Does that make funding infinite?
No but it does illustrate we have plenty of money to spend as a nation if we really wanted to. Hell, even closing "loopholes" (they're flawed by design, see: mining tax, etc) would bring in a shitload of funding.
Polo dealt with the difference between fact and opinion enough for me not to add my own comment on it (i'd basically be restating it).
When a larger portion of your wage goes to the government than is dedicated to your housing and services, that (in my opinion) is a high enough tax rate.
It's funny you say services there too since so much tax money goes towards providing said services for free or at low cost. Police, fire, post, safe food/medicines/water, health care, education, infrastructure. The rich have more so they pay more, its as simple as that.
How am I advocating eugenics? I'm just talking about the reality of the cycle. You say yourself "the socioeconomic advantage inherent in these schools which provide most of the boost". I don't necessarily agree with the "most" part, but that's I'm talking about: it's not just the quality of the school that creates the divide, but the parents and the home environment also. I'm not trying to be elitist in this argument, it's just realistic.
It's quite simple, we need to fix the socioeconomic divides. I acknowledge they exist, i acknowledge wealthier homes are likely to produce better educational outcomes, which is why i advocate a more equal and fair distribution of wealth. I bought out the eugenics thing because it came of to me as elitist and suggesting that rich people are somehow genetically superior or have some innate superiority when really, the thing that set them aside from the pack, by-in large, was being born into a rich family.
Sure, increasing funds for public school's may improve their performance. But ultimately, it's impossible to bridge the gap in the quality of education provided at a public school compared to a private school. The amount of extracurricular activities that private school's provide due to a surplus in funding can never be matched by a public school.
But in terms of extra-curricular activities, sporting facilities and the like, it would take a looot of funding to catch up.
One does not need swimming pools or an orchestra to be well educated. Pretty grounds or nice architecture isn't needed either. Depending on the nature of the extracirricular activities, they boil down to just not being all that important.
In reality though, if you are bright enough you can easily squeeze your way into a scholarship/selective school (Not that this means that everyone else doesn't have the right to a high quality education).
So a few escape while the rest have to fight for scraps? This isn't a satisfactory or fair condition. Also, keep in mind, before these kids pick up a pencil or open a book, their future has been somewhat predetermined by their economic background. Before they even attempt a scholarship test, their economic background has affected their prospects. It's no accident that even selective schools have a disproportionate amount of middle class/upper class children. It's not so easy as having academic talent and sitting a test when the very odds are stacked against you to do well in that test in the first place.
Ultimately, the root cause is (partially) socioeconomic factors. We will never fix this issue unless we fix the socioeconomic inequality in our society. You can tack on all the band-aids you want but those don't go to the root of the problem. Failing that, quota's should be introduced into these selective schools to ensure a more representative mix, not only that middle class/upper class parents are tutoring their kids into these places so they don't have to pay for a private school.
If there was no difference between public and private school's, there would be no reason for private school's to exist.
Why should there be a reason for them to exist? You say it like its a crucial element of our society that private schools have a reason to exist.
All private school's provide is a secure option for well-off families, so that they can know that their children will have a decent education, and that they will be taken care of. Obviously there is a price to pay for peace of mind
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They provide a place where well off kids can hang out with each-other and be isolated from the rest. They're inherently exclusionary and elitist. Scholarships are but the scraps they hand out (not entirely out of altruism either, they may do it to boost their academic standing by poaching kids from other schools).