I am a math professor, and FYI your (1)-(3) are not common practice in math departments which I've seen. Math professors and TAs are generally happy to encourage students to learn on their own. As for administrators, if they tried to impose (1)-(3), then at most US research universities they'd get the raspberry.
Of course, MIT might be special -- it sounds like a ton of students show up to office hours, and I can understand how MIT's math department might want to manage their TAs' workload. Unfortunately, the TAs are there to do research, and they are not required or expected to go the extra mile in teaching. Wanting a long one-on-one session after each lecture... yeah, unfortunately no TA is going to see that as their job, and any TA who does will get behind on their research and burn out quickly.
You probably know this already, but MIT is highly atypical. Depending on what your target market is, I'd research what is going on at state universities. Google "student success in calculus" to get a sense of some of the ongoing discussion. If possible, find a professor or TA at such a university, and offer to take them lunch somewhere nice if they'll talk about their experience in teaching service classes.
A lot of universities want to do better in this regard, especially at the "service course" level, e.g. calculus and below. And there is lots of money out there, although university budgets are weird and the politics are byzantine, which means that your efforts would need to line up with some administrator's agenda to get a piece of it. Good luck.
I am a math professor, and FYI your (1)-(3) are not common practice in math departments which I've seen. Math professors and TAs are generally happy to encourage students to learn on their own. As for administrators, if they tried to impose (1)-(3), then at most US research universities they'd get the raspberry.
Of course, MIT might be special -- it sounds like a ton of students show up to office hours, and I can understand how MIT's math department might want to manage their TAs' workload. Unfortunately, the TAs are there to do research, and they are not required or expected to go the extra mile in teaching. Wanting a long one-on-one session after each lecture... yeah, unfortunately no TA is going to see that as their job, and any TA who does will get behind on their research and burn out quickly.
You probably know this already, but MIT is highly atypical. Depending on what your target market is, I'd research what is going on at state universities. Google "student success in calculus" to get a sense of some of the ongoing discussion. If possible, find a professor or TA at such a university, and offer to take them lunch somewhere nice if they'll talk about their experience in teaching service classes.
A lot of universities want to do better in this regard, especially at the "service course" level, e.g. calculus and below. And there is lots of money out there, although university budgets are weird and the politics are byzantine, which means that your efforts would need to line up with some administrator's agenda to get a piece of it. Good luck.