you shouldn't have students learn things that they don't have the proper foundation for.
I think that in education the problem usually isn't students learning things they don't have the proper foundation for, but rather people disagreeing on the goal of the learning. You don't elaborate your point and so I'm unsure what you mean precisely, so what follows may be a tangent.
Almost all academic subjects - in math, computing, natural sciences, history, literature, economics - have 'foundations' one could learn. In math, these are axiomatic formulations and proofs (as opposed to results), and often complex underlying theories. In computing, these are enginnering artifacts - software and hardware designs, implementations, and algorithms. In the sciences, these are the more fundamental laws of nature (which may be described by a slightly different science), as well as a great deal of organized facts, especially in biology. In history and literature, these are even more history and literature which provide the necessary background context.
One can always point towards a lesson (which isn't at a graduate level) and claim students are missing some fundamental background. So does that mean we shouldn't teach calculus without the underlying proofs, or programming 101 before operating system design, or classical physics before modern theories? That depends on what you want to accomplish.
When I studied undergrad CS, most courses had several versions you could choose from. All freshmen in the sciences & engineering faculties had to take a course on real number calculus, but there were as many as 5 variations, billed as calculus for math, physics, CS, engineering, and biology/chemistry majors, respectively. The math majors spent most of their time (and were tested mostly on) proving theorems. The engineering students studied solving really hard instances of the equations. And the biology students did the minimum and skipped some of the hard proofs entirely.
Did the biology students not "learn the proper foundation" for calculus? That depends entirely on the use they expect to make of it. The tradeoffs of the harder courses are clear: more time and effort spent studying, and more students failing the course and not graduating. (Also, things one learns but never uses are usually forgotten after a few years.)
In many cases it's harder to match up the optimal lesson for the goal. In grade school we studied history. Which historical subjects should be taught? How should the available time be spread across them - studying a few eras in depth, or many on a shallow level? How useful is it, and against what goal should it be judged, to learn about any one historical setting without understanding its causes and effects - what came before and after, what was happening elsewhere at the same time, why people behaved as they did? But any mandatory education system must make centralized decisions about the accepted minimum that everyone should know.
You're right, I wasn't clear enough about what I mean. Sorry.
1) Dependencies often have the connotation of getting deep into theories and proofs, but in a strict sense that's only a subset of dependencies. Like you said, what's relevant is what you're trying to accomplish. I'm completely on board with the idea that a bio major may not need to know all the theory behind, say calculus. But for whatever it is that the bio major is learning, it still has dependencies.
2) Try thinking about it like this: say that the bio major doesn't understand something and i...
Technology has made it easy for us to reach large audiences. And to do so at no marginal cost. If a musician writes a song and puts it on iTunes, it doesn't cost him any money for one more person to download it.
The fact that technology has made it easy for us to reach large audiences has implications on the consumer side of things as well. As a consumer, I can go on iTunes and choose the best music to buy. To understand my point, consider a different world. In this world iTunes doesn't exist. In this world the best music is 200 miles away, but mediocre music is only 5 miles away. Because traveling 200 miles is inconvenient, I choose the mediocre music.
In today's world of iTunes, this doesn't happen. Technology exists that allows us to reach large audiences and to do so at little/no marginal cost. And so, the consumer can (and will) choose the best the market has to offer.
Now for the implications on the supply side. We've already seen that consumers can and will choose the best the market has to offer. "The best the market has to offer" is usually provided by a small number of talented people. Think about it: the best artists, performers, writers, athletes etc. These talented people end up serving a large proportion of the market, and are paid accordingly. This... is The Superstar Effect.
Because of these joint consumption economies, there is a unique opportunity to create and capture value. If you are the best, you capture insane amounts of value. Thus, there is a huge incentive to be the best.
So, should you invest in an attempt to outdo The Superstar and capture this value? Well, investment decisions are all about expected value. Balancing risk with reward. In this case, the potential reward is huge. Astronomical. These joint consumption economies allow you to reach tremendous markets. However, the question is "how big is the risk?".
Outdoing The Superstar is a large and complex task, and I won't pretend to have all the answers. However, I've had this nagging suspicion in the back of my mind for years. My suspicion is that people drastically overestimate this risk, and that with a good plan and enough resources, you could have an excellent chance at "outdoing The Superstar".
Before moving on, let me go through the logic one more time:
Outdoing The Superstar
People seem to view large ventures like starting startups as a roll of the dice. They say things like, "9 out of 10 startups fail". I don't see things that way. I don't see it as "a roll of the dice". I see it as a deterministic puzzle that can be solved.
I should qualify that previous statement. I'm not trying to make a philosophical point, just a practical one. People seem to be afraid of what I'll call, Large Puzzles. Because of their size and complexity, people seem to be put off by them, and they fall back on outside view arguments like "9 in 10 startups fail".
I'll admit that Large Puzzles are complex, but I maintain that with enough resources and with a good plan, a lot of them are very solvable. I sense that a lot of these large joint consumption winner-take-all industries are ripe for the taking, and that with enough resources and a good plan, they can be taken.
My confidence isn't that high though. I don't understand these Large Puzzles well enough to really say. What I'm referring to are "relatively strong suspicions", not "beliefs" (my thoughts are cloudy enough such that I'm having trouble being more precise than this, sorry).
Investing
This is a bit of an aside and a rant, but here we go. Investors currently seem to be heavily biased towards investing in businesses that can be built incrementally. They want to...
Education
The Large Puzzle that I understand best is Education (which causes my System I to care disproportionately about it). I'll indulge myself and say it: the education system today is shit.
I think that Elon Musk said it well. He said (paraphrasing):
I think that this division of resources is really the core of the problem. Things you could do once you pool resources: