Selection bias is the most powerful force in education

Theoretical knowledge is absolutely extremely useful, but the way we teach it is pretty much a non-starter.

We need to humanize our education systems. The concept that we all sit around in school for 20+ years and then go out and find something to do with all of that knowledge is based more on maintaining rigid financial/power structures than it is based on effective information discovery and utilization, and there's no reason that a useful piece of information recovered partially-intact from the caverns of memory here or there should continue to justify such a lumbering, monolithic system.

There are no guarantees that the system will provide even what you've enjoyed; as you said, a peer with similar education had either not been taught or had not remembered the needed concept.

Humans need it "on-demand". We learn and master a trade experimentally, most naturally in the context of an apprenticeship. We can't compartmentalize book learning and practical employment, putting years-long gaps between them, and expect the eviction algorithm in peoples' brains to have not pruned much of the relevant information. We need it cemented with immediate, meaningful, recurring experience, and we need systems that will make it easy for us to remember and reference as necessary.

The existing educational apparatus is none of this. It is just a cash cow for the banks and universities, enslaving most of its "graduates" to decades of debt servicing. That, IMO, is the primary reason it continues to be enforced, because there is very little that is rational about it.

Likewise, as an EE I studied differential equations, La Place transforms, z-transforms, s-transforms, the fourier transform, and the dft transform. I'm a digital logic designer and have never had to directly do any of that stuff, but understanding the duality of time domain and frequency domain has been invaluable to me over the years.

You are rambling. I do not mean that as an insult, just as an observation that might help your writing. Maybe you could do it like (1) Get a book on writing. (2) Read the book. (3) Do the exercises. Seems to work for you.

However, the way you learn best doesn't have to be the way that is best for everyone else. See, when I took calculus in high school, I (1) Got the book. (2) Flipped through it in an afternoon. (3) Decided the exercises were too simple to bother. (4) Went to school where the teacher said the book was worthless and he wasn't going to use it. (5) Graduated high school with credit for freshman calculus due to an agreement with the local university. My point: if you are smart and have a good source of knowledge, it doesn't matter whether it's a book or a teacher, you're going to learn something.

Now, what happens to people who aren't smart, but try to do (1)-(2)-(3) anyway?

First they have to do (1) correctly. You mentioned there are plenty of old, good, cheap books available. I mentioned that the book I got was not good. (It wasn't old or cheap either.) Do you know of a place that aggregates recommendations for the right books to get?

Second, they have to do (2) correctly. Reading a book is simple, right? Except if it was written in by someone who knows their stuff, but doesn't really know which parts are hard, because they all seem equally easy. So the average high school student is going to get stuck on a sentence like "Obviously, a convex polytope in R^n is just a finite intersection of closed half spaces." because they have trouble remembering what all those words mean and where they were defined. Add to that that they might not yet be comfortable with intuitively manipulating the underlying concepts, despite doing the exercises.

(3), the exercises. Consistently high-quality exercises are hard to come by. (Again, if you have any recommendations ...) I have seen exercises that introduced a new concept just to be able to define the problem. I have seen exercises that included a hint for an intermediary step to the solution, except the hint could only be arrived at by a mistake in the correct derivation.

If a student gets stuck somewhere along the way of doing (1)-(3), what they need is someone who can find out what the student doesn't yet understand and then explain it to them. Essentially, a teacher. If you have the necessary perseverance, you can probably replace the teacher by trying other books until one has the right explanation to help you across the hurdle. Most students would probably still prefer a good teacher.

Ok, most teachers aren't actually good. But most books aren't actually good either. It all comes down to being able to select the right ones.

I'm not a fan of bussing. It is unfair to the good kids. "Bad" kids know how to deal with other "bad" kids. They grow up in that environment and know the rules of the game.

Good kids grow up in a different environment. The consequences of not knowing to handle oneself around "bad" kids are very high. There is no doubt that on average "bad" kids are much bigger bullies with lower empathy.

The consequences of not knowing how to conduct oneself around good kids as a "bad" kid are much lower in severity. For the most part, the parents of good kids set limits to the aggression of their children. For example, the biggest social rejects at my upper middle class schools weren't ever really bullied. People pitied the complete rejects and most people thought anyone who would bully the rejects is a complete douchebag.

I can't imagine how the social rejects or even the normal nerdy kids at my high school would have fared at a "bad" school.

Then there is the minority immigrant issue. Segregation is good for certain minority groups that do not have the language skills and cultural knowledge to integrate into America. They segregate themselves into a separate community that can provide support for its members. Desegregating these communities and their children will have negative effects.

The children of these immigrants will have the worst time dealing with the "bad" kids because they may have stunted language skills and lack cultural knowledge and context to be able to effectively navigate bad situations.

And to get a better picture of the winners and losers:

- > 90% of African Americans are born in America (and presumably have parents, family and connections who know English and understand American culture).

- Spanish is ubiquitous in the USA and the Hispanic population is huge. Hispanic people have a much lower need to congregate into a community compared to other minorities.

I think this depends on what you frame what an opportunity is. Giving everyone the opportunity to try and meet a certain criteria in order for you to accept them into whatever job/institution you represent is a binary opportunity in theory. They'll either meet the criteria or they won't. If you frame being able to cultivate the skills to meet your criteria as being an opportunity in itself then that negates your offering as being an 'opportunity'.