The traditional works

Bloom's 2 Sigma Problem.

Bloom found that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students who learn via conventional instructional methods—that is, "the average tutored student was above 98% of the students in the control class".

Woof! You want better student performance? One-to-one tutoring get's you there. Oh! It's too expensive?

Here is a very good discussion of the phenomenon.

There's a elementary school environment that's actually replicating this effect in groups pretty well right now. The only catch? It's basically the opposite of a Montessori school environment--highly structured, highly ability grouped, with scripted lessons at every level: Direct Instruction. It's been known to be highly effective for a while now, but it's pretty far out of favor culturally.

One of the few schools to use it as the basis of their program for math and English, a libertarian private school in North Carolina called Thales Academy, is reporting results exactly in line with the two-sigma bar: 98-99th percentile average accomplishment on the IOWA test. Their admissions process requires an interview at the elementary level, but no sorting other than that, so it's not a case of only selecting the highest-level students.

Other processes have been reported for high-ability students, particularly that of Diagnostic Testing-Prescribed Instruction, where students are placed into accelerated classes designed to teach only what they haven't already mastered. For a highly selected group of students in the 99th percentile of aptitude, two-thirds were able to go from testing in the 50th percentile on algebra tests to the 85th. In a day. As they mention, that was a stunt, but they went on to replicate it in a stabler classroom environment over eight weeks (cited by me in another comment).

In general, the 2 sigma problem is likely more or less applicable to all students, and--in optimal conditions--they could be learning much, much faster than they typically do in schools. The solutions I mentioned above are scalable but generally culturally out of fashion.

I would have sworn that either the Washington Post or the New York Times had a big article on the remarkable results of Thales Academy within the past couple of years, but I am not finding an article in either paper. Perhaps it was this article from Reason magazine, A Libertarian Builds Low-Cost Private Schools for the Masses by Jim Epstein.

Direct Instruction:

Direct instruction (DI) is a general term for the explicit teaching of a skill-set using lectures or demonstrations of the material to students. A particular subset of direct instruction, denoted by capitalization as Direct Instruction, refers to a specific example of the approach developed by Siegfried Engelmann and Wesley C. Becker. DI teaches by explicit instruction,[1] in contrast to exploratory models such as inquiry-based learning. DI includes tutorials, participatory laboratory classes, discussion, recitation, seminars, workshops, observation, active learning, practica, or internships.

DI relies on a systematic curriculum design, delivered by implementation of a prescribed behavioral script.

Direct Instruction, in a major evaluation of a wide range of instructional philosophies called Follow Through was found to have the largest impact and the most consistent impact in terms of improved student outcomes. Later replications have been consistent with the original findings.

So if we know what works (subject to additional replication), why aren't we simply implementing Direct Instruction? TracingWoodGrains' explanation is pretty oblique, though correct. Why don't we do Direct Instruction? Because it is "generally culturally out of fashion"

Direct Instruction might be good for student academic performance and increase their knowledge and their test scores (subject to yet further replication). But it does not address a range of other issues dear to the heart of many advocates and interest groups. With Direct Instruction, the centrality of teacher quality is a substantially less determinative factor than is desirable for those interested in teaching as a profession. Direct Instruction is to the professional reputation of teachers as Intuit or H&R Block is to the professional reputation of tax experts.

Direct Instruction has nothing to do with other issues which enthrall the education sector - it does not fix inequality, equalize learning outcomes, it does not address differences in learning styles, it does not (as a goal) bolster self-esteem, it does not (as a goal) inculcate critical-thinking, it does not (as a goal) foster creativity, etc. All it does is increase knowledge and test scores.

All these other things are nice additional objectives. And if we had any techniques that demonstrated that they can meaningfully and effectively fix inequality, equalize learning outcomes, bolster self-esteem, inculcate critical thinking, foster creativity, etc. then it would be good to accomplish those as well. But so far, we have not found any means of achieving those goals. And we have thrown out traditional (DI) teaching as a barrier to achieving those other goals. We have chosen to lower knowledge levels without achieving the competing goals.

The obstacle to the type of material results of Direct Instruction is primarily that there are too many interest groups and advocacy groups more interested in inequality, equal outcomes, self-esteem, critical-thinking, creativity and other nice but non-achievable goals to allow focus on actual knowledge results.