Problem SOLVED: Bloom's 2-Sigma Problem

From Wikipedia:

"Bloom's 2 sigma problem refers to the educational phenomenon that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students educated in a classroom environment...

"The phenomenon's associated problem, as described by Bloom, was to 'find methods of group instruction as effective as one-to-one tutoring.'"

In other words, when a student is tutored "one-to-one using mastery learning techniques," the average "D" student becomes a "B" student, and the average "C" student becomes an "A" student.

(Note from the the original study: "one-to-one tutoring" was small groups of 3-5 students.)

When I originally encountered this problem, I had been researching the methods used to teach child prodigies like Mozart and Beethoven. What struck me about the "2 sigma" improvement, or the move up 2 letter grades, was that examples like Mozart would have been off the charts in terms of progress above their peers - literally dozens of "sigmas" above the rest in terms of skill and the time in which they advanced. 

I appreciate that Benjamin Bloom was trying to improve the average educational outcomes of students across the country, but what I was working on was something altogether different, yet it shared at least 2 components in common with Bloom's conclusions:

1. All instances of the prodigies I studied learned one-on-one, and

2. All instances used Mastery Learning as the standard before advancement.

But as time went on, I noticed an unusual phenomenon with my private students compared to my small-group students; often, they were lagging behind. 

How could this be?

Until then, I would have thought private lessons were the golden standard of education. In terms of quality, what could be better than one student and one expert?

It turns out, the difference has to do with the mindset of the private student versus the mindset of the small-group student; a private student can be continuously prodded during a lesson to focus and to strive, whereas a small-group student must practice and strive on their own in order to advance. In other words, the difference is initiative - a difference which I believe carries over into their practice habits between our sessions together - and, which I believe also carries over into how they learn when practicing new content in the form of pre-recorded video lessons.

I believe this model of learning, today called a "Flipped Classroom," is the solution to Bloom's 2 Sigma Problem. It requires a shift in thinking from students and parents, as well as a shift in teaching by the teacher, as well as a tremendous amount of additional preparation by teacher in the form of making pre-recorded lessons, using them, observing their efficacy, and remaking them to improve the flaws - sometimes many times.

But the rewards are obvious; once made, it creates a smoother and stronger path to education for our students. To use an analogy, the experience of learning becomes something like traveling down a highway where once was walking through a dense jungle.