grades that is quite reliable is that an A in a given department at a given school is better than a B, which in turn is better than a C. In other words, the meaning of grades is relative. They are how we compare students to each other.

Almost all teachers will fix how they compute their grades if the outcome does not sort the students correctly. If a student deserves an A, and your calculation yields a B, you will find a way to tweak the percents, or the scores, or the participation points, or the extra credit, or something, to make sure the student does not get cheated by a pseudo-objective algorithm. (Admittedly, if the calculations yield an A, rather than the B we expected for a given student, most of us would let it be.) This makes sense, because teaching is as much an art as a science. Given a small enough class and enough of the right sort of contact with the students, a competent teacher knows better how to sort the students than any formula. (Yes, better assessments yield more accurate grades — that’s what I meant by “the right sort of contact”.)

In the rare case of the teacher who delivers much worse or much better grades than expected by their school, they will be taken aside by an administrator, and told that their practice is out of line. This does not require looking at the students’ work — it is more evidence that grades are strictly a relative measure.

In short, grades compare students to each other. They have no other meaning. This is why colleges are interested in grades. If grades were not about sorting students, they would be useless. Just to be clear: grades do not compare students only to others in the same section of the same class, but with the somewhat broader group of students in the same cohort at the same school. And moreover, it is of course true that the rankings are only meaningful if you accept the teacher's and the school's assumptions and values.

One might argue that grades are a measurement of how well a student meets the standards of a given class. This is true enough, but the standards in question only exist in relation to the specific students currently enrolled at the school. If almost every student met a given set of standards, no matter how valid those are, it could not and would not be used as a way to assess achievement in the class and determine the grade. In fact, such a set of standards would make for a course that is too easy for the given population. Conversely, a set of standards that is met by almost no one makes for too difficult a course. The only standards worth aiming for are precisely the ones that sort students into A, B, C bins.

Some will maintain that this is an argument against a system with no grades at all. Without grades, it would be easier to set your expectations too high or too low, or to have a bimodal distribution, with some students doing very well, others clueless, and little in between. Giving grades can help us calibrate challenge and access in the classes we teach. In other words, giving grades is not per se wrong. In fact, it can be useful.

But that does not negate this fact: grades are about comparing students to each other. Students know it, parents know it, teachers in practice know it. Educators who believe otherwise are deceiving themselves.

In the next post in this series, I argue for de-emphasizing grades.

--Henri

1. Henri, thank you again for coming out to do your summer workshop on our Head-Royce campus. May the learning never stop!