Now I didn’t get exposed to calculus until high school but I’ve always thought that I could have handled it much earlier. It seemed to me that each year through middle school was spent retreading topics that I had already been exposed to as if we forgot everything over the summer vacation. I found it all very tedious and boring.
So, what is the earliest age that calculus is commonly taught? I’m not necessarily talking about the occasional genius, but perhaps an advanced placement or track.
Algebra is being taught earlier now than when I was in school. One of my sons got a little in fifth grade, but didn’t see it again until 8th, so that’s probably an anomaly. Another got it in 7th, along with many other students.
Calculus is generally after several years of algebra, plus geometry, so I’d be surprised if it’s regularly taught before high school anywhere.
Are you guys sure you mean calculus, not algebra? Is this a British/US terminology thing?
I mean calculus, yes. There is no British terminology difference. And let’s face it, basic differentiation and integration is very easy.
I think that the usual age in a state (read public in American term) school to bring in calculus is sixteen now, as it is an a level thing. But it used to be in o level.
I wasn’t exposed to Calculus until I took a class called Calculus in college.
The teacher of my 400 level Advanced Calc class, a Chinese man (I think) said back in China (or maybe Japan, I’m not sure) said what we were doing to finish up our majors, they do at the beginning of college to start their majors which would imply that they did an awful lot of calc in high school. Also, there was one extremely advanced high school kid in that class.
The only math we did in high school was high school level algebra, trig and geometry. Looking back on it after taking a LOT of math classes in college, it was pretty basic stuff, but plenty hard for the average high school kid, especially considering the majority of them really didn’t like math.
ETA, I never learned anything about basic differentiation or integration on high school. If they taught that, it wasn’t in any of the classes that I took. There may have been AP math classes though.
For reference, here is “elite” maths for high school students, in that they are based on the a level syllabuses - and so require no more knowledge in theory than would be taught to any sixth former - but are for entrants to Cambridge, and thus require considerably more lateral thinking.
It is probably worth mentioning that UK high school students specialise a lot earleir, from age sixteen they will be doing between three and five subjects.
See the description of “Advanced Placement Calculus” at Wikipedia or the College Board website for a description of Calculus as it is commonly taught in American high schools. Note the prerequisites:
The typical student who takes Calculus in high school does so in their senior year (12th grade, starting when they’re around 17 years old), though some might take it as a junior (I did), and quite a few don’t take it until sometime in college.
A kid might get introduced to some of the ideas of calculus earlier, before they have a full, formal course.
I got basic calculus as a senior but it was more or less an “invented” course for four of us nerds. Limit theory leading into differentiation and integration combined with some basic applications which I particularly appreciated as I’ve always been of the opinion that for math, story problems are everything. Not much point to it (in my mind) if I can’t do anything with it.
All this calculus talk reminds me to shamelessly invite folk to another thread I started here (and am about to even more shamelessly bump so more dopers can get invovled) - if you know some calculus, why not get a certificate from MIT?
I was always one of those people that liked the word problems when everyone else hated them. Looking at a list of 20 arithmetic problems was just plain boring. But digging those same numbers (and a few extraneous ones) out of a paragraph breaks up the monotony.
OTOH, when everyone would say “What are we ever going to do with this” I’d think to myself “Are you kidding? What use is the book Hatchet ever going to have in your life?”
It should be noted that I have a pi sign tattooed on my back.
I didn’t learn (and I use that term loosely) Calculus until I was in my senior year, and even then I’d say only half the kids in my class took it. I find learning Calculus at the age of 13 rather extraordinary, then again math was always my least favorite subject.
I did it in either 10th or 11th grade, so I would’ve been 14 or 15 (I think it was 11th grade, so I was 15). It was a standard part of the International Baccalaureate Maths syllabus - Subsidiary Level, not Higher - so maybe half my class was doing it.
People are going to differ in their abilities, of course, but if the OP is asking for when it is “commonly” taught in the US, the answer is: never. The vast majority of HS kids in the US never take calculus.
As for when it is regularly offered in public school, I would say senior year. There are always going to be outliers, but if you take the “normal” fast track math curriculum of Algebra I in 8th grade, Geometry in 9th, Algebra II in 10th and Trig (or what we used to call something like Functions Alanlyt) in 11th, then there really is no time before 12th grade to take Calculus.
Exactly. I can sorta appreciate math for math’s sake, but for me, especially as an engineer, it’s all about using it as a tool with which to bludgeon problems. One I learned that it was actually useful for stuff, there was no stopping me. A book you might like: The art and craft of problem solving by Paul Zeitz. It’s also a pretty good video series.
Not to hijack my own thread, but did you know that pi is wrong? It’s a little silly to write 2pi to represent one turn or pi/2 to represent 1/4 of a turn. It’s not really wrong; it’s just that tau would make things more intuitive and elegant.
I meant common to distinguish from the savant who goes to Harvard as a 12yo or something. I was assuming some sort of AP or advanced track. I was particularly interested in other countries. China, India, etc. for example that seem technically adept.
I did an independent study my senior year of high school where I taught myself calculus through integration by parts. I was a math major in college and did teaching assistant work for calculus my sophomore and junior years. I ran into a number of students flunking out of college calculus who had had calculus in high school. The reason they were flunking out of college calculus is because they did not properly learn high school algebra, trig, or any other fundamental math.
It seemed to me that too many schools rushed math students through the fundamentals, just so they can say that they teach calculus in high school.
My son starts high school next year. Calculus is offered as a Senior year course for most students. The Kiddo will be taking it as a Junior, and some students can take it as Sophomores.
There are students at my daughter’s high school taking pre-calculus as 9th graders. My daughter was on that track as well (Algebra I in 6th grade, Geometry in 7th, Algebra II/Trig in 8th) but after a disastrous 8th grade bout with taking Algebra II/Trigonometry as an online class, we decided to have her repeat the class in 9th grade. It was the right choice, she is getting a much better grasp of the fundamentals this year with an actual teacher to guide her, and the students we know who chose to go on are generally struggling with pre-calc this year.
So, my daughter’s plan is pre-calc in 10th grade, and probably AP Statistics in 11th grade and AP Calculus in 12th. (The last two may switch order.) I think the other students on her original track will run out of math classes by 12th grade unless they enter the PSEO program which allows them to take classes at a nearby college.
One third of my class took Algebra I in 7th grade (everyone else in 8th). The Saxon Math program did not (may still not) have a separate year devoted to geometry, so this left me taking precal, calc AB, calc BC, and AP stats in grades 9-12. Not the least bit unusual. I’m no math genius, so I believe that most children 1) without learning problems 2) with diligent parents and 3) who are given proper instruction could easily manage a more accelerated program.
I strongly recommend she take calculus directly after precalc. This stuff gets rusty fast if you don’t use it. Unless it’s changed, AP stats is a joke. A nice way to take a break her last year. Or she could take calc BC. Both courses are available online if the school doesn’t offer them; that’s how I had to take them.
It’s a little silly to write 2pi to represent one turn or pi/2 to represent 1/4 of a turn. It’s not really wrong; it’s just that tau would make things more intuitive and elegant.