https://wikipedia.org/wiki/Bloom's_2_sigma_problem

  the average student tutored one-to-one using mastery learning techniques performed two standard deviations better

A tutor can notice gaps. You can't.

I TA and tell my students that if they don't come to office hours or ask questions that they might as well be getting their degree on YouTube.

I don't mean this in the sense that they have to ask for every class, but the advantage of attending school (besides the piece of paper) is to get direct help. But I'm not attending a top 10 university and honestly most topics are covered by one of those universities and they post their lectures on YouTube or their own OCW.

Out of interest, roughly what proportion of students do come to the office hours?

Really depends on the class. One class I had basically no one. This one usually about 2-3 (out of 40) but more as we're nearing the end of term. Sometimes people come to say hi (again, class dependent). Largest I've had was like 8.

> I would go to office hours and the teachers were seriously so helpful. This was the only way I survived. I learned that you don't have to be a 'numbers person' at all to be good at math. You just have to understand what's going on under the hood, and this may require lots of questions and outside help. But most importantly, you just have to practice

I agree with all of this and it's how I got through extensive math. I'm not a "natural" at math and I'm not sure that really exists or possibly very people that are. I made sure to get to the office hours and I was surprised that there was almost no one there most of the time. I figured the cost of tuition is best justified by using as many hours of one-on-one time with an expert in the subject to better understand it yourself.

And to your last point about practice, I can't emphasize this enough. I would do the same problem sets over and over until I had them down. And it wasn't just memorizing the steps but rather getting to the point of being able to recognize the pattern. This made math "easy" at that point which is a weird phenomenon. Something that seemed so confusing and impossible suddenly becomes "easy". And then you can move on to the next step.

I understand rote learning is not popular because it is painful. But I do believe "drilling it in" over and over gets the job done. But it takes the will and the effort. It's been a long time but I think I could still solve most the math I took back then.

> I made sure to get to the office hours and I was surprised that there was almost no one there most of the time.

One of my biggest regrets about university is not taking advantage of office hours. For me it was a combination of 1) social anxiety and 2) thinking that if I really belonged in this program (physics) I should really be able to figure everything out on my own. I know now that this is a stupid way to think but it's the way I felt at the time.

> I made sure to get to the office hours and I was surprised that there was almost no one there most of the time. I figured the cost of tuition is best justified by using as many hours of one-on-one time with an expert in the subject to better understand it yourself

Truth!