Parental involvement, for example, is crucial for motivating students, imparting various skills (ie time management, studying) and setting appropriate expectations[1]. This is more a matter of cultural and structural factors. Parents that have the time and motivation to care for their children's education could have a significant effect without worrying about per-student outlays.
Perhaps there's a way to replicate this by restructuring school to provide positive parent-like influences? I don't know, but it's not a matter of throwing money at the problem, one way or another.
[1]: I remember seeing a few studies on this. "Student Motivation: An Overlooked Piece of School Reform" looks like a reasonable overview of the subject: http://www.cep-dc.org/displayDocument.cfm?DocumentID=405#sth...
If instead we had a model that allowed students to participate in an institituion independant network that created classess and assigned teachers based on smaller resource loads, week long classess as opposed to 2 year long courses, we could have a system that much more easily lends itself to individual needs and gives more freedom to all students regardless of income level. This same problem could also be tackled by bridging the teacher-student polarity. Students are very capable of teaching themselves in small groups and acheiving goals at the same rate as if they were with teachers. By removing the teacher from the model you reduce resource costs hugely.
Here students are giving by the system what they put in. By participating and working with multiple small groups of students we build social skills and open the door for more specialized and specific learning at every level, not just the private school. If the digital revolution needs to shake things up anywhere in education its in the model and class structure.
tl;dr:A system that gets rid of large classess and focuses on connecting students to teach themselves can provide the same(and highly effective) educational opportunities to all (at a very reasonable cost).
"Even increasing per-pupil spending in public schools to that of the Phillip's Academies is arguably impossible in all but a handful of the top GDP/capita nations, let alone all the private tutoring and traveling and internships that Johnny has access to."
It is reasonable to expect that we can educate kids at a standard where income doesn't affect outcomes for most folks.
With vouchers applicable to private schools, you don't have to burden yourself with the entire cost or keep him in a school that he/she is not compatible with. At the very least, vouchers amongst public schools seems like a no brainer but I've met a lot of resistance from some friends that are teachers.
The effect of vouchers in the real world is that the best schools get a little bit better while the worst ones get a lot worse.
I'm going to risk calling you out on this, because I think what goes unstated here is that public resources cannot compete with private ones when it comes to education. It's sad to look at Johnny Trust Fund, and see that he is born with a true educational leg up over poor children, and there's really no way around it. If Johnny's parents have the will and motivation to spend hundreds of thousands of dollars a year educating Johnny, they can. I'm sorry, but no country can compete with that. Even increasing per-pupil spending in public schools to that of the Phillip's Academies is arguably impossible in all but a handful of the top GDP/capita nations, let alone all the private tutoring and traveling and internships that Johnny has access to.
So, yeah, if you manage to educate poorer children as well as wealthy children, they would achieve similar university performance, but getting their educational background to parity with one-another is so far out of the realm of possibility for most nations that I don't think it should even be mentioned.