A Review of Grading

29 Apr, 2023

not numbering my posts anymore sorry guys :(

(Note: This is a post that I originally wrote on Substack.)

I'm gonna experiment with my writing style - this one will be in a thinking process or something¹.

This post will be dedicated to a critique on the math system in-place. It is a little hard to extend this thinking to other subjects, as the beauty of math is that it is "perfect" in the sense that absolute certainity is guaranteed. While 1+1 is always 2 (in base 10) in math, in other disciplines 1+1 can be 2 or 1 or 3 (think of particle interactions, a synthesis reaction).

Motivation (Behind this Post)

The other day, I was looking at my math test, and it was graded in a weird way. By that, I mean I got points for parts where my answer was wrong. Like, I completely missed the domain part of this question. Yet I still got 6 out of the 7 points for this question².

In most math classes, only the final answer deserves recognition. The thinking or "work shown" is not counted, and can be as viewed as an accessory to the final answer, more of a nusiance to write out than an actual part of the problem for people like me.

Motivation (of the regular grading system)

Throughout elementary (primary), middle, and high school, the only part of a problem that is graded is the answer. Which makes some sense. Many people interpret concepts differently, and it is unreasonable to expect a teacher to understand each individual's thought process through each problem, as this would simply require too much time and effort.

But by placing emphasis on the answer, students are misguided; they learn that math is not about the process, but rather just on that final answer. And instead of gaining a true understanding of a concept, students will try to "imitate" their teacher's steps, often to varying degrees of success.

And besides. Do people even have fun imitating other people?

Emphasis on the Process

Let's go back to the picture of the test I took above. See those check marks? Those are where the points are - each checkmark represents one point earned.

In the point grading system above, students are rewarded for their thought process and for how they do the problem, and the answer is merely a byproduct of the steps they took. In this way, finding the answer seems more natural, and students can focus on learning how the problem was solved rather than what the final answer is.

Some shortcomings

However, not everything is perfect. One big flaw I would recognize in this system would be how the points are split. Due to the fact that there are simply so many tests to grade, a thorough review of each test is not possible. However, I would object to the "meaningless" or obvious points. In the world of grading (especially in math competitions such as the USA(J)MO or other proof competitions), 1+1 may not equal 2, it usually equals 1³.

For example, imagine a problem where the statement is on how to play a flute⁴. Certain steps, like assembling the instrument should be worth 1 point, and steps like setting up the music or fingering the right note should also be worth 1 point. But the key to playing the flute is the air that is blown, and this should be worth more than 1 point. For example, if someone is able to assemble the flute, and put their music on the music stand, and can hold the right fingering, they may get 3 out of the 4 possible points on this example question, which for me is absurd.

Conclusion

The grading system used today in math classrooms all across the country (and the world to some extent) is flawed in that students only focus on the processes that lead to an answer, with no recognition how one might develop the idea in the first place, or for how the process works.

Also, there's a better grading system for math problems out there, one that seeks to evaluate the student's process of finding the answer. However, the implementation of this system as of now is still flawed, and many changes still need to be made.

Or nothing is perfect and everything can be improved.