This is a very, very long post.
There's a lot that I feel I ought to reply to here (I'm one of those unsatisfying-to-argue-with hedonic utilitarian moral realistishs (kinda)) and I think Pearce has a point or two (though I've talked with him about our many differences of opinion).
But it's a very, very long post.
Imma have to pace myself.
BJ Novak in "One More Thing, Stories and other Stories" has Stories (surprise surprise) about this - from a principle who decides (on principle) - fuck it - no more math, to a summer camp run by an eccentric genius for gifted kids to do drugs, have sex, and have fun while avoiding paralyzing levels of self-awareness. It's very refreshing fantasy.
l could easily write about this topic for literal days.
At 16 I tried writing my own choose-your-own-adventure math hypertextbook (US middle to high school algebra and geometry - "common core"), only to be stymied by a vast swath of misty unknowns. Who needs to know what? How deep? To the foundations or just to do some particular task? Why? How do you know if someone has learned the deep ideas? Is it just a novelty effect you're seeing? Is that a problem? How do you structure infrastructure to optimize for the ideals of a fractious mass in a decade-long person manufactory/child jail to fuel the economy with educated workers And democracy with educated citizens And keep millions upon millions of vulnerable serfs with no legal liberties interested and happy and healthy and not shooting each other while ruled over by underfunded low-IQ taskmasters who can't educate without incurring excessive bureaucracy to get extremely overworked students to be competitive in getting to collages that usually don't work.
I was an afterschool math tutor at Mathnasium. I was in the strange position of working at a service business for whom the vast majority of our direct clients did not actually want our services. The only other example I can call to mind is private prisons. That fits very well with my own extremely depressing and disempowering, suffering experience of my ten + years of mandatory education. I was not legally allowed to leave the building without exceptional circumstances and the permission of a superior.
Improving education is an absolutely bizarrely ridiculously hard problem.
The feedback cycles to know if someone has retained their schooling are typically very, very slow. Gamification and digital tracking of activities is useful for this - but remove students from the on-the-ground gears-level problems that their education is supposed to help them solve. This is where I first discovered the idea of an alignment and control problem, in the context of the classic "as soon as a measure becomes a target it ceases to be a good measure". Grades, though empirical, are shit tools for determining how and if things are working - and why they aren't. In math, kids almost always don't know how even to try to solve real-world, unfamiliar problems they haven't already been taught step-by-step how to solve. During exploratory periods of development, children in many places have almost no autonomy over what happens to them or what they do during an average day. This is catastrophic for the development of learning people.
What if it's not transitive?
Wouldn't that kinda throw a wrench in the idea of modeling it as continuous scale?