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Comment by jcranberry | Hacker News Reader

I'm certain they grade homework and return it.

Right, but at the pace that many of these courses go, and with how the material continually builds throughout the semester, not getting answers until a week after the quiz, and hence two weeks after the lecture taught the material, is setting up a lot of people for failure.

By having access to multiple worked examples of problems, students at least have a fighting chance of learning how to solve problems _in parallel_ with the course material, rather than having to wait days or weeks to even know what they did wrong, while getting more and more lost.

Remember, these are Princeton students, some of the most brilliant and motivated minds of their generation, and the averages are _abysmal_. That indicates there's a greater systemic issue.

Unstated premise: the most brilliant and motivated minds of their generation ought to all be able to grasp mathematics. I for one don't believe this premise. University level mathematics requires a level of abstract thinking that most people are simply incapable of.

I respectfully disagree. Learning mathematics is just as much a craft as learning an instrument, or how to paint, or how to write prose, or how to layout a PCB; it requires a lot of hard work, but if you're consistent AND have the right tools, you can learn it just like any other subject.

Believe it or not, the number of practicing mathematicians and PhD students who have the innate grasp that a Terry Tao does are few and far between. The vast majority have to work hard to earn their skill.

Someone who is tone deaf will never be proficient with a violin, or a theremin.

No amount of hard work would have allowed Stephen Hawking to succeed at sports.

Some pursuits are simply unavailable to those without the requisite immutable attributes. This is not politically comfortable, but it is true. I think the only legitimate question is whether mathematics is such a pursuit, and I'd like to be proved wrong on that point, but trying to convince me that anyone can do anything they put their mind to is wasted effort as it is so plainly contradicted by the available evidence.

Note that the contradictions you mention are _physical_ in nature; it is true that there are some functions that some bodies can perform that others cannot. Mathematics is not one of those things.

Is the brain not a physical thing? Do you believe that all human brains are physically and functionally equivalent such that one brain should be able to learn to do anything that another can?

What about those people in this world with genetic abnormalities that affect brain function? Would you expect someone with Prader-Willi syndrome to be able to become competent at mathematics if they only worked hard enough at it? At what point does “hard enough” become “virtually impossible” or even “definitely impossible”?

While I feel your point is incredibly pedantic, perhaps I should have qualified with some form of "at least X% of people that do not have rare genetic disorders can learn math, X >> 50". However, I think such statements are usually implicit when talking in generalities.

Got it. Your previous statement didn't really seem like you were speaking in broad generalities and instead seemed more absolute, like math is something that could always be learned by any human brain. Clearly that's not the case, which was the point of gpp, I think.

> Is the brain not a physical thing?

Why, sure - from the physics standpoint all the human brains are essentially the same, they all consist of the same protons, neutrons, electrons... (Also, they are close enough to being spherical.)

People have wildly different personalities and creative abilities. why do people think the "math part of the brain" is exactly the same in everyone?

> University level mathematics requires a level of abstract thinking that most people are simply incapable of

You're begging the question. Please substantiate.

I had an organic chemistry professor who would not return anything until the end of the semester, homework, quizzes, test, nothing. I had the impression she was a procratsinator and just didn't do the work. It was beyond frustrating. She also got her ph.d from Princeton coincidentally!

One reason for not returning work immediately is it makes it harder to accept late work, because students will share the answers with each other.

The most lenient late policy I've experienced in my (ongoing) university experience has been that you can submit 1 day late for a 30% penalty. Most of my classes lock the dropbox immediately at midnight.

Simply returning work shortly after the late work window closes should suffice, no?

I did this at Loyola New Orleans (an intro physics lab class) and I'll tell you why. I didn't trust the kids to not lose their work. They could come to my office and collect it and if they challenged their grade, I had all the material to hand with me. Online reports were graded on Canvas at any rate.

You made your class educationally worse and blame the students because you didn't ask for a photo of their work?

Canvas had photos of it online - you misunderstand.

> I did this

Glad to hear you didn't actually do that. Returning digitally is still returning.

You might be surprised. My daughter took first year university linear algebra last year and graded assignments and tests were often returned weeks later, in some cases well into the exam preparation period. I told her this was unacceptable and she should complain, but you can imagine why a young, shy first year student might not be able to get over that potential barrier.

Another thing that one might not have considered is the perception of women and math. Of course your daughter might not want to protest against unfair mathematics teaching structures given that her struggle is societally used to represent that all women struggle at math. <relevant xkcd comic here>. I would also hesitate to protest unfair practices in situations where I was a minority because I know anything short of quietly excelling is a negative representation of my entire demographic.

this is an exceptionally bad take imo and seems extremely degrading towards women

> you can imagine why a young, shy first year student might not be able to get over that potential barrier.

If she continues on to functional analysis she can just tunnel through.

Grading the homework is not the same thing as providing feedback. A big red X tells you that something is wrong, but not what you can do to fix the problem or even why that thing is wrong.

Okay, so go to office hours or a math center (if available, apparently quite common).

I certainly don't want to be misquoted as claiming that mathematics must be learned in a vacuum. Just that access to a large collection of questions and answers is not helpful. Your own argument goes through just as well to show that access to the answer isn't helpful either: you know you got the wrong answer but you don't know why.

Sure, you can do that. But from a UX perspective, the system is clearly badly designed.

For proof based homework typically a grader will tell you which step failed with a short note saying why ("this mapping is not well defined", "here is a counterexample", etc)

It is cryptic at times bit ultimately developing rigor and intuition is something that in my experience will always involve a certain amount of struggle and confusion that no professor can or should alleviate

My university certainly didn't in most cases.

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