I appreciate your math, but it is slightly flawed.
You can get a bigger n, not by increasing class sizes alone, but also by letting teachers teach for longer per day than children learn. I.e. use you math per hour taught, not for salary.
What this means in practice is, use teachers for higher value added work, but let computers (or somebody less qualified) oversee other parts of the learning process.
What seems to work fairly well (I remember a study about it), is to let students read material at home, but solve problems in class. That's the opposite of the traditional getting lectured-at in class / exercises as homework approach.
Khan academy is another vector for leveraging teachers. It does not replace a good teacher, but it can augment a teacher.
The problem is that if you tell schools to implement "computer supervised" coding learning, they will tell the students to write a factorial implementation and then they'll test it for bit-perfect match with some "perfect" solution.
This way they will verify correctness, good indentation, meaningful naming of variables and so on. Because somebody in the school/government heard that this is what professionals care about.
IMO launching a media campaign which pushes schools to "teach" every child to program, without any plan prepared by professional teachers and developers and then permanent, ongoing support from such professionals, is asking for disaster. And the grandgrand...parent provided an example of such disaster.
You can get a bigger n, not by increasing class sizes alone, but also by letting teachers teach for longer per day than children learn. I.e. use you math per hour taught, not for salary.
What this means in practice is, use teachers for higher value added work, but let computers (or somebody less qualified) oversee other parts of the learning process.
What seems to work fairly well (I remember a study about it), is to let students read material at home, but solve problems in class. That's the opposite of the traditional getting lectured-at in class / exercises as homework approach.
Khan academy is another vector for leveraging teachers. It does not replace a good teacher, but it can augment a teacher.