I suppose ChittyBang and I are approaching tests as a way to express how well we mastered the material presented by the professor.
Yes. I agree with that. It is how you are assessed on your mastery of the material.
But I think you're confusing yourself by associating your absolute score (say, 35%) with your absolute understanding of the material.
And that's a mistake. There's literally no reason to expect that correlation to exist.
In the example we've been using (my organic chem class), if you got 35%, you had mastered the material to the expectation of the instructor (i.e. ~100%). That's because the test was intentionally designed to assess the limit of what you knew.
In another exam for another class, they may only test you on a subset of the material, and 90% may represent mastery of the material.
But there's no reason to say that for every test, one particular % grade absolutely represents your mastery of the material. I think you're kinda hung up on that.
Traditionally, if you do not do well on a test (your 35%, for example) you did not master the material, or the professor should adjust his/her teaching. It's hard to understand why you think it's okay for a test to be impossible like that. To me it means the professor did not present the material in a way you could apply it to the test given, or that you did not have "the means to reach the end" if that makes sense (whether that be due to lack of prep on your part of lack of resources on the prof's part).
I disagree with "traditionally," but since I doubt either of us are experts on the history of education, perhaps we can just let that go.
It doesn't bother me AT ALL that his exam was like that. His exam truly found the complete extent of my knowledge. In fact, I'd argue that his test was a far better reflection of how well I had mastered the material than some multiple-choice exam that assessed some sub-set of random points from some lectures where, if you happen to study those exact points you did great, and if you hadn't, you did poorly: neither of which might be a truly good representation of your overall mastery of the material.
Think about it. Let's say I cover 10 points in a lecture. Let's say I give a multiple choice exam that tests on 4 of them. Let's say Student 1 memorized 60% of my material and happened to catch all 4 points tested. He gets 100%.
Let's say Student 2 memorized 60% of my material and didn't happen to catch those 4 points. He gets 0%.
In reality, they both have a 60% mastery of my material, but because my test covered a subset of the material, they got drastically different outcomes. In both cases, the absolute % they got on my test had no connection to the % mastery of the material.
That's a pretty exaggerated example (obviously), but the concept is fair. When my organic chem teacher gave us that exam, it forced us to apply everything we had learned in the course, and it gave him a way to measure our true mastery of all the material.
Honestly, it was one of the most satisfying exams I've ever taken, because I walked away knowing exactly what I had learned in the course.
I know you're going to say: "Why not just test all 10 points?" That's just not a practical reality. You can't test students on every last little bit of data you threw at them. But by giving them a test that forces them to apply all the concepts in a test where you know they're going to come up short, you effectively test their mastery.
But frankly, that logic tells me that the test was unfair to begin with.
The only reason that "logic tells you that" is because you've got it wired into your brain that the percentage passing on the test EQUATES to the percent understanding of the material. That's just not true.
Personally, I think you're just hung up on thinking "If I got 35% on a test, I would view that as meaning I understood 35% of what I was supposed to know." If you throw that preconceived notion out, I think your objection goes away.