It's disgustingly arrogant to assume that. They are showing exactly the understanding needed to answer the question. They obeyed the instructions, and they paid good money to have that opportunity, but they are being punished despite doing exactly what was asked of them. Whether the instructor has the legal right to do this or not, it certainly feels like fraud.

If the question setter failed to set a good question, that's the question setter's fault, not the student's fault. Punishing the student for somebody else's mistake is injustice.

I've been teaching college algebra for 20 years. There is nothing arrogant in what I said. The student needs help and it is clear that this is so to anyone with experience teaching such courses. After many years and thousands of students I've developed an intuition on when a student needs help and when I don't need to worry about them.

If you had to bet a million dollars, based solely on the solution presented and knowing the course was college algebra, would you put the money on them passing or failing?

It's not a question of probabilities. You're advocating punishing people for wrongdoing you anticipate them doing in the future. This is the argument behind racial profiling, and it's widely considered immoral. Would you mark a black student down because they're statistically more likely to fail in the future? If you suspect a student lacks understanding then you should actually test that understanding, not just assume they're going to fail and punish them preemptively.

The solution provided was not appropriate for a college algebra level course because it is not a valid solution as it is not a way of doing similar problem with a trivial numerical modification. You may disagree with me and that is fine.

In addition to the solution demonstrating an inappropriate level of understanding of the material it demonstrates that the student needs help. I mentioned my experience and intuition because you accused me of being incredibly arrogant when I stated that such a solution indicates that the student needs help. Now you are injecting race and raising the question of racial bias on my part.

I think if you reflect on what you've written in response to me you'll see that your statements are not supported by the evidence and your accusations have been inflammatory. Your conclusions about me punishing students preemptively, and raising racial bias on my part are false, unjustified, and not called for on this site. It is expected that a higher level of decorum be demonstrated by everyone on this site.

We simply disagree on the topic of grading and that is fine. I don't think further discussion with you will be productive for either of us. I will read any response you have but will not further comment to you. Please refrain from responding to me in the future. Based on this present interaction you are not the sort of person I wish to discuss things with.

I disagree that students should be punished for answering the question asked of them. You think it's acceptable, and you could have even justified it by saying that it teaches trickery and deception. I don't think that's a good way to teach, but I could accept that reasoning.

But that's not the justification you gave. Instead you said it's evidence for likely future wrongdoing. By bringing up race I am in no way suggesting you are racially biased. Indeed, it would have been pointless to bring it up if I thought you were. The point was to give an analogous example of punishment for anticipated future wrongdoing that I assumed you would accept as wrong. If it's wrong in one case it's wrong in the other.

Your intuition about the student's abilities is probably correct, but intuition is no basis for justice. People should not be punished before they've done anything wrong. This is a fundamental ethical concept. The student deserves a fair trial by exam question, not instructor vigilantism.

I have a standard rubric for questions like these, and would have scored the response above 1/5 for an attempt being made with an incorrect or unclear argument. My expectations are very clear.

I disagree with your characterization of grading as punishment. Added value in teaching is about 10% instruction and 90% feedback. If I let this opportunity to fix the student's reasoning pass, I am doing a far greater injustice to them than if I fail them on a quiz.