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"Sadly, the problems of education in America have been identified since 1955!"
Friedman discusses "underinvestment in education". One can attribute the current problems to its opposite - educational OVERinvestment (and concomitant waste). The problems resulting from these were identified not in 1955, but as early as 1611:
“Concerning the advancement of learning, I do subscribe to the opinion… that, for grammar schools, there are already too many… the great number of schools which are in your Highness’s realm doth cause a want, and likewise an overthrow [surfeit] – both of them inconvenient and one of them dangerous; for by means thereof they find want in the country and towns, both of servants for husbandry and of apprentices for trade; and on the other side there being more Scholars bred than the State can prefer and employ… it must needs fall out that many persons will be bred unfit for other vocations and unprofitable for that in which they were bred up, which will fill the realm full of indigent, idle and wanton people…”
Francis Bacon, in a letter to James I, 1611

I disagree with you on your point that we have over invested in education; we have grotesquely mis allocated our "investment dollars".

At the primary school level, we have done little more than invest in the coffers of the teachers unions. At the secondary school level, we have under invested in vocational schools (big time) and over invested in worthless liberal arts programs. How much money has the government spent subsidizing bachelor's and master's degrees in completely worthless fields, such as painting, psychology, literature, tribal studies, etc. , etc.

Do we really need to subsidize a degree in which the thesis paper is titled: "Homosexuality in ancient Mayan Times", or as I heard on the Glenn Beck Program the other day (this was true) "Lesbian underrepresentation in dolls". Are you kidding me?

I'm in the military. And in the military the government makes targeted investments in education. The military will pay for you to go to school, get a degree and then get a commission (ROTC), but they will only pay (in most cases) if you choose a degree path chosen by the military, such as engineering, aeronautics, physics, political science, nursing, or area studies (like middle eastern culture). Why? Because that's what is needed. And there's no reason why the Government shouldn't do the same things for civilians.

Have you ever heard of the "engineer gap"? Well, it's a huge problem that's rarely mentioned. Simply put, Americans are going to secondary school in higher and higher numbers, but they're no longer getting engineering or mathematical degrees. Asian countries, particularly China and India, are producing engineers at an alarming rate (particularly China, and many are concerned about the longterm strategic implications of this). If we only paid for degree paths in fields the economy is sorely lacking in, such as engineering or advanced computer sciences (why do you think Indians are getting boatloads of work visas to come to the US? Because there aren't enough to do the job!)