The title "College algebra" in the US indicates material that is well pre-groups/rings/etc.; it is about the basic skills of computations involving manipulation of variables, often involving such topics as solving linear and quadratic equations, and perhaps inequalities.

At least at my university, the reason that such classes have a high failure rate is that the university is incentivized to have high enrollment numbers by admitting students who do not have the background to succeed at college mathematics at the level of calculus or above, and so need some pre-calculus courses; but someone who does not have a solid grounding in pre-calculus mathematics will often struggle to learn it when it is taught at a rapid pace at the college level—especially by professors most of whose teaching experience is with college-level math.

My high school AP calc course started out somehow getting behind in the first week. After that, the teacher kept assigning homework for material we wouldn't even cover until the day it was already due to be turned in. It was pretty brutal for someone like me who was accustomed to coasting through all of my other courses.

I took a bit more math in college. It wasn't easier; the professor simply kept pace with the material. If you needed help, you had to go to a TA or the professor out of class hours (an option that wasn't really available for a high school setting).

I can easily imagine that many students who were exposed to college level math for the first time in one of those courses would flounder and drop out (though I didn't witness much of it myself).

But what incentivises the students to take a class that so many won't pass? I don't really understand the American university system but surely the sensible choice would be to take a course you're most likely to pass?

I guess its possible to learn stuff from a course you fail, but you should be able to find a course that you're likely to pass and learn something from?

It's mandatory for the degree, that's the motivation. It's typically required for all students who didn't score high enough on entrance exams or take enough math courses in high school. They also likely don't talk to their advisor and say, "I want to take something else, like prob/stat or calculus, to substitute for this requirement." STEM majors will find it easier to substitute another course than non-STEM majors (because they likely have the background to skip it from HS course work). Engineering universities and the like usually send their first year students straight to calculus, though.

It's a "weed out" class. When a huge number of people want to be STEM, but there is no way they're going to last, it's better to have a tough class that sets that expectation early, so they have time to pursue a more achievable major. In my case, huge State university, Freshman year Physics was the weed-out class. It was not advanced or (to me) particularly difficult, but there was a LOT of content, we moved very fast, and the workload was punishing. If I recall correctly, our first class was over 1000 people in a huge auditorium forum. By the time we took final exams, we were down to around 100 people.

So the 75%+ who don't pass this course don't graduate or what? They have to change degree?

I've never heard of so many failing a college algebra course, at my second university it was around 25% failing and mostly because they'd relaxed the entry requirements in order to increase enrollment.

However, for non-STEM and non-Business majors college algebra is rarely a prerequisite for any other courses so you can still continue your major without it, you do need to pass a math course before graduating though. They also have other math courses that can be used that aren't college algebra and may be easier.

At my university, CS was called math-CS, it required intenses calculus courses with a similar failure rate.

Of those who failed : ¼ retook the course, ¼ pivoted to the bussines-CS program (given by the CS department) , ¼ pivoted to bussines-IT (given by the business and management school) and as far as I know, the rest disappeared from the university.

> Stuff like basic groups/rings/fields or is it a more advanced class?

No, it's usually basics like functions, graphs, and trigonometry. It's basically a remedial class for what students didn't learn in highschool.

Maybe I'm massively out of touch but I'm pretty sure a good teacher could teach that stuff to almost anyone.

Like this stuff isn't particularly complicated, I'm not a very good teacher but I did teach some undergrad seminars during my PhD and I think even my worst students were capable of understanding functions, graphs and trig.

That's not the issue. College algebra courses are super compressed, they're basically trying to teach the whole of junior high + high school math in a single semester. That's barely teaching, and the natural outcome of such a cursorily taught course is to act as a 'weedout' course.

Yup. My observation (having not had to take College Algebra myself, but knowing people who did) is that it's a class to make sure people who fell off the math train back at operations on fractions or factoring or whatever, don't get any farther.

I was a tutor in business school on behalf of the MBA program. Basically, there was a small group of students who were... not prepared with respect to math. We're talking really simple algebra, maybe the simplest of differentiation (e.g. maxima of a simple quadratic function).

One of them told me one day "I don't understand graphs." I tried but it's impossible at that point to make up for an apparent total lack of at least high school level arithmetic/math.

I mean, what do you want them to do? Invest resources in splitting up material into multiple courses when they should have learned it before even coming to college? It's not their fault public schools suck.

State universities kind of do have this responsibility. My school is doing more or less this, restructuring some of the math sequences that have a high failure rate, like precalc/calc 1.

Also state universities are where most of the public school teachers and administrators trained, so they probably deserve a little of the blame for the state of public schools.

IMO the only stuff a student "should have learned" is stuff that they can't get onto the course without knowing. Allowing someone onto the course, for which "x" is a prerequisite, who doesn't know "x" is entirely the university's responsibility.

All public schools do not suck but especially urban schools can have a lot of problems and many of the students don't have a great home environment either,

You are in touch with your kind of people, the kind who graduate from university.

If you were doing a PhD you were at the kind of university that has a PhD programme. Probably it was one of the 200 or so US universities out of a thousand that are selective, rejecting more students than they accept. I doubt there was a single student in your seminar who wasn’t in the top 30% by academic aptitude of their age group.

> According to the U.S. Department of Education, 54% of adults in the United States have prose literacy below the 6th-grade level.

https://en.m.wikipedia.org/wiki/Literacy_in_the_United_State...

I would assume that class that is described as:

"4 hours a night 6 days of week and I got a C. Less the 25% made it to end. Don’t think many of remaining passed.

Got a lot out of it though."

Actually is abstract algebra and not highschool level. Nobody teaches remedial classes in such a way that only 25% make it to the end.