I live in an Asian country where the graduate students are not allowed to teach until they get the job of a lecturer/professor, i.e. only after Ph.D. one has any chance of teaching a class. This is because not many people opt for higher education in my country, so there aren't many classes to teach.

However, in the USA it is mandatory for graduates to teach undergraduates to be able to fund their graduate studies and this is called TAship. While going through various maths graduate program webpages, I have found the following statements regarding TAships:

- TA appointments are limited to 15 to 20 hours per week, averaging no more than 15 hours per week.
- Typically, TAship has been a 50% appointment (20 hrs/week), which involves teaching recitation sections or lectures, participating in course duties.
- A 1/4-time teaching assistantship (TA) requires about 2 classroom hours per week of teaching.

I am unable to understand the terms like "20 hrs per week", "50% appointment", and "1/4-time TA". In particular, I have the following doubts:

- Who counts how many hours a week I am working? How does the department ensure that I work exactly 20 hrs per week?
- 50% of what equates to 20 hrs per week?
- 1/4th of what is 2 hrs per week?

Thank you very much for your time.