I wonder how much of it is philosophy? I know within math circles some have been crying out for students to be exposed to calculus much, much early, even in grade school and there is a lot criticism of the Algebra 1 then 2 sequence in high schools. I don’t know how many schools have really gutted out the traditional sequence of Alg 1, Geom, Alg 2, Precalc except in the sense that they reward credit for Alg 1 taken in 8th grade. My kid’s school actually would make kids take Alg 1 all over again even if they had earned HS credit and passed the state-mandated exams unless they could pass their placement test. I also heard that they would make IB students take Alg 2 in the summer at local colleges and then make them RETAKE it at the high school. So, at that school accelerating even to the point of being able to take Calc at all was reserved for very, very few students. But I could see a high school being much more liberal about it so long as students were passing placement tests. My kid actually left HS so she could learn calculus and not have to wait for college.
My kid took BC as a sophomore, multivariate calc as a junior and now is taking linear algebra as dual enrollment at our state flagship. I thought this was really advanced until I heard about his friend who took so many math and other STEM classes in college during high school that he had enough to graduate as a math major from the same university. Presumably he did this at the expense of ECs and some humanities, and I don’t really know why because he still apllies to top schools and I doubt they’ll accept these credits.
On the other hand, for my kid advanced courses have been very valuable in exposing him to “real” math which solidified his interest and will likely make it much easier for him in college.
I guess it is all a matter of perspective. I look at the Harvard stats provided by UCBalumn and think an amazingly high percentage , 25%, had math beyond calculus, particularly if you exclude from the likely pool students who are athletes and those from underresourced schools who likely didn’t have access to such courses. Over 92% had some type of calculus as well-which must include most of the hooked populations. Yes, I think more high schools are offering, and more kids are taking, advanced math. 46k taking bc calculus by 11th grade must be doing something senior year, besides taking AP stats.
Not all high school students who complete calculus BC in 11th grade have access to subsequent college math courses (can depend on scheduling, commuting, and cost).
That’s right, UCB. So for those students whose high schools do offer such courses (And are Harvard types), a lot must be taking those courses to get to the 25% stat.
FWIW, in my older son’s class of 640, there were only six kids who were taking Linear Algebra, which was offered for the first time that year. I don’t think there are many more kids on that track now because the middle school is so uncooperative. The val was not taking Linear Algebra and got into both Harvard and Yale. I’ve never heard anyone in Harvard’s Math 55 complaining that it was too easy!
We have 20 out of 100 in linear algebra. I expect schools vary greatly.
In our experience, our elementary/middle school (STEM based) really pushed the kids ahead based on their abilities. The parents tended to get caught up in their kids being “ahead” and so “advanced” - we did with our son. He took Multivariable Calculus in 11th and then Differential Equations as a senior. Looking back, I think he would have been just fine to slow down a bit - he “gets” math, doesn’t love it, but does well in it - I’m not sure how great the DE class was he took - it was online and had no support. He is not going to major in math in college so he started back with Calc 1 his first year at UChicago. Even so, he said it is completely different than what he was taught in HS - the proof based math (I think that’s what he called it) is tough. He’s learning a lot and enjoying it, but starting back at Cacl 1 was a great choice for him. Depends on the school and what the students goals are - but I’m glad he chose to start with Calc 1
With our daughter we told the school “no” when they wanted her to advance to Algebra I in seventh grade. We knew for her it made no sense - she needed the foundation and she would not be well served by being two years ahead of the norm. She ended up in Algebra I in 8th grade which was a great fit for her.
It’s hard when the school is pushing the kids ahead, I’m not sure how parents are supposed to know what is best - especially with their first child…
Presumably, he took one of the honors courses (16100 or 16110) with more theory and proofs instead of the regular (15100) or with-precalculus-review (13100) courses?
That is not exactly the same as throwing away all of his high school math acceleration.
http://collegecatalog.uchicago.edu/thecollege/mathematics/#mathematicscourses
I wonder about the quality of teaching for those high schools offering post-BC math classes. What are the credentials of the faculty?
I minored in math at at liberal arts college. I took BC calc in high school then Calc 3 at college. After that the math department required a course called Logic and Proof before you could take any other math classes as a major or minor. It got everyone on the same playing field as far as proofs.
Of course back then ('88 for high school) even goign straight in to Calc 3 in college was highly unusual.
In theory, aren’t high school teachers supposed to have bachelor’s degrees in their subjects, as well as teaching credentials? So the high school math teachers should have had multivariable calculus, linear algebra, and differential equations, as well as more advanced courses like real and complex analysis, when they were in college.
But, in any case, high school multivariable calculus and other more advanced math courses would generally not be accepted for subject credit since they are not college courses (although some college math departments may grant subject credit by exam once the student gets there). That is why it is preferable to take those more advanced math courses at a college.
As @ucbalumnus points out in the Uchicago case, calculus in high school is a good preparation for a proof based calculus sequence in college and enables the student to skip the beginner level calculus classes. The advanced versions of college calculus are sometimes designated as “honors calculus” or “real analysis” and will still start with single variable function and limits, differentiation and integration but on a more theoretical and proof based basis.
I would hope they have a degree in math or a related field, most/all of which would require math past calc 2. In my case, the instructors all had advanced degrees, including doctorates in a couple of instances.
Knowing many of these kids, and with the 25+ hour/week it takes to do problem sets, I would concur.
My freshman d took BC as a senior. She is a statistics major and went straight to Calc 3 instead of repeating 1 or 2. She has a 99 right now so it did not hurt her at all to not repeat 1 and 2 once she got to college, though I know a lot of engineering students do. My son will most likely take BC next year as a junior and will have to take Calc 3 at a local college his senior year. One thing to keep in mind, some universities do not except Calc 3, and other classes for that matter, if taken at an out of state college.
I doubt it has much to do with the state the college is in, and more to do with the perceived quality and level of the class.
My likely math major son took Calc BC as a junior and is doing two semesters of advanced math at a local university senior year. He’s deliberately not taking multivariable calc because we reasoned it’s such a foundational class that it would be best to take it at the school where he’ll be getting a degree. He’s taking linear algebra and intro to logic, set theory, and proofs instead. Don’t have any idea how it will work out as far as getting credit wherever he winds up, but he’s hoping to at least avoiding having to take linear algebra again; he wasn’t a big fan.
Related to this topic - I think HS students don’t appreciate that college course grades taken in HS ‘stick’ with them, esp. if they stay within public universities. Getting credit for advanced math in HS is great - but if the class doesn’t go well a bad grade can hang around for a long time. For example, if you’re applying for a scholarship or grad school and they want ‘all college transcripts’ sent to them.
I’ve not experienced this first-hand, but the topic came up recently around dual enrollment more broadly and some students being unaware of the long term effect of less than stellar grades in a college credit course while a high schooler…
Hopefully most grad schools would discount grades from courses taken while still in HS, but you never know…
DS requested to take Calc BC as a freshman but was only allowed to take AB which was a full year course at his high school. He had already worked through the AOPS Calc book in 8th grade but wanted credit for Calc. After the first semester, the teacher moved him to the Calc BC course and he had the top grade in the class and got 5s on BC and the AB subscore.
Luckily, he has gone to a math circle for years and some professors there helped him get involved in a research project which was more of writing a program but in order to do so he had to learn a bit of Linear Algebra. The professor met with him and taught him the math he needed to know to write the program. DS really enjoyed this project and it did not stop him from other ECs, including being a captain of his JV soccer team and being pulled up to varsity at the end of the season. (I mention this as someone upthread indicated many of the top math kids can only do math.)
For this Spring semester he hopes to audit Linear Algebra at a nearby college. He will not get credit for it but he has a lot more credits than needed to be a sophomore and he does not want to graduate high school early. The school has been great about letting him do this. DS really likes math and we have always tried to keep him interested/challenged even when it looked like he might have to repeat it. So far it has worked out well and we intentionally slowed him down after reading the Calculus Trap. He felt he learned a good bit doing Calc BC after having done AOPS Calc…not the theory but he said the problems were very different in BC and it was a good course overall.
DS is good at math but through various competitions, we are very aware there are many many kids his age that are much more advanced. Often they have parents that are much better at math than his mother or I…To date, his struggle has not been the concepts in math or physics etc but it has been drudging through the homework. His only B came last year when he blew off a project in AP CS A as it was not interesting and he procrastinated and gambled as he thought his A was high enough it would not knock him down to a B - he did not know the weighting of the project. A potentially very costly mistake for him in admissions.
He has not taken math courses early to try and be in a math race, etc, he likes math and it does not take him as long as it does others and he is still able to do many other activities. I think the problem is when other kids that are not as good at math see it as a race and try to take courses they are not ready to take. He also realizes that he will probably not get accepted into a tippy-top college given he is a white male so he is not taking the courses for admissions purposes.
Logic, set theory, and proofs is probably more foundational to upper level undergraduate and graduate level math, since the latter is all about proving things. Also, linear algebra courses may come in computational-oriented and theory/proof-oriented versions; math majors may be required to take the latter after or instead of the former.
In terms of transfer credit, it would be a good idea for him to try the old final exams of courses that he is allowed to skip if he has any uncertainty about whether to skip them.