I think at my high school, the highest level course was calculus I and II, and physics I and II. They may not have offered any physics courses at my high school, but some classmates in college said they took it. Then again my professor from Poland said they taught him physics in 4th grade.
Do high schools anywhere teach more advanced math and physics? Does it vary regionally or do they usually stop there?
Where I was from, if you wanted to take courses more advanced than this you had to take them at the local college and do half days at high school.
Where I grew up our HS had Physics I & II. We only had Algebra I, II, & IIa, no Calculus. We also had 3 Agriculture classes as well as two Auto Mechanics classes. However ,we could, on the school district’s nickle, go to the local Community college for some higher level classes.
The town 7 miles away offered Calculus I & II. They also offered Physics I, II, & III. They had no Auto Mechanics, nor any Agriculture classes.
The next town down stopped with math at Pre-Algebra, & a watered down Physics I. They also had no Auto Mechanics, nor any Agriculture classes.
My cousins in the next state over had Math through Algebra II and Physics II & no Calculus. Their agriculture program was very very good. Their school district also would pay for higher level classes at the local college. While it offered no Agriculture classes, It had very good Math & Physics departments. One of my cousins got both their HS diploma, & an AAS in Physics from the local college, on the same day.
When I was in high school, back in the Enlightenment Era, the highest math they offered was Calculus (a year-long course. There certainly was no Calc II). And the math really was a pretty linear progression from Algebra I to Calculus. Beyond that I don’t think it’s clear which courses are “higher”, but there were no courses on Differential Equations or Group Theory or Probability and Statistics or suchlike.
I went to a small Catholic four-year high school, 35 years ago.
For math, the progression was Algebra I - Geometry - Algebra II - Pre-Calculus. Nothing beyond that was offered. When I got to college, and had to take a math placement test, I got placed into a semester of Trigonometry before I could go on to take the two semesters of Calculus which I needed in order to get into the business school.
For science, we had a general science class as freshmen, Biology as sophomores, Chemistry as juniors, and Physics as seniors. During my senior year, the school offered, for the first time, an Advanced Science class as an elective for seniors. It was taught by the Physics teacher, and thus, had a strong focus on that.
My high school offered international baccalaureate (IB) courses. All IB courses are offered in “lower” and “higher” variants. The higher classes are supposedly more difficult than advanced placement (AP). We did calculus for both 11th and 12th grade. Made first year of engineering a lot easier.
My public high school offered all the basic AP courses when I was there (2 years of calculus, a year of physics, chemistry, and biology). If you ran out of math courses, we had an arrangement with Northwestern University that allowed students to go there for more math. I didn’t take upper-level math classes, but several of my friends did; this guy was part of my wider circle of friends.
Multi-variate calculus and DEs! That’s amazing. When I went to school, there was an experimental AP program (which I was not permitted to take) and I ended up taking calculus in my second year of college and advanced calculus and DE in my third year (along with modern algebra, but that is another story).
In my experience teaching calculus, the AP calc was crap, just a cookbook course and it was better to just start over and do it right.
Same for my kids’ school. I, myself, took Calculus as a Senior. My own children are scheduled for it as a Junior and a Sophomore, respectively. The normal trajectory for all students these days is calculus as a senior but going into middle school, some kids elect the accelerated tract (of which there are two). It does make it awkward when as freshmen, their classes are 90+% juniors and seniors (and mostly kids of color, which makes the achievement gap all the more in the face of everyone).
And as long as I am on my soapbox, I went to a combined choir, band, and orchestra concert last night at the high school which has a minority enrollment of 60%. And the choir was the most diverse with 3 kids (out of 50?). And this is in very progressive (but educationally challenged) Seattle! The school really is a fantastic community overall, but ultimately wealth and parental education are the determining factors for the vast majority of students.
In my public HS there was a class with multivariate calculus with exactly one student. This was a guy who just… knew stuff. Understood everything the first time around. Aced Calc, Physics, Chem, British Lit (!), History. Very nice guy, the most normal person you ever met. It’s creepy that a normal person could be that smart. Anyway, he’s now a galaxy brain math professor at UNM.
And not to brag, but I was the only one in AP German 5. All my other grades were shit but apparently I was born to max out high-school German.
In my high school and in the local public schools, Calculus was the highest math course offered in the schools. It was a full year course and was the equivalent of first-semester Calculus in college.
That said, at most of the local high schools if you were some kind of math wunderkind, they’d arrange for you to take higher math courses at the local community college. I knew a girl who did that- in middle school, she was taking math courses at the high school, and then in the latter half of high school was taking math courses at the community college.
When I was at school many years ago, calculus was part of the AO level syllabus, for 15-16 year olds, though I remember our maths teacher giving us a first taste of calculus much earlier.
My school offered Calculus but in order to take it, you had to take one of the precursors (Algebra I, Geometry, Algebra II, and Trigonometry) in summer school or something. Since we moved in the middle of my freshman year and Arizona’s curriculum did not match up with California’s requirements to graduate, I had to take something else during the three summers before my senior year anyway. In all honesty I probably would have been reluctant to take a summer math class just so I could take Calc.