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In most high schools (in America), I think it is safe to say that the highest math subject offered is calculus.

But why is it calculus rather than number theory or some other branch of mathematics?

While calculus has applications, I'm sure other branches of math have applications just as well.

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    $\begingroup$ See also matheducators.stackexchange.com/q/2105/376. $\endgroup$ – J W Feb 6 '16 at 13:19
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    $\begingroup$ Calculus, statistics (incl. hypothesis tests associated to cont. distributions), and to a lesser extent computer science have all been introduced in many high schools. Two factors stick out in my mind, (1) the connections to STEM/business-related careers, and (2) at least in the US, the number of AP courses taken overtaking SAT/ACT scores as a college-admissions credential. $\endgroup$ – user1027 Feb 6 '16 at 15:00
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    $\begingroup$ There's a sort of pyramid structure where calculus is the foundation for physics, physics is the foundation of chemistry, and chemistry is the foundation of biology. That makes for a long list of majors, including related fields such as engineering and computer science, in which calculus plays a foundational role. At the same time, I think the reason schools require pharmacists and physical therapists to take calculus is simply that they have too many students and they want to get rid of some. So for that purpose, number theory would work -- as would ancient Greek. $\endgroup$ – Ben Crowell Feb 7 '16 at 0:26
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David Bressoud wrote about this last year on his blog in a multipart series called Calculus in Crisis. This post deals specifically with "the rush to Calculus". If you trace his arguments across all the posts in that series, the line of reasoning that emerges is this:

  • Economic pressures are driving more and more college students to pursue STEM careers (whether or not they are ready for them).
  • The rapid growth in the number of STEM majors has caused a boom in enrollments in calculus (again, whether or not students are ready).
  • High school students end up taking calculus in high school because they feel the pressure to major in STEM disciplines, and taking calculus in high school lessens the load when they get to college.
  • And finally, since there have been so many students in the past taking calculus in high school (Bressoud estimates 40-45% of traditional first-year college students are students who took calculus in high school), there is now an expectation that high school students will take calculus, and that expectation is reinforced by parents, administrators, and guidance counselors.

There are no such forces pushing for the adoption in high school of number theory or abstract algebra or whatever, so that's mainly why you don't see them -- where's the demand?

I do think that statistics is making serious inroads into high school mathematics -- I don't know the numbers of how many AP Statistics courses are being offered right now or what their enrollments are, but anecdotally it seems like a lot more of my students are coming in with AP Stats credit than they used to.

And personally I would like to see high school math look a little more like computation + data science + discrete math and linear algebra, some combination that is accessible to a larger group of people and more broadly useful.

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I think calculus is just seen as the most relevant, and not for bad reason. The majority of students who are going to take calculus are engineering students. These students need ideas from calculus more than they need to know about something like axiomatic set theory (although linear algebra would be a good class to offer in addition to calculus).

Basically, engineers need to calculate the occasional integral. Although they can do this with a computer nowadays, they should still know what an integral actually is. They're never going to need to know how to solve a Diophantine equation on the spot

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  • $\begingroup$ I wonder whether it's still true that the majority are engineering students. The impression I get from my own classes is that if engineers are a majority, it's just barely. Related: matheducators.stackexchange.com/questions/10524/… $\endgroup$ – Ben Crowell Feb 7 '16 at 0:22
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    $\begingroup$ It appears that only about 30% of calc students in the US are engineering majors. $\endgroup$ – Ben Crowell Feb 7 '16 at 14:58
  • $\begingroup$ Calculus is seen as the most relevant for getting ahead in STEM programs in college, not necessarily as the most relevant branch of mathematics in a mathematical sense. Most people who push calculus in high school have no idea how even to determine whether or not a branch of mathematics is relevant or not in the first place. (If they did, they wouldn't be pushing calculus so hard because let's face it, calculus is really not that relevant for most people.) [/duck and cover] $\endgroup$ – Robert Talbert Mar 3 '16 at 19:38
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"While calculus has applications, I'm sure other branches of math have applications just as well."

Educating yourself on the applications might answer your question. And make your teaching more informed.

I have been a chemist, engineer, military officer, and finance professional and dabbled in applied psychology and economics. Calculus is needed for that stuff. Number theory is not.

Math courses are arranged (in high school and first couple years of college) to service the mass of students who ARE NOT math majors. Learning about their courses and what math is involved in their HW problems, derivations, etc. would help to inform you on why certain classes are part of a standard curriculum and others are not.

P.s. Richard Feynman (pretty good math guy, won the Putnam with no study as last minute team member at MIT) started out as a math major. He ditched it because 'the only use of the things you learn are to become a math professor and teach more math majors'. He went to EE instead and then to physics.

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  • $\begingroup$ I sympathize with Feynman. This is the year I'm applying to colleges and such, and I've come to the unfortunate realization he came to. Stuck somewhere between physics and computers. :-) $\endgroup$ – Simply Beautiful Art Nov 29 '17 at 23:41
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Calculus is the greatest piece of human technology in history, and it is taught because it continues to be not only the most efficient technology but also the most broadly applicable. A highly "applications" based perspective on calculus would say that as a technology, a symbolic technology, more problems have been solved with the tools of Calculus throughout history than any other part of mathematics. It is important to note that the problems solved by calculus that I hint at are not at all limited to mathematical problems: calculus has solved the largest number of human problems in science and society than any other part of mathematics.

It happens to be the tool of our times, and perhaps in the future there will be some other such symbolism which can earn even higher respect for is use as a technology, but so far we are lucky that Calculus continues to be the most efficient tool in human history.

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