Next month (August) I am supposed to go back to the US to continue my math PhD programme in a Public State University. I hold a TA position as everybody does in my department. Nobody, I say again, nobody holds an RA position. My duties, as equal to almost everyone, are two recitation sections of 60 students each. Every section meets 3 hours a week, that is 6 hours a week for both, plus preparing material, grading a weekly quiz (120 for both) plus grading homework weekly (120) plus grading classwork weekly (120) plus holding office hours plus organizing and keeping grade records plus going 4 hours a week to a center called "math help room".
I saw many US students leave the programme. They get fed up. The vast majority of the students are Chinese and they seem happy with it but I do not. The workload is too heavy and there isn't much time for learning or research. I have seen most people get their PhD at my department with only one publication that even says "to appear" on the resume of the PhD graduates. All advanced PhD students at my department spend even more of their time on TA duties than doing their research, as opposed to my country (Mexico) where advanced PhD students do not have TA duties.
Is that normal? Is my math department a scam?
I was surprised and happy at first that I was accepted to a US university to do a math PhD. But I could not get admission to a PhD in my country nor Spain nor Brazil, which are not supposed to be as good as a US university. Is my reasoning ok? Why did my department accept me when lower schools rejected me? Do they only want to get staff for their recitation sections?
Is my reasoning correct? Or is the main objective of a PhD here in the US just teaching?
Since you said that you come from Mexico, I presume that you are on a F-1 visa. If so, then as a condition of your visa, you are permitted to work on-campus only up to 20 hours a week. Keep time sheet to see if you work more than that. If you do work more than that, talk to whomever is responsible for assigning the TA work in your department to reduce your load down to 20hrs. Do not be swayed by "this should take less than 20hrs" if in reality it takes more than 20hrs.
Disclaimer: I am not a lawyer. The text above is not a legal advice.