There are many approaches to raising children. You can be supportive of your child by giving them confidence, teaching them to learn from their mistakes or allowing them the independence to make their own decisions. I fail to see how not knowing some details of your child’s class schedule is an issue as long as you child is achieving.
I remember stressing out if my D got into accelerated math in 6th grade or how many AP classes she chose to take in HS. She is about to start college and I am not certain if these were the things to have worried about. She may have leaned more from her after-school and summer jobs and from the decision to stop playing a sport she once enjoyed than from any class in school.
Heck, I don’t even parent all of my kids the same way. They have completely different personalities, skills, and goals. Life in our household is not a one-size-fits all. (It would be far easier if they all had fallen out of the same mold b/c then I might actually master this nailing jell-o to a tree job called parenting.)
@ucbalumnus is correct, CalcAB and CalcBC do not include all of Calc3, which finally makes the fact that no school offers Calc3 credit for BC make sense to me.
I do think the pace for bright high school students is appropriate, half of college pace, and that is what I think is the value of these courses for the GT crowd. Taking AB and BC in high school means college calculus will either be a breeze, if you take Calc I and 2 again, say for a top 50 engineering school program, or should have you ready for Calc3 where you just need to learn the rest of multivariate calculus. Also a good BC teacher in high school may cover some Calc3 material well. In most top 50 or even top 100 STEM programs, it is GOOD to have an easy or easier class since you are being evaluated and many times weeded out, and a GPA in freshman year is a terrific thing.
Now, if you are a really high math profiency person, you could easily be taking BC in Junior year or going to community college and taking Multivariate, DiffEQ, or even higher math classes while in high school. but this will never be more than 0.5% of students. At UCB, these could be a dime a dozen, but not in state-flagships or even GaTech or other high STEM schools.
OK, if our public schools were to really dedicate extensive resources to GT students, I think you could get a higher % to be in Calc3 in high school and be able to pass a placement test at a top 50 school to skip Calc3 and enter really higher level math. But if you need a class of 30 … BC is a fine goal for a high school senior.
These tracks all only make sense if you are within a band around your abilities. If you are not a math person, you shouldn’t be in Algebra 1 in 7th grade, but if you are high ability, you also shouldn’t be in Algebra 1 in 9th grade or later.
I do know someone who successfully transitioned from Algebra 9th grade to CalcAB in 12th grade and is now going into a good engineering program, but it took some hard work and tutoring program to get there.
In my state (ohio) post secondary is the primary option for GT students to move beyond the traditional HS curriculum (my school offers 20+ AP classes, we are a top ranked school in the state). But be careful - many schools post secondary options/agreements are with CCs- that may or may not be accepted by competitive universities. My D had a friend who took all post secondary classes senior year- and turned out none of them were accepted for credit at their university. In contrast- my D took 4 APs, scored 4/5s on all- and all were accepted at their school (NYU)