What Does Zero Mean Anyway?

As a math person, the moment I read the title, “The Case Against the Zero,” I became rather excited to read what this was all about. Reeves opens this article with the question: “If you are using a grading scale in which the numbers 4, 3, 2, 1, and 0 correspond to grades of A, B, C, D, and F, then what number is awarded to a student who fails to turn in an assignment?” He then remarks that most people answer this question with “0,” and that in the scenario we have described, that is a “rational system, as the increment between each letter grade is proportionate to the increment between each numerical grade—one point.” Now, however, he transitions over to the 100-point grading scale used today, where “the interval between numerical and letter grades is typically 10 points,” and when the score of a zero is applied, the discrepancy between a D and an F is no longer one point (as in the case of the 4-point scale), but now it is sixty. From here, Reeves builds his case against the zero, stating that the effect of a zero on one’s grade is unnecessarily severe, and mathematically unsound because of the disproportionate effect. He adds that receiving just a few zeros could cause a student to fail a class, and could lead to a life of academic failure. To prevent this, he argues that instead of giving a student a zero if they do not complete an assignment, educators should simply require students to complete the assignment. He concludes by suggesting that we change to a 4-point system, and if a need for greater specificity arises, we can include however many decimal places we desire within that scale.

While I appreciate (and agree with) the desire not to devastate a student’s grade with a zero, I think there are many alternatives to what the author is proposing, and I think that there are some flawed arguments in this article. The idea that we should require students to complete an assignment if they did not turn it in when it was due is not novel. Often times teachers take off 10% for each day an assignment is late, and understand if extenuating circumstances arise, giving students chances to bring up their grade. Furthermore, if Reeves understands the need to differentiate, then he should realize that grades are not dispersed evenly for a reason, and that his suggestion falls into the same trap he is trying to prevent. Why should a C be equal to 2 points on a 4-point scale? Is knowing 50% of the material adequate? Is knowing 25% passing? Would we want our doctors getting 50%’s in their classes? The reason we skew the scale toward the high end—in my opinion—is because we have high expectations for students and because knowing 50% doesn’t cut it. If 75% was an A, how would we know who our top students are? What would be the incentive to score in the 90’s? And on the 4-point scale Reeves proposes, doesn’t he realize that a 2.00 and below would become the new F and we’d be back where we started?

Chapter 8 of Integrating Differentiated Instruction & Understanding by Design, on the other hand, makes an excellent case against the zero in a matter of two paragraphs. Here, the authors argue that teachers should not assign zeros to missing work because, while we want to promote positive work habits in our students, we also want to accurately represent their level of understanding in our grades. What if one student has clearly mastered the material and never turned in any work, and another student has a modest understanding of the material and has turned in all of their work? Who get’s the better grade? One solution that both Chapter 8 and the Reeves article offer is to assign an “Incomplete” for missing work and incentivize students to complete the assignment—after all, the point is for them to learn, right? Another alternative to the zero that Chapter 8 offers is to report grades in three separate components: achievement, progress, and work habits. This way, students’ achievement in these areas could be more accurately reflected in their grades, whereas with our current system, the same grade can mean many different things because of how many components are included in that single number. Personally, I think that would be a great system, and would address many of the problems Chapter 8 brings up in terms of student motivation and grade validity.