Calculus is never considered a difficult subject in math. The AP version that’s taught in HS is also highly simplied. Geometry should have been a better measure of a student’s math aptitude among the subjects taught in middle/high school, but it’s so diluted in the current curriculum that it can’t serve that purpose.
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I’ve seen a lot of “advanced” math kids being tutored by parents. My kid was in a highly gifted program and to remain they would have frequent tests and one would have to score at least in the top 1% of any national tests. Most of the kids tested into top spots in national competitions. I would say 80-90% of the kids were being tutored by parents. We never even so much as looked at anything. And we certainly didn’t tutor our kid. Our kid didn’t like the high level math tournaments. Wasn’t interesting enough.
There is no fear among kids who have excellent skills. Yes, as they move along they might find a challenge here and there. That’s normal.
There is a huge chasm between the kids who “feel” math and those who have excelled or are advanced due to exposure/parental pressure. At some point, it just gives. Parents think they are doing their kids a favor, when in fact, they are not. There is also a trend where boys are pushed along more than girls and some cultures push their children into math as a matter of pride/course.
Oh yes, and we lived the “advanced” math track too. 6 kids tested into the program and 24 ended up there. Slowed the entire thing down. It was a joke.
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Depends on the kid. Often kids who are highly gifted in some area ( and in particular in math), can’t fit naturally into another grade above. It might be that kid is just one year ahead, but what if they are 3 years ahead or 5? There are many kids for whom the school program does not meet their needs. So skipping a kid ahead a year isn’t going to help at all. Not to even mention that it’s often a different school altogether.
Why is hard bad? I don’t mean miserable, over-your-head hard where you don’t have the proper foundation, but hard in that you have to work for an A or B. For years math has not been simple for my daughter — it takes awhile for her to learn concepts but once learned, she’s good. She’s on an accelerated track, works hard for her As and as a result is proud of them. I think colleges look to see if applicants have taken calculus to see if they’ve pushed themselves.
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I completely agree–I suspect half if not more of that track would not be able to handle BC after precal. All the schools around here have it separated AB and BC. Part is also the AP scores, I suspect. 98% 3-5, 90%4&5. That would not be the case if everyone took BC after precal but I am sure the top kids from the Alg1 in 7th path would be absolutely fine going straight to BC. Just not an option.
Yes! The tutoring! outside private tutoring is common at the school in advanced tracks(I am not talking about specific learning needs–completely different story)–parents get tutors to keep in the honors-AP tracks, especially science and math. We haven’t done it. Teachers have extra help time, and advocating for yourself and going to the teacher is a great life skill. They tell the kids they want them coming to problem sessions and extra help yet many still don’t, yet need a tutor? IF my kids needed regular outside tutoring to stay on the track, then to me it means the track is too hard and we would have moved them. Of course we would have gotten a tutor for a learning issue–we just don’t have that situation, so no tutor. Self-advocate, ask for extra problems to work for practice. The parents are a huge part of the rat-race issues in our school.
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IMHO CC math is taught in a manner that is very slow and repetitive and at the same is theory without a lot of practice. Many kids are ready to move faster in the early grades and thus parents supplement. kids will be able to explain subtraction and division five ways but don’t actual get lots of repetitive practice. Parents get annoyed and supplement. That supplementation leads to acceleration. At the same time some kids move ahead with a lot of theoretical knowledge but weak computational skills. Be the time you get to high school you have kids at all sorts of levels.
My D21 took Algebra in 6th (she was allowed to place into this after a series of tests). She took AP Calc AB in 10th, and BC in 11th and never found math “hard”. Hardly did any homework and never required any outside tutoring or help from anyone. I think a lot of students are pushed by parents into these accelerated math tracks.
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D’s HS used placement tests regardless of what was taken in middle school. There was still a ton of parental pressure so the school allowed students to double up in math sophomore year. Not one of those students ended up staying in the accelerated math track.
I think that brains handle math differently. Many bright kids can progress through math at lightning speed, if permitted. And they do learn it. There are kids who, if they only had the opportunity, could be doing BC Calc by 6th grade, even earlier. But not every brain can understand the why of higher math. Some can’t do it at all, some can learn the how, but eventually, if they don’t understand why it works, they start being unable to do it.
I had one son who was kept out of the two-year accelerated math class because he missed the cutoff on the aptitude test in 3rd grade by one question. The teacher was astonished - she said that he was better in math than she was. District refused to make an exception. So I just taught him accelerated math at home. When he went into middle school, again, by test, he missed the cutoff for honors math. I overruled it, made them put him into honors math. He said it was ridiculously easy for him. I wish I had insisted then that they also skip him to join his friends who’d made the gifted math program, so that he’d be two years ahead in math, but I didn’t want to push it.
Fast forward through 7 years of honors math, with A’s in middle school, and mostly A minuses and an occasional B+ in high school. Now he’s in BC Calc, getting an A minus in it. He says I should have just skipped him to join the double accelerated group, in 6th grade, so that he could have also taken AP Stats in high school. He talks about calculus to me, and from how he speaks about it, it’s clear he understands what he’s doing.
Now here’s the funny thing. My math aptitude tests were much higher than his. I did very well in math… until second semester Calculus, when I hit the wall. I could manage to do it by brute force memorization, but I really did not understand why it worked, or if I glimpsed it, it was quickly gone again. I knew I’d gone as far as I could in math. But in elementary school, if they’d let me move ahead at my own pace in math, I probably could have been in Calculus by age 11 or 12. Who knows if I could have understood it at that age - but I sure had trouble with it at age 16, 17, and 22.
My point is that early math ability does not necessarily equate with ability to do highest level math. Our kids who are gifted in math are often held back by the slow elementary school curriculum. Even the programs that prepare them to be two years ahead in math, doing Honors Geometry in 8th grade and Algebra 2 in 9th, are too slow for many gifted kids, who if they’d been allowed to move ahead as fast as they could, would likely have been in Calc by 6th grade. But that doesn’t mean that they could then do it! They might hit the wall at that point, just as they might have had they been held to a slower pace and not reached Calc BC until 12th grade. Brains all work differently, and early ability in math is not necessarily linked to ability to highest level math, later on.
Being “afraid of the difficulty of calculus” does not mean that it won’t be an easy A subject. It means that the student isn’t confident in their ability to be successful in calculus. This lack of confidence could be an accurate estimation, or it could be completely inaccurate.
People (both HS students and adults) fear that all kinds of things may go wrong. Whether those fears are well founded or not depends on many factors. For example, I live near the ocean, and have known several people who fear getting bitten by sharks when they go in the area beaches. They’ve probably never seen a shark in the wild, and shark attacks are near non-existent in my area (one event per decade or so), so an external observer might say they should not fear getting bitten by sharks. However, fears are often do not follow statistical calculations of chance of event. Instead fears depend on feelings. They’ve heard sharks are dangerous and sharks look scary, so sharks scare them.
Similarly many of the students who fear calculus probably have never done a calculus problem and have aced all their pre-calculus classes, so an external observer would expect them to ace calculus. However, the student heard calculus is hard, and they have a lot of pressure (both internal/external) to get near perfect grades, so it leads to a fear that they won’t be able to maintain their near perfect grades in calculus.
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I have a lot of conflicting thoughts and experiences about this, stemming from having an algebra teacher (esp honors) for a mom, an accelerated math kid who went through public middle school where advancing kids was extremely politicized, and now, having that same kid who is +2 at a boarding school through sheer force of will - and is exposed to +3 and +4 kids from around the country and globe.
My mom: most middle school brains are not yet developed to do the abstract thinking to really get algebra, and the trend to normalize algebra in 8th grade is wrong.
My kid’s middle school: put 2/3 of the kids in algebra, but do away with the geometry track entirely because no middle school kids should be doing geometry. They are only doing geometry because their parents are making them. The only way to control the insane parental rat race is to get rid of geometry.
My kid in middle school: algebra is sloooooow, and my teacher focuses on the boring mechanics. I will teach myself geometry in my spare time, if the school won’t do it. (Signs up for AOPS - finally, math is fun!)
Kid in high school: why didn’t he get to go to a school like these other kids who are so more advanced than he is? Oh wait, some of them are struggling with concepts and are grinding through, and the school has other “advanced” kids repeat courses they took in middle school. But even so, those who do algebra in 9th grade are seen as remedial by the international crowd.
My take aways - math education and what qualifies as standard expectations are all over the map, especially compared to what other countries are doing. What is +2 here is +0 elsewhere, but content, approach and depth make it impossible to compare. I do believe my mom is basically right about adolescent brain development, and in those countries who teach geometry very early must be doing it in a simplified way appropriate for the adolescent brain. I think my kid’s middle school is right to tamp down on parent pressure, but wrong not to offer some way for the few kids who need to accelerate a way to do it (for my kid there was a reason to accelerate- it was seriously affecting his mental health having a teacher who was killing math for him).
Long way of saying- I can totally see a kid who is not developmentally ready for algebra, then pushed into geometry by overzealous parents and then knows he will be put into a calculus class with math whizzes in 10th grade - that would be scary, especially when calculus is touted as (wrongly in my opinion) as essential for “getting into a good college”.
Acceleration does not equate learning how to problem-solve. In my home country, that routinely sends several kids per year to international math olympiads, calculus is taken in university. However, regular math is deeper and getting a good grade requires problem solving and not speed exercises with multiple choice questions, or writing about math in your own words.
The AMC problems do not require calculus. Very few kids in our top STEM school do well on the AMC, albeit being accelerated in math. The kids that do well, do so because they learn how to problem-solve outside of school.
This said, my son also took calculus BC as a sophomore after testing out of 7-th and 8-th grade math in 6-th grade. He was one of only 3 students in the school district allowed to do so. If there was an option for him to not skip but dig deeper in the material and do AMC-type problems in class, we would have preferred that. But this is not an option, the option is to blast ahead if you are bored in regular math.
And no, calculus is not difficult. The subject he had to work harder at was Geometry honors.
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Both of my kids participated in what passes for accelerated math in our town. If I had to do it again I would have kept my older child out of the program (which he did qualify for without parental influence). He is taking pre-calc as a junior but just on the regular pre-college track. Despite getting good grades in math in HS he tells me he “doesn’t know” math. His comment is that American students are taught information to pass tests, not given the tools to truly understand the concepts. I think for a lot of kids on the bubble like my older son, they don’t dig deep enough into the topics in the accelerated MS track to really develop true understanding. With younger kiddo it has been the opposite - he has breezed through and clearly understands at a much higher level than his brother.
I’m a +2 parent who is letting my son drop down his junior year. He’s unlikely going to be an engineer or go into a STEM field.
Many of his friends are better at math and early on I let him go advanced as my son wanted to stay with friends.
I’m an idiot at math. My oldest has a LD in math. It was not me pushing for math.
If a college won’t accept my son because he didn’t take AP Calc, we will accept that.
My son was in an advance track in Math, the school called us one day when he was in 3rd grade and said he was moving up. Looking back, I should have said no, because even back then he wasn’t a Math kid. He is an ELA kid, his reading and comprehension was way higher than Math yet no program to accelerate there.
By the time he got to Geometry (his teacher unfortunately died at the beginning of the school yr) and they had an unqualified sub the rest of the yr, he started to hate Math. He is in Calc AB now because the BC class was cancelled (they couldn’t find a teacher and only 5 kids had signed up ), he finds it a lot easier than precalc and hopes not to take more than the 1 prerequisite Math class in college.
Agreed that the teachers can make a huge difference. My D’s calc teacher had her PhD in math and spent the last two months of school introducing topics beyond AB/BC so that her students would be more prepared for what they’d be learning next in college. She had a class full of engineering hopefuls and she ran that class like a college course. AP Physics C was the same way. There was no teaching to the AP test but the vast majority of the class scored 5s.
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Actually no. Some of the best math students are the ones that come out of remedial algebra. It has more to do with maturity than math knowledge. Plus math at the college level moves twice as fast. I usually don’t recommend rushing math in high school, because high schools vary widely how well they teach it. It’s common for kids to get overconfident in college and get burned.
If you’ve already taken calculus in high school, most universities will still require you to take it again at the college level.
Please cite examples, since I am hardpressed to find enough instances where colleges require a retake of Calc I to say that “most” do this.
It is common, though, for a college to require a retake of MVC and beyond.
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I agree with some on this thread. Math programs vary a lot. Some go quite deep and can be great preparation for college later. Some just don’t offer enough depth for some kids.
I honestly think that a kid going into STEM fields in college is not going to have enough math even if they are plus 3-4 years to skip those courses entirely in college. Maybe Calc, but not advanced math topics. This is particularly true if they will need math for their career or they attend a school like Caltech/MIT etc.
IMO, if kids aren’t getting 4-5 on APs ( if taken) then they haven’t completely learned the material.
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