While my experience relates to learning in higher-ed, I completely agree with those three categories... Though a helpful nuance may be that it's a spectrum, not hard boundaries, and every subject/exercise can have a distinct relationship with the learner and context.

When rubber hits the road with a learning objective, I think the two most important axis are: how much does the student want to learn (this), and how easy is it for the student to learn (this)?

Both can depend on a variety of factors... For example a masters student paying their own way mid career maybe really wants to learn as much as they can, but a specific research report assigned during a busy work week, and some family emergency, etc. may mean they treat the assignment as "I just need to get this done" instead of "I want to get as much as I can out of this", and one way that can show up is how much they depend on an LLM to do the work for them...

re: not teaching math to kids is a pet peeve of mine.

the number of adults i've met who cannot add two fractions together is depressing.

at some point each of them had decided "i'm just bad with numbers, hahaha" and they gave themselves permission to stop trying math. worse, society gives you a pass at not knowing math. we need to apply the same constant social pressure to mathematics skills that we do for learning to read.

"Having multiple parallel tracks for different types of students is controversial."

It shouldn't be. The research overwhelming says its a good practice. The type of people who say this type of thing are the exact type of ideologically motivated people who are destroying school systems in blue districts. Ironically this group both hates private schools and creates the environment that pushes parents to pay for private schools. I've personally seen the bad consequences of schools that do this and I know people who aren't here anymore because of it. So please, for the love of god, stop talking about topics you know nothing about.

If we had budgets that allowed for one teacher per ten students, I imagine many problems in education would already be solved.

I'm not the parent comment author, but my guess is that they probably meant persuade or inspire as much if not more than coerce. Most respectful interpretation and all...

Why is it obvious that an educator should do their best to teach a student something even when they don't want to learn? Well for one, it's their job, and two... Children especially are not good judges of which knowledge and skills will benefit them later in life.

In broad strokes, learning leads to better life outcomes just like brushing your teeth leads to better health outcomes, or any other example you may prefer. Brushing teeth is a chore so a child won't generally pick it up all by themselves without some nudging. If you don't do the nudging you're essentially letting a child be free, yes, but also willingly letting them end up worse off when they're too young to know any better. Learning is the same.

We "coerce" children to do all sorts of things. We make them go to sleep. We make them learn to use the toilet.

Why not?

In a way, I think coercion is a requirement to be ethical. Ethics is determined based on what current society believes to be the right thing to do. We see that there are a variety of different cultures and ethics around the world, which would indicate that humans wouldn't just automatically follow a universal set of rules.

Thus to be ethical in your society, usually means you must follow the rules determined by a collective group of your nations ancestors or you will be shunned/jailed/harmed/etc. Which is essentially coercion. "Act this way or be punished."