I mentioned my D19 upthread, but some interesting thoughts from my D23 (same district, different high school). D23 is in 10th grade, currently finishing up precalc, which is the “regular accelerated” track here. She’s doing fine in her math classes, and says she’s understanding everything, but isn’t really enjoying it.
(Possible important context: The field she’s interested in has varying math requirements—many places it’s just the basic gen-ed college algebra or higher, I’ve seen a couple places that require first-semester calculus but never anything higher.)
She’s transferring to our district’s “middle college” (read: dual-enrollment, located on the local college campus) high school, and so had to take a placement test. She gets five tries, and so took her first one cold; she placed into college algebra (non-remedial, the level fulfills gen-ed requirements most places) but was very close to placing into college precalc, and so figured that she could wait the required one week and then place higher.
Until she basically said, why would I want to do that? It’s going to be rough enough transitioning to the speed of college courses anyway, why make my first semester of it any harder than it has to be? Besides, she pointed out that in a college schedule she can take a course a semester, and thus could be taking calculus the following fall anyway if she decided she really wanted to.
We discussed it back and forth, and finally I (and my spouse) agreed that sometimes our kids know what’s best for themselves, and we have to respect that. There this weird cultural feeling that more advanced is always better, but there’s a good reason that calculus is a required course for some college majors, but not all college students.
And if calculus isn’t required for anything our kid is interested in, why in the world should we be pushing her to take it?
I don’t understand the race with math. I have a friend who’s son is studying engineering. The boy is having a terrible time with the math and it comes down to he did not really learn algebra. He, like your kids’ peers raced to try reach the highest level of math without really building a strong foundation.
My oldest had a perfect SSAT math score( no prep). This score is actually a smaller % then the SAT (since its often no prep and based on K-8 learning and taken by students who wish to attend private-high schools). We were told most kids with 800 in SSAT were from China and other nations which teaches math at a faster clip.
My kid decided to take the lower level course offered. Still a couple of years ahead of the track. Flew through it but wanted to ensure foundation was solid.
My youngest is 4 years ahead in math. It was actually very hard to find schools to accommodate this level in high school.
I can’t see any reason for pushing ahead for parental bragging rights. At some point, the kid hits the wall. This could be very detrimental esp if the kid is in high school. I’ve heard all sorts of crazy things regarding compressing learning into shorter timeframes. We saw a lot of crazed parents in the math circuit. We never coached our kid. Most did. My kid lost interest due to the vibe.
Very advanced math done by very young students has its own particular challenges.
Honestly, if you/your kid is a math kid, it’s going to be developed either way.
I don’t think it’s parental bragging rights since it brings kids up to the level that accelerated math kids are at. No parent is going to brag about their kid taking Calculus in 10th, since that’s the norm for bay area kids that get into the MIT, Cal Tech, Stanfords of the world. Most can take it in 9th but because seniors and jrs have priority for Calc, they can’t take in 9th.
CA seems to be more accelerated than other states. Regular sequence varies a lot by state. Many MIT students are advanced relative to others, certainly. But I’d bet money MIT is looking more at depth then sequence.
Many kids can move along based on their curriculum. But only a tiny fraction can be MIT/Caltech students.
My kids have run into loads of kids with exposure to higher levels/faster track then what is usual. This is esp. true of kids from some foreign countries. But they are not necessarily better at math. Actually in top events, they tap out. The really strong kids are the ones with a stronger acumen and aptitude. When THOSE kids dig deep and study hard, they can’t be beat. Though I’d concede that if you have early exposure, aptitude and interest, then you might be ahead.
My point: Exposure to faster tracks does not make you better in math. There are many kids in top college math programs who never made it to Calc BC.
The normal sequence in California is algebra 1 in 9th grade, leading to precalculus in 12th grade. The +1 sequence for those good at math is one year ahead, starting algebra 1 in 8th grade, leading to calculus in 12th grade.
There were a few years when the state wanted every 8th grade student to take algebra 1 (if not already ahead). That did not work too well due to high failure rates and was stopped.
Someone brought up the sequence in CA. I know nothing about it. I have read about kids in public schools in CA being able to take advanced math earlier then what is offered in MA.
My comment regarding parental-bragging rights was also not made in the context of CA. I’ve seen many parents push for advanced math when their kids don’t test in. Public schools have to allow access to the class. Then their kid slows down the class. How bad was it?
Well my kids are now in private school where you test in, keep up or do poorly. Guess what? No issues.
The funniest thing ever was a parent who told me that her child was being math shamed. Yep, kid wasn’t in advanced math. Parents solution eliminate advanced math for all.
High school junior here. My school has an accelerated track for math, so I took AP Calc AB in 9th grade and AP Calc BC in 10th grade. As juniors, we’re free to take AP Stats as a math course, and senior year has multiple math capstones. Despite finishing calculus quickly, those two classes have been my worst grades throughout high school. Good thing the AP curves left me well-off (and the credits will be helpful), but it was not a very fun experience and I certainly wasn’t the best in my class.
Though I was never “officially” on an accelerated track, I did self-study calculus in 9th grade. Despite that, I definitely felt afraid going into my senior year when I took Calculus AB. In my case, I think impostor syndrome played a large part. I always fear that everything up to now has been a ‘fluke’ and that this is where it all comes crashing down. Thankfully, nothing has crashed yet.
I will say, however, that I never quite understood this phenomenon of “accelerating” students who perform well. In fact, the very notion of “gifted” children as opposed to “normal” children seems absurd. My college roommate took these “gifted” classes in high school. According to him, someone who took the classes I took when I took them would not even be given the opportunity to study calculus at his school.
The vast majority of people have the same, very high learning potential. I would go so far as to say that if I were accelerated in this way, I probably would not be anywhere near as comfortable with mathematics as I am today. Slow and steady is a better approach to learning.
Expectations depend on the courses that are offered at a particular HS, which can vary widely, including among HSs within a particular region. The vast majority of HS students who apply to such colleges attend a HS that offers calculus, and taking calculus can be expected. However, most applicants do not attend HSs that offer any math classes beyond calculus, and such applicants are not expected to take math beyond calculus during HS, nor are they expected to take calculus before senior year. This results in a large portion of admitted students not taking any math beyond calculus. For example, Harvard’s freshman survey asks about most advanced math class. In the most recent survey, the results were as follows. 3/4 of entering Harvard students said they did not take any math beyond AP calculus during HS.
6% – Most Advanced Math = Pre-calculus
69% – Most Advanced Math = Single Variable Calculus
20% – Most Advanced Math = Multi-variable Calc / Linear Algebra
5% – Most Advanced Math = Beyond Linear Algebra
MIT and Caltech probably have a larger portion taking post-calculus math than Harvard, but I’d expect the majority of admitted students still did not take any math beyond calculus in HS and certainly did not take calculus in 10th grade. I interview students attending CA HSs for Stanford. At the schools where I have interviewed, some HSs offer post-calculus math, and some do not. The different area HSs also have different accelerated math sequences, sometimes getting to calculus in junior year and sometimes senior year. There isn’t a consistent pattern.
Rather than expecting everyone to take post-calculus math or take calculus in an early year, all of the discussed colleges require incoming students to take a math placement test that helps assess the widely varying math backgrounds among different incoming students and choose an appropriate first math course at the college. Students who pursue a math-heavy majors are expected to start at varied levels in freshman year* and develop a solid math foundation as an underclassmen.
*Caltech is somewhat of an exception. Caltech students are expected to take a similar freshman year advanced single variable calc (uses proofs) class, but students who do poorly on the math placement exam take a special section of that course that moves at a slower pace, meets more often, and gives more individual attention to specific weak areas of particular students.
This type of thinking is very damaging to students whose abilities are quite different from the median (in either direction). Students who are less capable need more time to learn, and students who are more capable need a faster pace in order to stay engaged. Socially, it is also important to be around kids with similar abilities.
Math enrichment, or more broadly academic enrichment, isn’t the same thing as acceleration. IMO, little in the HS math curriculum (including calculus) can demonstrate math aptitude, with perhaps the lone exception of geometry. Current HS math curriculum emphasizes practicality over development of mathematical ways of thinking. Geometry courses in HS have been so diluted for so long in so many HSs. There’re very few HS math teachers who are capable of teaching a rigorous course in geometry. A rigorous course in geometry would teach students ways (often multiple ways) to solve problems, to use their imagination, to visualize (especial in 3D geometry), or to abstract when visualization isn’t even possible (e.g. beyond Euclidean). Advanced students should seek out opportunities outside the standard HS (or even college) curricula.
There are some kids that really enjoy math and do not really struggle with advanced math. The problem comes with others that are maybe good at math and like it but cannot go as quickly, but for various reasons want to stay at the same level as the faster group.
Math is not a race but the course you are ready to take should not be determined by your age.
There is talk in my current district to eliminate the accelerated math track. Compared to the area we moved from, the “regular” track is already accelerated. Regular track was to get to pre-cal by senior year where we used to live. Here, the regular track is to calc. Lots of parental angst about the proposed changes and how they will grandfather kids who are already accelerated in, and how that will look going forward. Right now the district sends the super accelerated kids to the university in town for their math courses. Not sure if that will continue or not. Apparently that is 20% of students so not an insignificant number.
There are plenty of “advanced” students in my area due to parental pressure and outside tutoring. Kids get sorted into the regular or advanced math track in elementary school, but parental angst really ramps up in middle school and parents send their kids to tutoring centers or math circle. Many of the kids forced onto the accelerated math track struggle with Calculus because they simply don’t have a good foundation; they were rushed along too quickly to properly learn the material. The poor quality of math instruction at the high school level, where most of the calculus teachers in our district do the bare minimum, just compounds the issue.
So true. In the 1970’s there were many gifted programs in local public schools in our state. These met the needs of kids and were successful. In recent years, the idea that grit or working hard was more important than natural ability has taken hold and these programs were eliminated. IMO, kids who have specialized learning needs of all types, should have access to public schools.
What has happened is, parents with resources find schools for their gifted kids. And those without resources go without the additional learning.
To think that all kids have similar needs in learning is absurd. Just like people have different heights, people have different skills. We don’t expect kids who are great at sports to play on a middle school team. And, we shouldn’t expect kids who are intellectually advanced to repeat material over and over.
It saddens me that low SES kids with high abilities are at the mercy of a system which ignores their needs.
Our experience: The math specialists at the highly ranked public school could not answer basic questions in math ( based on Russian math ec courses). They tapped out at 6th grade level. This happened with multiple specialists and both my kids.
I believe general math education in most high schools is very low. There are exceptions here and there. I do agree that most schools don’t test depth of learning. And math level is not the same as math ability.
We didn’t stick around for high school there. There were a handful of mathy kids( who were quite bright), their needs were never met. Will these kids pursue MAth/STEM hard to say. I do know, the US needs more kids going into STEM in the years ahead. So we are undercutting future value by not figuring out potential solutions.
This conversation of the validity of accelerated math and math anxiety isn’t complete without discussing Jo Boaler’s work at Stanford:
Her basic premise is that there is no such thing as a “math brain” and that all kids are capable of doing and enjoying math at a high level if presented properly. Pulling certain kids into a math track ignores the needs of the rest, and ignores “growth mindset” in favor of labeling kids.
I get the concept- that math is not taught well in this country, and kids develop an aversion to it as a result. Don’t label sone kids as good at math because then you label everyone else as bad. And if a kid labeled as good struggles, then anxiety and depression ensues.
As a parent of a kid with a math brain, though, I know they exist. Holding those mathy kids back serves no one and hurts the mathy kids.
My kid’s elementary school used Boaler’s work to justify an all out attack on the gifted program. Sad, really. It should be about building everyone up, not taking programs away from kids who need them.
This is exactly the type of thinking that makes US the laggard in math education. Kids are talented in different ways. Some in math and others in other subjects. They aren’t the same. The nature works in a wonderful and mysterious way to ensure diversity in the distribution of talents. Enforcing uniformity is, to say the least, against nature.
I agree, but I would also say that such people are rare (in either direction). I do not believe I have ever met a person that was especially good or especially bad academically because they were born that way. Stronger students tend to come from educated households with parents who are involved in their education. Poorer students often lack that advantage. Of course, there are exceptions, but this has been my dominant observation. All this to say that, for most children, whether or not you would classify them as “gifted” depends far more on their upbringing than on any innate cognitive abilities.