What a grade should do
Before proposing a formula it helps to write down what a good grade should accomplish. I wanted a system with five properties:
- Sensitive to a student's own skill and knowledge, typically measured with exams or open-ended projects.
- Dependent on continued engagement, measured through homework, class participation, and project milestones.
- Able to use the full range of allowable grades, rather than bunching everyone near the top.
- Aligned with learning rather than point chasing, so the path of least resistance to a good grade is understanding the material, not outsourcing it.
- Fair, understandable, consistent, and not intimidating.
The reason this matters now is the fourth property. If completing the homework is the cheapest route to a high grade, and an AI tool can complete the homework, then the grade rewards the tool instead of the student.
Why the usual approaches fall short
Most courses use one of two grading shapes, and neither satisfies the list above once AI enters the picture.
The standard approach weights homework and exams roughly equally with some participation points. It rewards engagement, which is good, but it is not sensitive to a student's own knowledge: it is easy to fail an exam and still finish with a high grade. It compresses the grade range, because diligent but shallow work floats everyone upward. And it no longer incentivizes learning, because the homework half can be solved by AI.
The exam-heavy approach swings the other way, letting exams and projects account for nearly all of the grade. This is hard for AI to manipulate and it uses the full grade range, but it stops requiring engagement, so a student can skip class and homework entirely, and it lets students who arrive with background coast without learning anything new.
The insight: multiply, do not add
The two failures are mirror images. The standard approach requires effort but not mastery; the exam-heavy approach requires mastery but not effort. A weighted sum cannot fix this, because in a sum a high score on one component papers over a low score on the other. That is exactly the loophole.
So instead of adding the components, multiply them. A grade is the product of an engagement score and a skill score. With a product, a near-zero in either term drags the whole grade down, which means a student now needs both to do well. I call this multiplicative grading.
The calculation
Concretely, a final grade is built from three components, each expressed as a percentage:
- Component A — active engagement. A weighted combination of homework, class participation, and project milestones. Students are expected to land around 100 percent here, and they can earn extra credit. Crucially, I grade homework on completion rather than correctness, so that using AI to get through a problem set does not directly inflate the grade.
- Component B — skill and knowledge. A weighted combination of exams and open-ended projects, where understanding actually has to show up.
- Component C — an optional course-evaluation multiplier that can nudge the whole result.
The final grade is the product A × B × C. Because A sits near 100 percent for an engaged student, the engagement term mostly acts as a gate: do the work and it stays out of the way; skip the work and it pulls everything down. Component B is where mastery is rewarded. Run the same checklist against this design and it satisfies the properties the other two could not: the standard approach fell short on three of them and the exam-heavy approach on two, while multiplicative grading stays sensitive to skill, still requires engagement, uses the full grade range, and rewards learning over point-chasing.
What I expected, and what happened
Before implementing it, I wrote down what I expected: high-performing, engaged students should do at least as well as they would under standard grading; skipping homework or participation should have a substantial effect; completing homework without understanding the material should not produce a good grade; and the overall distribution of grades should be wider.
I implemented multiplicative grading during the 2024-25 school year. The results lined up with the hypotheses:
- Unattempted homework dropped from 5.5 percent to 0.2 percent; a different class that year came in at 0.8 percent.
- The median grade changed by less than one percentage point between semesters.
- Exam and project grades went up slightly.
- The grade distribution kept a familiar shape but spread out more.
- Students spent a similar amount of time on homework in both semesters.
What I concluded
The grades ended up reflecting mastery more honestly while still rewarding effort. High performers continued to earn good grades; students who had not mastered the material no longer received artificially high ones. Homework completion climbed to nearly 100 percent without students working more hours, which suggests the change was about incentives, not pressure.
I will be honest about the softer findings. Student impressions were mixed, which is fair: a grade that can be pulled down by a weak exam feels less forgiving than one built from a generous sum. But anecdotally, despite nearly identical median grades, I felt that the standard system had been quietly inflating grades, whereas the multiplicative grades were earned. I would rather defend a grade I can explain.
An open question: multiply, or take a geometric mean?
I am still turning over one design choice. Multiplying the components treats a grade like a logical AND relaxed onto the continuous range of grades: you need engagement and mastery, and a low score in either one drags the result down. That is the behavior I wanted, and it works cleanly precisely because the engagement component sits near 100 percent for most students, so the product stays close to the skill score.
But if a course does not expect engagement to land near 100 percent, the raw product turns harsh: two middling components multiply into something well below either one. A geometric mean — the square root of the product, for two components — would keep grades closer to what a weighted average produces while still requiring both parts to be present. The catch is that the geometric mean compresses the range and lifts grades overall, which works against part of the reason I left a weighted sum behind in the first place. So it is a genuine trade-off rather than a free improvement, and one I am still thinking through.
Related
This is the written version of a talk; the slides cover the same argument, and there is a longer white paper. Multiplicative grading pairs naturally with Scaling Oral Exams, and the broader case for both is in Teaching Computer Science in the Age of AI. Both are used in CSE 5114.