What is the term for schools where students stay in one class all day and the teachers change rooms?

Fixed classroom system as suggested in the following extract:

“How a fixed classroom structure can help children navigate the social jungle that is school“:

In most East Asian public schools, teachers – not students – are the ones who move in and out of classrooms. Students stay put, in fixed seats with fixed classmates. Despite some shortcomings, such a system has at least one big advantage: fixed classes provide default social groups in which students forge deep bonds and that serve as psychological anchors. Although a fixed classroom exposes students to a fewer number of schoolmates, the bonds they create may be more lasting.

Here are other usage examples of fixed classroom with the above meaning form Google Books.

From: Challenges of Modernization and Governance in South Korea.

In 2009, this system was introduced as a test case in a few schools and in 2010, it was adopted widely. This was a relatively bold move, given that for six decades, the category of general high schools, geared to the college entrance examination, has maintained the fixed classroom system.

Under this method, students stay in the same classroom and teachers move from classroom to classroom.

Peripatetic Method

There can be no impropriety in terming the plan, under which the teachers go from classroom to classroom to give instruction in their specialty, according to the method of the celebrated Greek. By this method each class remains in its own classroom all day.

Peripatetic Method

the plan of having the teachers go from classroom to classroom to teach their specialties, the "Peripatetic Method" as he calls it, instead of having the classes change rooms

Peripatetic Method

It is said that Aristotle, the fabled Greek philosopher who lived more than 300 years ago, walked about, teaching and instructing as he went from place to place. This method of teaching became known as the Aristotelian peripatetic method.

Merriam-Webster defines the adjective "peripatetic" as:

going from place to place usually as part of your job

The TESOL has a reference to it:

Time should be made available for planning, especially where the NEST is peripatetic and moving from classroom to classroom or school to school.

The acronym NEST in the above quote stands for "native English speaker teacher."

I don't think there's a specific word for that. Most of the people I asked said it was called self-contained classroom.

Some classrooms are self-contained, with one teacher and one group of students all day (or very close to it). US elementary classrooms are often like this, with a group of students staying together all day with one teacher aside from "specials" for something roughly like an hour per day 3-5 times a week. This is also used by some special education classrooms in higher grades.

Some schools use a cohort model, where students are with the same group of kids all day (with one or more teachers). I've heard that term used by US teachers in grades 6-9 (ages ~11-15). In some schools, students will move together as a group to the next classroom when it's time for the next subject, but I believe you can use the term if the teachers are moving as well.

Both of these words are kind of slippery because they can mean multiple things (e.g. a group of kids in the same grade can also be called a "cohort").

What is the term for schools where students stay in one class all day and the teachers change rooms?

I guess the classes in which students move from one class to another are called moving classes. And when teachers move from one calss to another, they're called moving teachers. I've also heard rotating/ roaming teacher for the teacher who changes rooms.

After elementary school, students proceed to junior high school (also called middle school), where they usually move from class to class each period, with a new teacher and a new mixture of students in every class. Students can select from a wide range of academic classes and elective classes.

Guide to the education system in the US