Looking at the web site of my old high school, it does say that regular geometry does include some proofs, but honors geometry has greater emphasis on proofs.
@ucbalumnus - I think we’re in complete agreement that good students can master the BC curriculum in 1 year. However, I also wanted those parents / students who are trying to decide whether AB or BC was the right choice in their particular instance to know that BC goes at a college pace, not a high school pace.
Another small point that hasn’t been mentioned - in college, calculus sections are often taught by graduate students or instructors who may not be native English speakers. Many students find it easier to understand high school teachers who are often native speakers.
I’m definitely not an expert. I first formed my opinion after observing my own children’s curricula, and conversations that I’ve had with fellow grumpy old (former) professors in a university math department have mostly confirmed it. My kids attended much better schools than I attended (they had future math olympiad finalists / winners as schoolmates), but in their geometry class they proved only a minority of the important theorems and proofs weren’t the basis of their homework and tests. An example which this article uses http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/
is that students are simply told the angles of a triangle add up to 180 degrees; it isn’t proven. In contrast, when I took geometry we pretty much proved everything building up from the basic postulates (at least until we got to solid geometry); we even had a few ruler and compass constructions on tests. And I went to a fine but not particularly wonderful high school.
I think geometry courses now emphasize knowing and applying the theorems (not proving them); “experiencing” geometry in the everyday world, the role of transformations and symmetry, and computation using coordinates. I’m not saying that’s all bad, but it’s not formal deductive reasoning.
Also, if I remember right, when I took BC Calculus epsilon-delta proofs were on the exam; they definitely aren’t nowadays.
My son is in a strong large public high school with a block schedule. The strongest math students took AB 1st semester and BC second semester of their Junior year. Then completed Calc 3 the 1st semester of their senior year. I don’t know of students that skipped the semester of AB. Anyway, seemed to work out great for my son. Helps to have a terrific math teacher that stays with the same group of students through all three courses.
@wayneandgarth - what you are describing (Fall AB/Spring BC) is actually more likely Fall/Spring BC. That is the way the basic BC curriculum is written.
@Dreadpirit - because its block scheduling (four 87 minute periods per semester), you take only four classes a semester but one semester of a class is a full year of a traditional high school schedule.
So he covered a normal full year of AB in the 1st semester and a normal full year of BC in the second semester. He then was able to cover all of calc 3 in the 1st semester if his senior year.