by Erik Schreyer, Mathematics, ’18-19

The way in which we grade student papers and just as much which student papers we grade has a great impact on how students study and what students take out of a class. This of course does not come as a surprise and does not need to be debated.

I am in the fortunate position of having spent several years in two university systems with fairly different approaches to grading and how final grades are made. All throughout my Bachelor’s and Master’s degree in Mathematics I have been studying at The Rheinisch Westflisch Technische Hochschule Aachen University in Aachen, Germany. In this time of course I have been on the receiving end of corrections, grades, and comments many many times and know how the German, or more appropriately the Aachen, grading approach influences my study behavior and the value I place on the feedback I received. It needs to be noted, that this leads to a subjective view. At the same time, however, I have also been tutoring and grading as a Teaching Assistant for various lectures both at the end of the Bachelors and during the Master’s program. This first part of this post will be a description of the grading system at the RWTH.

After my Master’s, I came to the Math Department at UGA to for a PhD. In my time here, I have been grading and instructor of record for various classes. Accordingly, I want to review how classes are structured at the University of Georgia in the second part.

Finally, we will discuss advantages and disadvantages and the possibility of implementing a hybrid setting consisting of elements of both systems.

In almost every class I had as an undergrad Math major, we had weekly homework typically consisting of plus minus four exercises that would lead to a four-to-five-page handwritten paper. Being Math, those papers were not tightly filled texts but included formulas and computations etc, just to put it in perspective. Every homework got graded on some point scale (not receiving a letter grade but just accumulating points during the semester). The typical ruling was, then, that one needed around 50% of the total number of points to be allowed to participate in the final exam. The grade a student received for the class was then entirely determined by the grade achieved in the final exam. The exam time always included an exam right after classes end and a makeup exam before the next semester, such that a failed exam does not automatically leads to a lost semester.

Let me summarize the system at UGA by pointing out the differences. First of all, homework and the final exam are accompanied by midterm tests (typically varying in number between one and three). The biggest difference, however, is that every graded item is part of the final grade.

Some of the advantages and disadvantages are apparent. For example, having only one exam that determines everything one is at risk that ‘having a bad day’ means a semester of work is lost. It also potentially increases exam anxiety by putting that much weight on one test.

In the Georgia system, one is at risk that being a slow learner and struggling at the beginning of semester means that a good grade is essential lost. This is questionable in particular with respect to the learning objective of the class; one should be awarded for having met all learning objectives at the end of the class, which is not something that should be influenced by the first week of classes. The idea behind having grades all throughout the semester is to aid the students in diligence and ‘staying on top of everything.’ Having to meet a certain required amount of points has the same idea in mind. The biggest difference, which is somewhat subtle, is how the grading changes and how the reception of comments on papers on the student side changes.

If every comment and grade one receives has an impact on the final grade, the students tend to ask the following questions:

“What do I have to do to get full points?” “What do you want me to change?”

Instead, what we want the students to ask is:

“What is wrong/what can I improve?” “Why is my argumentation not consistent?”

This is problematic in the sense, that the first questions are not aimed at learning and improving but rather to maximize the GPA outcome of the class. It is not the fault of the students or the instructors but an understandable consequence of the circumstances.

If the points received are entirely aimed at evaluating and improving the content of the paper, the second kind of question becomes more likely to be heard. On the other side of grading, instructors with good reason sometimes tend to be lenient, especially if the solutions are close to being right but are missing one or two subtle arguments. If the points are more of an indicator and less important, it allows instructors to mark every mistake and take away points, the second part of which demonstrates to the students that the comment is not just esthetic but meaningful.

There is an argument to be made about students not being as diligent at the end of class as at the beginning, after meeting the required minimum of points. However, from a student perspective this can have benefits. For example, a student who is struggling in one class but is doing fine in another is able to shift attention toward the latter and be more efficient in studying without having to bother with homework about something the student already understands.

Now, the argument that having only one source for the final grade is problematic seems strong enough to be skeptic of the usefulness of such system. For that reason, I want to explore a sort of hybrid between the two.

The most straightforward and in my opinion the easiest to implement and transition to is to split the homework into two categories. Every second week, homework is graded without counting for the final grade with students needing at least, say, 50% of points. In particular, this would point out smaller mistakes and their importance for the content of the class. Ideally, we could implement a study in classes with multiple sections to determine the implications.