Sure you can, it's been done, it's not rocket science.
The problem with today's school system in America (and likely elsewhere throughout the industrialized world) is that it's very much aimed at teaching the wrong people the wrong things in the wrong way (and that's when teaching doesn't take a back seat to day-care). The main goal is for everyone to memorize as much of a broad swath of "material" as possible, it's very much a teaching-to-the-test least-effort system. It's not geared toward maximizing each individual student's learning. Nor is it geared toward teaching competency and fully mastering basic yet key skills. Nor is it geared toward teaching useful skills that are key building blocks in the workplace, as a member of society, and as a functioning citizen of a democratic republic.
The steps necessary to improve this situation are fairly straightforward. As a start, reduce class sizes and hire better teachers, which is possible without increasing per-student expenditures provided the bloat in non-teaching staff and unnecessary expenditures is cut back (per-student spending has more than doubled in the last 3 decades, adjusted for inflation, the money has not gone to improving education, it has been frittered away). End the farce of overstuffed curricula. There is a monomania about covering as much material as possible, so long as students can retain enough to pass a test, but students don't retain much of the material and when the fundamentals are neglected they miss out on that too. Take the basics back to basics, emphasize the fundamentals (reading, writing, mathematics, fundamental science), learning them, knowing them, mastering them. Continue to refresh and test students on those fundamentals throughout their entire K-12 educations. And provide enough funding to allow gifted students to work at a faster pace, either within existing classes or in classes of their own.
I could go on, but that's a good start. Unfortunately, the biggest impediments aren't knowing how to improve, it's all of the interests and bureaucracy protecting the status quo.
You make many assertions, but you haven't provided any reason to think that your approach is any better.
As a start, reduce class sizes...
This, in particular, is something that I've done a fair amount of research on. Although the jury is still out, the best conclusion I've been able to arrive at is that for most kids, class size isn't strongly correlated with achievement, at least not within a reasonable range. Class size only seems to make an appreciable difference for kids that are "at risk", i.e., those that don't get much academic support at home.
So I might be jumping on you for just one small aspect of your opinion, but from the part of it that I do know about, I have the impression that you're just jumping on board with conventional wisdom that hasn't had much testing.
You might be able to improve some things like this, but to deliver it as a factual answer is a disservice.
I was unclear: I meant that it's strange that people complaining about the educational system both criticise it for being 'aimed at the best' and simultaneously for being 'aimed at the worst'. I wasn't saying it couldn't both be true, but if it was, they wouldn't be complaining about a single extreme being the case.
Seems likely that it is "aimed at the average," and the complaints come from people who notice the "better" side or the "worse" side not being served and complain accordingly.
I'm curious what spending bloat you are referring to - because hiring more and better teachers is limited by money. It's limited by other things, too - such as figuring out a reliable metric for "better."
The problem with today's school system in America (and likely elsewhere throughout the industrialized world) is that it's very much aimed at teaching the wrong people the wrong things in the wrong way (and that's when teaching doesn't take a back seat to day-care). The main goal is for everyone to memorize as much of a broad swath of "material" as possible, it's very much a teaching-to-the-test least-effort system. It's not geared toward maximizing each individual student's learning. Nor is it geared toward teaching competency and fully mastering basic yet key skills. Nor is it geared toward teaching useful skills that are key building blocks in the workplace, as a member of society, and as a functioning citizen of a democratic republic.
The steps necessary to improve this situation are fairly straightforward. As a start, reduce class sizes and hire better teachers, which is possible without increasing per-student expenditures provided the bloat in non-teaching staff and unnecessary expenditures is cut back (per-student spending has more than doubled in the last 3 decades, adjusted for inflation, the money has not gone to improving education, it has been frittered away). End the farce of overstuffed curricula. There is a monomania about covering as much material as possible, so long as students can retain enough to pass a test, but students don't retain much of the material and when the fundamentals are neglected they miss out on that too. Take the basics back to basics, emphasize the fundamentals (reading, writing, mathematics, fundamental science), learning them, knowing them, mastering them. Continue to refresh and test students on those fundamentals throughout their entire K-12 educations. And provide enough funding to allow gifted students to work at a faster pace, either within existing classes or in classes of their own.
I could go on, but that's a good start. Unfortunately, the biggest impediments aren't knowing how to improve, it's all of the interests and bureaucracy protecting the status quo.