Yes, there are many opinions on this thread, and this fact supports an observation:

The 'theory' or 'principals' of what 'education' should be are a MESS!

One of the posts mentioned Dewey: Yes he wrote:

John Dewey, 'Democracy and Education: An Introduction to the Philosophy of Education', The Free Press, New York, 1966.

although this is clearly not nearly the 'first printing'! Since my father was in education and had some influence from Dewey, I read that book. Dewey summarizes what 'education' actually is, and, really, is essentially forced to be, all other theories or principles aside, as just:

What the older generations pass down to the younger generations, with a lot of what was wrong and, hopefully, with some improvements.

So, here's an 'application': If have a broad 'public' education system where use essentially just a broad sample of the older generation to teach essentially everyone in the younger generation, then have to expect that what gets 'passed down' will have nearly all that was bad about society in the older generation and relatively little that is new and advantageous!

Here is a telling example: I was a college professor at Ohio State University. At one point I was asked to represent the faculty at a lunch for parents. Yes, many of the parents were quite skeptical of what was being taught or not taught. So, one question went:

"Why are you teaching my child calculus? I've never needed to know it."

I was a bit slow to see all the emotional, social, educational, and rational issues and, not wanting to say something wrong, said next to nothing. In a sense, it can be safer not to argue with 'the customer' or with a poorly informed and angry question. But here is what I might have said:

"We're trying to educate for the future, say, teach things that can be useful at some points over the next 50 years or so.

"Calculus is a pillar of Western Civilization: Although not everyone uses it, without it we would be in deep trouble in strength of materials, design of structures, electric power generation, distribution, and use, electronics and essentially everything involving electro-magnetic waves, engines of all kinds, airplanes, essentially everything in mechanical engineering, nearly all more advanced military technology, and in many subjects from more in math, all the physical and social sciences, statistics, finance, and more.

"We're not necessarily trying to teach what is already in very common usage but what is less well known and can give an advantage over the next 50 years. So, from its track record, calculus looks promising. That is, we believe that so few people know calculus well that more people could get an advantage from knowing it.

"For a specific example, before my graduate studies, I was in a new, rapidly growing company. At one point the Board of Directors wanted some projections of the revenue of the company. Many people could describe hopes, intentions, assumptions, dreams, etc., but there was a lack of anything with a more solid, objective, rational basis.

"While I didn't want to get involved, I thought for a while: What do we know? What do we want to know?

"Well we knew what our (daily) revenue was then. And, from our capacity planning, we knew what our planned, eventual daily revenue would be. So, for the projections the Board wanted, essentially we needed to 'interpolate' between these two revenue figures, that is, say how fast we would grow.

"So what could we observe about what was causing our growth? Well, broadly the growth was due to 'viral' effects, that is, happy customers talking to target customers not yet customers. So, each day in the future, the amount of this 'talking' by happy customers was proportional to the number of happy customers and, thus, to the revenue. And the number of potential customers hearing the talking and becoming customers was proportional to the number of potential customers.

"So, let t be time in days with the present day t = 0. Let y(t) be our revenue at time t. As in calculus, let y'(t) be the first derivative of y(t), that is, the rate of growth in y(t).

"Let b be the maximum daily revenue from our capacity planning.

"Then the rate of growth y'(t) is proportional to the current revenue y(t) and the capacity yet served b - y(t). So for some constant k, we must have

y'(t) = k y(t) ( b - y(t) )

"So, this is a non-linear ordinary differential equation initial value problem. With a little calculus, really just classic integration by parts, we can get a simple algebraic expression for the solution. This solution will have one constant c we so far do not know. But we have reduced the problem of projecting out to the future to selecting just one constant c. And we can estimate c from our growth over the past few months.

"So, on a Friday my SVP Planning and I selected a value for c and drew the graph of the growth. My SVP left on a business trip, and the Board meeting started the next morning.

"At noon I was in my office working and got a phone call to come to the Board meeting.

"The Board meeting was in disarray and no longer 'meeting'. Our two Board representatives from our main investor were unhappy and standing in a doorway to the hall with their bags packed.

"At about 8 AM the graph had been presented to the Board, and the two investor representatives asked how it had been calculated. For the next three hours or so, all the top management struggled to reproduce the graph and could not. The representatives then became angry, lost faith in and patience with the top management, made plane reservations back to Texas, returned to their rented rooms, packed their bags, and as a last chance returned to the offices for an answer.

"I arrived, reproduced a few points on the graph, and the investor representatives canceled their plane reservations, unpacked their bags, and stayed, and the company was saved. It is now a major company you know well and have used often; you value their work highly.

"This success was all because I knew calculus well and was about the only one there who did.

"So, we believe that in the next 50 years, calculus can be an advantage."

Yes, there is some question at how well even this answer would have been received!

Generally, then, in the real world of the broad population, it is difficult to know what to teach, how to teach it, or to get it learned!

Here's my take on the US 'way out': As we can tell, in K-12 and maybe more, the most important educational advantage is the family life of the student. So, in some families, education is understood and emphasized. So, education is really not just from the K-12 classrooms, not nearly!

Broadly, then, the secret to good education is to have parents who care do what they can at HOME. In extreme cases this solution can be just 'home schooling' and, at its best, can totally blow the doors off essentially anything from 'organized' education.

So, as in many things in the US, really good results are the responsibility of each individual, their family, their local community, etc. and much less well served by the county, state, or DC.

Topics with big advantages are essentially necessarily understood by at most only a tiny fraction of the population. Or, if a large fraction of the population understood, then much of the advantage would be gone. So, education with big advantages cannot be from the public school system! Sorry 'bout that!