But first, I think I need to make US education a little more plain because it's so different from British.
Public school = publicly funded education. Parents are not directly charged for tuition or books, although they're expected to purchase supplies such as notebooks and writing supplies for their own children. There's been an increasingly movement towards having students wear uniforms in some areas, but this is very new. For the most part, children attend in their own school district or catchment area. A district can have several elementary schools, fewer junior high schools and one high school, or the high school maybe shared among several districts (or towns) or even serve an entire county (administrative area smaller than a state) if the population is low enough. This is why Americans get very confused - the British meaning of "private, exclusive boarding schools" makes no sense to us. All children are eligible for a free public education. If they have special needs, the local school district has to provide for these. If it cannot do so itself, it has to find a place that can do so. Special needs do not include religious restrictions, and technically there is no religious education permitted in the public schools.
Elementary school is either K(indergarten)-6 or K-5, depending on the school district. There may be some K-4s as well. Curricula is decided on the state (the minimum requirements of basic knowledge for advancement) and district (what extras they want/can afford) levels. Kindergarten starts at age five, and the kids are supposed to master some subset of basic skills, such as colors, alphabet, writing their names and counting to some specific number. Elementary school classes have one main teacher, who spends most of the day with them and teaches most of the required subjects, although, depending on the finances of the district, there may be specialty teachers for science, art, music, reading, computers, and languages. The physical education - phys. ed. or gym - teachers are always trained for this subject. Depending on the subject and the school, students may stay in their main classrooms or get herded to a specialty classroom. All students are expected to master reading, writing, social studies (history, civics, community) and mathematics to certain levels. These are tested via standardized tests of the fill-in-the-dot variety. Special help is available for students with problems and extra funding is given for this.
The next level is junior high school. It can also be called Intermediate School or Middle School, but they refer to the same thing, more or less. Again, depending on district, it can begin as early as fifth grade and as late as seventh, and it can end as early as eighth grade and as late as ninth. The only true generalization I can make is that 7th and 8th grades (more or less ages 12 and 13) are always included. In my experience as a student, I moved between 7th and 8th grade to a different state, and from 7-9 JHS to a 6-8 JHS. I felt like I'd lost a year. In my experience as a teacher - *sigh*. Not a time of life conducive to learning.
These schools are organized like high schools - there is generally a homeroom (usually first thing in the morning) for daily attendance, handouts, pledge of allegiance, and general announcements before the students go off to their daily classes - each subject in its own classroom with its own teacher. Depending on the size of the school, students have either individual schedules to suit their needs or go with their classes as a unit.
Again, there are state minimum academic requirements - usually English, history, math and science, with a phys ed requirement. I think daily schedules (the same classes in the same order every day) are most common, but I've experienced weekly schedules (more like in Hogwarts, when you had different subjects in different orders on different days of the week.) There will probably home economics (sewing/cooking) and shop (woodworking, etc) classes and computers.
In HP terms, Harry begins at junior high school age.
High school is usually 9th -12th grade, although there are some 10th - 12th schools. We also call those years freshman, sophomore, junior and senior. It's possible to "drop out" at age 16, but it's highly discouraged. At this point, students start making some decisions about their futures - if they intend to go to college (note: college and university are interchangeable at this level. The major difference between them is that universities can grant degrees beyond bachelors. So can some colleges, though.), they usually take the "college prep" track, with classes on levels and subjects that colleges want to see in their applicants. While it's possible to double up on some courses - I took two sciences, for example - there is no further specialization at this level. A student wishing to major in English in college will take pretty much the same classes as a potential future engineer. Students who are certain they do not want to go to college can take technical tracks or even attend specialized high schools to get training in technical/service careers. However, even these high schools have to follow state and local academic requirements.
This one reason many USans are shocked that Hogwarts seems to have no academic subjects besides History of Magic. While we understand the rigor needed for magic classes, it feels to us that these kids are being short-changed - even more so for students like Hermione and Percy. Even our least academic tracks/high schools have that.
We have nothing analogous to O- or A-levels. At 10th grade, college bound students will take the PSATs, and in 11th and 12th, they'll take the SATs, which are standardized fill-in-the-dot tests (the SATs just this weekend gave their first exam with an essay portion.) These have no bearing on their grades or their coursework - they're a tool administered by a private firm given during non-school time to be used when applying to colleges. PSATs are also means of getting college scholarships. Students pay to take them and they are administered on Saturday mornings - non-school hours. They test knowledge of language and mathematics and nothing else, and one can take SATs more than once. There are more specialized boards, but these also only have meaning for college entrance committees, not for grades.
This is one reason I'm looking forward to Book 6 - I haven't the faintest idea as how classes would be organized after OWLs.
Just as Wizarding Britain has a lot in common with Muggle Britain, I assume Wizarding US has a lot in common in with Muggle US. In fact, I assume it has *more* - that American Wizards have found ways of incorporating or copying technology into magic. Those magic globes used in St. Mungo's? American Wizarding invention. There may be more contact between wizards and Muggle relatives.
I'm going to assume there is a reason why magical training doesn't begin until age eleven, even if I don't know what it is. So.
The children of wizarding families would go to wizarding elementary schools because they *do* have magic and it's just safer that way. These schools would be functionally identical to standard US private elementary schools - basic state curriculum plus whatever extra the schools wanted/could afford to teach. If there were standardized tests to be given in that state, the wizarding kids would also take the test. At the age of eleven, they'd go to one of three schools - East, Middle and West. East is, obviously, Salem. They probably have a choice as to which one to attend. And they'd be boarding schools just for logistical reasons. They'd also meet fairly often for mixers and quodpot and Quidditch games.
Muggleborn kids would get their letters at the beginning of summer, and they'd be offered a chance to go to a summer camp where they can get introduced to magic and the wizarding culture, so they wouldn't be so lost at the beginning of term. There would also be support groups for their parents and shopping expeditions into wizarding areas.
The schools would have to meet state academic criteria as well as magical requirements, although some classes might be able to do double duty. There would be no OWLs or NEWTs - just the same sort of tests and grades and homework as the other subjects. There would also be at least one wizarding university, with graduate school, law school and medical school attached. Possibly another, but I really don't see the population supporting more than one - maybe a two year institution or a small college for those who prefer such things. There would also be the possibility of entering Muggle institutions - I suspect there are wizard clubs in the major ones, plus they'd get summer credit from the wizard college.
Hmm, maybe that's what Salem is.
And US wizards? Do NOT wear robes except for formal occasions.