I haven't; I freely admit that what I'm talking about would never work in a classroom. That is why I also believe that it is the classroom model itself that is fundamentally flawed.

I think we could get into an endless debate here; I would say that the classroom model is a symptom of a post-industrial society where everything must be compartmentalized, sorted, and certified by a governing authority, which thus destroys the human connection with all of human endeavor; you, and I apologize for putting words in your mouth, would likely say that we never could have gotten to the point of a post-industrial society where you and I could debate the merits of industrialized math education on the internet without the classroom. Assuming my projection of your argument is accurate, I'm not even sure you're wrong.

It's just that whatever they're teaching today is bad, and I think it's worse than not teaching it at all. People come out of school and college technically skilled but intellectually hobbled. I don't know if the system itself can fix that, or even if it should be fixed.

As a starting reference, I mention "the Seven Lesson Schoolteacher": http://www.uvm.edu/~rgriffin/GattoDumb.pdf

Well, my experience is that the way it's being taught is the sort of an optimized version of teaching math given the culture/desires/abilities of those students that hover around the median. I've tried all sorts of things to motivate students and to teach them the why and purpose of the topics. You know what most of them want? What formula/method is used for which problem type.

I'd dare to say that by that point, the system had already killed any remnants of intellectual curiosity the students might had, and replaced it for the obsession with marks and passing exams that predates the system.

I don’t believe this is the reason. I think people in general don’t want to go through the intellectual pain required to understand. I think the system in k-12 is as it is because it maximizes the outcome of getting the most people to the point of having some understanding. The obsession with marks is the thing that leads to this outcome. Most certainly won’t go through the pain of learning without some gamifying the process.

I don't think we three necessarily disagree; we are alleging that the system causes people to be afraid of intellectual pain by virtue of its structure. Students feel the pain of schooling, in the form of shame and suffering, and assume that that is what intellectual development feels like, and that smart people are simply people who can endure more of it. Compare impersonal mass calisthenics to team sports workouts; both are painful, but the calisthenics are also mind-numbing.

As a college instructor at a community college, you're teaching math to people who likely have spent their whole lives watching other kids easily ace exams that they struggled with, who have never spent any of their genuinely free time doing math, and who just want to be let out of school. They are products of the system.

Granted it was many years ago, but I taught one semester of "college algebra" at a state university. My experience was similar to yours.

To be fair, they did admit that they “don’t know how to teach math”...

To be fair, I don't either! I missed that part. Thanks for pointing it out.