I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation.

I don't know how it is in the Math department, but in Physics there is almost a sort of hazing that goes on, where some subjects are just known for how grueling they are and how you just have to go through it

"To the contrary, we are delighted when someone shows even a spark of interest or aptitude" Not to read too much into it, but this kinda hints at the problem. You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut. The true horror is how many students are in the class and not getting it. And the teachers are not freaking out

From my university experience (which was a while ago) it was abundantly clear that most students hate their math/physics classes, were bored out of their skulls and the teachers are only interested in the engaged students that are getting it.

What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class

I don't know why you're catching downvotes, I think you're completely right. In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

Professors of undergraduates don't seem to think from the undergraduate perspective. Most undergrads have only ever known school, and are just following directions while fumbling their way to their first interview. From that perspective it doesn't make any sense why some classes have to be immensely difficult and high-stakes, and others can be a little easier. From the graduated perspective, you can see "the big well-intentioned lie"--in truth, no field can be condensed into 16 weeks, even if you're studying it and nothing else 14 hours per day. The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine. However, I don't see why this lesson has to be so painful to students.

I mean, have you ever taught a class? Do you know how it feels when we make sure a topic is covered both in class and recitation with plenty of time for questions and the students still stuff it?

No, I've never taught a class, so it's possible that the experience of teaching as a professor would irrevocably change my opinion. However, I have spent a lot of time tutoring math and directing bands and choirs, so I'm familiar with the frustration that comes from explaining concepts and then assigning necessary work with plenty of time to do it and then having people still show up unprepared.

I believe that there is a negative feedback loop in the current model of schooling: unprepared students produce jaded instructors produce unprepared students. The big problem with the current lecture method is that any interruption of the momentum of the course for the students' own personal benefit comes with a social cost, so it's better to just shut up and pretend you know what's going on. Furthermore, many lectures build on themselves, so if you misunderstand a concept at minute 3, by minute 20 you're checked out and by minute 50 you're clock-watching. That's why so many math lectures are silent with the exception of the occasional interjection from a star student.

Combine this with the fact that most students are insufficiently prepared for course material in the first place and you end up with modern STEM college: kids who don't get the material slogging through piles of completion-based assignments and exams and putting in the minimum amount of work to get the degree, after which most get the exact same job they'd have gotten if they'd worked harder anyway. They're almost incentivized against deep examination of any one topic, because all time spent working on one assignment incurs a cost against other assignments, or against leisure.

There are so many issues with the way education works at scale in the first world that going down any pathway would take a thousand words, so I'll sum up by saying that I believe that you have a point, and I also believe that the majority of undergraduates are underprepared, entitled, have underdeveloped work ethics, and lack both the discipline and drive necessary to really get something out of their education. However, I still think that the extreme burn-out classes cause more detriments to higher education than they bring as a whole.

> In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

While there's no excuse for it, I think faculty see so much apathy on such a regular basis that sometimes it's easy to mistake sincere struggle for a lack of desire to engage. For precisely that reason, I try very hard to recognize and reward my students who are willing to take the time to work with me, whatever their existing comfort or proficiency level with the subject is, but I know that there are times (probably many more than I'd like to imagine) when I don't rise to that ideal.

> Professors of undergraduates don't seem to think from the undergraduate perspective. … However, I don't see why this … has to be so painful to students.

I think you might underestimate how painful it is to faculty, too! Most of us are in this for the love of our subject, and many are even in it for the love of teaching, and it's painful to have something that's so beautiful and beloved for us be the cause of suffering in others.

Anyway—while I completely agree that it would be better if the learning experience could be the joy it should be, and free of the pain that it often carries, I do wonder if some of this might be intrinsic. There are certain topics that are just difficult, and on their first encounter with which most learners will find themselves lost and confused. But those topics have to be, or are believed to have to be, understood to be successful in the field, so that loss and confusion will have to be felt some time. Isn't it better if that's in the classroom rather than on the job?

> The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine.

This is a beautiful description. I know as a teacher that I try to communicate this to my students, but also that I surely fail much more often than I succeed.

> This is a beautiful description. I know as a teacher that I try to communicate this to my students, but also that I surely fail much more often than I succeed.

Thanks. There's an element of hopelessness in trying to explain the immensity of human knowledge to someone who's lived their entire life captured by mandatory schooling. It's just not an interesting thought to most of them. Their worldview has been so artificially limited that attempts to explain the limitations of their circumstances just appear to be more limitations. "Guys, there are more than six hundred thousand mathematicians working right now in the US, and they're working with concepts first thought of as long ago as 3000 BC and maybe earlier!" "Okay, will that be on the test?"

> Isn't it better if that's in the classroom rather than on the job?

If only we were having this conversation in a bar instead of a text forum. That's a huge question and it's clear you're actually interested in talking about your thoughts on it. It's also a subject that interests me.

When you say:

> But those topics have to be, or are believed to have to be, understood to be successful in the field,

I think that's where the big disconnect comes from. What's the point of school? Is it to know enough to be useful at a job, or to plumb the depths of knowledge? Is it some third thing? Ask any recruiter and they'll tell you the new hires aren't prepared to actually do anything useful, and ask any advisor and they'll tell you the new graduate students aren't prepared to actually do anything useful, so we can at least conclude that there's some kind of disconnect going on. Students spend thousands of hours and hundreds of thousands of dollars doing something that does not actually adequately prepare them for what people want them for.

I have a hundred different ideas about how to address this. One thought I've been mulling over recently is that a redefinition of grades is in order. From essay that we're commenting on:

"My colleague’s error consisted of believing that the more testable the material, the more teachable it is. A wider spread of performance in the problem sets and in the quizzes makes the assignment of grades “more objective.” The course is turned into a game of skill, where manipulative ability outweighs understanding...

In an elementary course in differential equations, students should learn a few basic concepts that they will remember for the rest of their lives, such as the universal occurrence of the exponential function, stability, the relationship between trajectories and integrals of systems, phase plane analysis, the manipulation of the Laplace transform, perhaps even the fascinating relationship between partial fraction decompositions and convolutions via Laplace transforms. Who cares whether the students become skilled at working out tricky problems? What matters is their getting a feeling for the importance of the subject, their coming out of the course with the conviction of the inevitability of differential equations, and with enhanced faith in the power of mathematics. These objectives are better achieved by stretching the students’ minds to the utmost limits of cultural breadth of which they are capable, and by pitching the material at a level that is just a little higher than they can reach."

At the undergraduate/introductory level, the only important question is "what awareness do you have of the breadth of this field, and what mastery do you have over the concepts that most agree are its "most fundamental"? You and I both agree that class is a "playground", and any "grade" is in fact meaningless. Rather than assigning As, Bs, Cs etc. as a percentile of subjective completion of arbitrary problem sets, As-Fs should be assigned at the discretion of the instructor as a holistic assessment of oral and written examination, completion of problems and problem sets, participation in the class, and general wisdom.

Students would of course resist this. They want to be graded on impartial, meaningless criteria. That's how they're taught from third grade, and it's the method that allows for the least possible interaction with the material. The only reason they want these grading criteria is so they can plan to spend as little time as possible on the class. This method of approaching learning simply has to be broken at every level of education. You shouldn't even have a GPA until college.

> At the undergraduate/introductory level, the only important question is "what awareness do you have of the breadth of this field, and what mastery do you have over the concepts that most agree are its "most fundamental"? You and I both agree that class is a "playground", and any "grade" is in fact meaningless. Rather than assigning As, Bs, Cs etc. as a percentile of subjective completion of arbitrary problem sets, As-Fs should be assigned at the discretion of the instructor as a holistic assessment of oral and written examination, completion of problems and problem sets, participation in the class, and general wisdom.

I'm not completely sure I agree that this is the solution—if we're re-inventing grades anyway, then I'd like to do something more radical than using the same old A–F and just interpreting them differently (although, even if given free rein to do whatever I liked, I don't know what I would do!)—but I definitely agree that grades, and the standard approach to them, are the most pernicious part of "education" (in the sense of the current schooling system). If there were any way to get away with it, then I would be happy to—indeed, I would prefer to—have all evaluative exercises be diagnostic and informative, only for the students' benefit, and to assign no grade at all, or an A for everyone; but this seems incompatible with a modern university structure (and anyway is essentially forbidden by university administration).

> You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut.

That's because happy students are all alike, but every unhappy student is unhappy in their own way. It's just not feasible to care in depth about why any one of the 70%+ is not learning effectively. They're probably missing some prior topic that's effectively a prereq for the class, but that's something that should be addressed by the student themselves.

> What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class

You are right, and I am! I don't think that's incompatible with also being delighted when someone shows interest or aptitude. In fact, the synergy is the best part, when someone shows interest or aptitude because they are willing to put in the work to follow the pathway that I have tried to open up for them.