By now, most US universities are 4-5 weeks away from the end of the fall semester. Whether it’s now, or just prior to the withdrawal deadline, student tend to demonstrate increased interest in their grade for their courses. They say that they want to know how they are doing. But they often prefer to know what grade they will earn at the conclusion of the course. The answer to the latter question could include all kinds of assumptions. But “What is my grade right now?” is a deceptively subtle question.
It seems direct. We could easily be curt and claim that it shouldn’t be complicated to tell a student what their grade is, and that it’s a failure of the teacher or of the education system writ large if it is complicated. While I entirely agree that a teacher should have an answer, it’s important to emphasize that “What is my grade right now?” is an ill-defined question. The problem is that a student can mean two different things when they ask about their grade.
Q1) What proportion of possible points have I earned so far?
Q2) What proportion of points will I have earned if my performance doesn’t change?
It’s important for teachers to ensure that their students understand which question is being answered.
First, I’ll illustrate when there is no distinction between the answers. Let’s say that there are two types of assignments: Exams, which are worth 75% of the course grade, and quizzes, which are worth 25%, of the course grade. So long as the two assignment types are identically distributed throughout the semester, Q1 & Q2 have the same answer. Below is a bar chart that illustrates a distribution of points over 4 weeks. The proportion of points for each assignment type is identically distributed over time (not necessarily uniformly distributed).
What is the student’s grade at the end of week 2 if they have scored 90% on the exams and 70% on the quizzes? By the end of week 2, there have been 30 possible exam points and 10 possible quiz points. The student has earned 34 of the 40 possible points so far. The math for Q1 is:
(0.9)(30)+(0.7)(10) = 27+7=34
34/40 = 85%
And, if they continue to perform identically in each assignment category, then they can expect to earn an 85% in the class. The math for Q2 is:
(0.9)(75)+(0.7)(25) = 67.5+17.5 = 85%
Both Q1 and Q2 have the same answer. And, honestly, principles or introductory courses have formats that often lend themselves well to having assignments distributed similarly over time. My own Principles of Macroeconomics class matches up pretty well with the above math. Each week, there is a reading, a homework, and a quiz. By the time students complete the first exam, they’ve completed about one third of all points in each assignment category.
Higher level classes or classes with projects tend *not* to have identical point distributions across time among assignments. Maybe there are presentations, projects, or reports due throughout the semester or at the culmination of the course. For example, my Game Theory class has two midterm exams, but no final exam. It has homework in the first half of the semester, and term paper assignments in the latter half.
The bar chart below displays a point-split among the same quizzes and exams, but they now are differently distributed throughout the semester. Quiz points have been frontloaded.
What is the student’s grade at the end of week 2 if they have scored 90% on the exams and 70% on the quizzes? By the end of week 2, there have been 30 possible exam points and 15 possible quiz points. The student has earned 37.5 of the 45 possible points so far. The math for Q2 is:
(0.9)(30)+(0.7)(15) = 27+10.5=37.5
37.5/45 = 83.33%
And, if they continue to perform identically in each assignment category, then they can expect to earn an 85% in the class. The math for Q2 is:
(0.9)(75)+(0.7)(25) = 67.5+17.5 = 85%
All I did was frontload 5 percentage points for quizzes and now the answers to Q1 and Q2 differ by 1.66 percentage points. That may seem like small potatoes. But consider that a) many students and universities use and care about the +/- system of grades, and b) a grade difference of 1.66 points was caused by a mere change of 5-point change in the distribution. Bigger changes result in bigger differences. Frontloading the remaining 5 quiz points from the end of the semester would result in a Q1 score of 82% – yielding a 3 point difference between the two calculation methods.
The differences between Q1 & Q2 illustrated above are even more pronounced once you begin to include extra credit. One point of extra credit has a smaller effect on the answer to Q1 as more and more possible course points have been earned.
If students only care about their ultimate grade in the course, then they will always prefer to receive the answer to Q2. But, students may also want to know how effective their recent study habits have been so that they can re-evaluate them conditional on the knowledge of the assignment point distributions. Q2 requires more assumptions if an assignment type hasn’t even occurred yet. Students can ask “Have I given this course the appropriate amount of attention given the types of assignments that we’ve had?”.
For example, my Principles of Macroeconomics course has the first exam at week 5. Students should have an average score that is greater than 90% by the end of week 4 because the reading assignments are simple, the homeworks are lenient, and the quizzes permit practice attempts. Students who have an 80% by the end of week 4 are going to have a rougher time once they encounter an exam.
Reasonable people can disagree about which calculation is more useful. And more mathematically inclined students can calculate their own grades anyway. Therefore, after every exam, I send a mail-merge email to each of my students in order to update them about their grade. I give them the answer to both Q1 & Q2, and I illustrate the impact of several alternative scenarios for their future performance. If there is information that a student wants about their grade, then it’s in that email.
In conclusion, teachers should take great care in making student grades and progress reports clear. Students should take great care to understand what they are asking and and what the answer means. Grades can be very important for students who are close to the margin for scholarships, academic probation, or failure. While students may care too much about their grades, teachers should be sensitive to the fact that the care is real none the less. Teachers owe their students a firm and clear indicator of performance.
*There is another case in which Q1 & Q2 have the same answer. It’s when the student earns exactly the same grade in each assignment category, regardless of whether the category points are distributed identically across time.
Economist Writing Every Day 