<p>That was something I learned after I started to ask this question. My initial interest came from the fact that of all the “fundamental” courses I took, calculus was the only one that vanished from my memory without hardly a trace. Also, I have a fairly math-y mind, and use algebra all the time, but really rarely come across things I would need calculus to understand. I assumed for years that science, social science, and medicine types used calculus all the time, but when I asked friends in those worlds they said no. I did work sometimes with economists, and I know they used calculus, but I didn’t have any trouble understanding their arguments without being able to replicate their math.</p>
<p>On that basis, I wondered what, if anything, learning calculus contributed to citizenship in order to justify its privileged place in elite education curriculums.</p>
<p>I asked a few math grad students and professors, and they said they thought it was stupid to insist on teaching calculus to students who weren’t going to use it and didn’t need it for higher level math. Obviously, a universal calculus requirement supports the salaries of lots of math professors and grad students, but the people I knew felt ambivalent about it. Then, when I raised it here, a number of math people said consistent things.</p>
<p>I don’t want to give the impression, though, that that position is universal. Lots of math educators will defend calculus. My children’s college, which devotes enormous quantities of thought to its core curriculum requirements, essentially requires two quarters of calculus for all its students. (Actually, it doesn’t require that, but lots of pressure is exerted on students to make them do that rather than substituting other math unless they are already past calculus.) But the arguments for calculus are often contradictory. There isn’t anything like consensus on why we need everyone to learn it.</p>
<p>I guess educators choose to teach calculus after algebra and trigonometry in highschool because:</p>
<ol>
<li>Calculus helps students understand that all basic math that they learn from middle school to highschool has a logical foundation. Without calculus, we cannot explain to students why the area of a circle is Pi * R * R. Without calculus the math foundation based on deductive reasoning of students will collapse.</li>
</ol>
<p>I think the need of high school math curriculum to be calculus focused stem from it’s links to Physics.
During my HS days there was no option of studying Physics without Calculus.</p>
<p>That doesn’t apply if you’re me, though - a person who has never taken a physics course in my life, and can’t say that I’ve ever felt that I’ve suffered due to that lack.</p>
<p>I’m one of those who is very math-y, but not very science-y. I was a math major, and took plenty of math courses beyond calculus, but I would say both professionally and personally, probability and statistics have been of far more use. I use the concepts of Type I and Type II error all the time. And I think there is a shocking statistical innumeracy in this country, which I think is far more of a problem than calculus innumeracy. I have to agree with JHS – I know I did it, and did it well, but I can’t say I either remember or use calculus.</p>
<p>Frankly, I am one of those people who are against mandating calculus as a requirement. However, I am in favor of folks taking higher level math beyond high school for the reasons given in this thread. I just think that kids should have a choice between taking Calculus,which is very applicable to scientific subjects and statistics,which is probably one of the most applicable mathematical disciplines for most other fields.</p>
<p>^^^
Again, I think it’s fine for people to take statistics, and if people just want a basic statistics course suitable for most cases I guess they can take non-calculus based stats which involves pretty much assuming a normal distribution for most things, and then looking stuff up in tables.</p>
<p>Buit I still believe that for a real thorough understanding of statistics it is difficult to decouple it from probability, and you need to examine the behavior of probability distributions other than the normal distribution. And I think that for continuous random variables this requires at least some calculus to actually understand. Not that I’m claiming to actually understand it, at least not anymore.</p>
<p>Of course, not that you will actyually use this in your day to day life , but I don’t do ANOVA testing in my day to day life either.</p>
<p>I think Pizzagirl had an important insight: Calculus became a de facto requirement because in the 40s, 50s and 60s Physics became a de facto requirement. Physics was the master science, the science of nuclear power, nuclear weapons, and the rockets and planes to deliver them, and the radar to tell us they were coming. And, notwithstanding the current vogue for pretending to teach Physics to 9th graders, even I believe you can’t learn Physics well without at least basic Calculus. </p>
<p>This also explains my experience, to some extent: Contrary to the normal pattern, I decided not to take Physics in 12th grade, in favor of Music Theory. I don’t know if I would have the guts to do that today, but back then my status as a top student in my school pretty much guaranteed my admission wherever I wanted to go, so I didn’t have to play by the rules all the time. But I never had my Calculus reinforced by taking Physics.</p>
<p>The interesting thing is that Physics itself seems to have been de-emphasized some, while the Calculus requirement has taken on a life of its own. Today, all students encounter some sort of dumbed-down version of Physics, but relatively few students take Calculus-based Physics. My son’s high school class had two 33-student sections of AP Calculus BC, and several other classes offering non-AP Calculus – probably close to 200 students taking Calculus at any time. It had one 14-person AP Physics C class, and no other calculus-based Physics. At his university, notwithstanding its de facto Calculus requirement, it’s easy to satisfy the Physical Science requirement without taking real Physics.</p>
<p>I think that I am pretty much written out on this, at least I probably ought to be after thinking about it on my way into work.</p>
<p>What I was thinking was that maybe more than which particular studies are valuable, the question is to what depth do we need to study which subjects, and which things are probably not that useful in general life or careers.</p>
<p>For example, I keep reading people say they use Algebra in their daily lives. But I’m a little buffaloed as to what that means. If it means I discover I only have half enough corn starch for my cookies, therefore how much vanilla do I need; or which is a better mortgage, or things like that, I guess I use basic Algebra in my daily life. But I really can’t think of the last time I needed to know how to complete the square, figure the convergence of a sequence, or do a partial fraction expansion. Or deal with exponents over 3 for that matter.</p>
<p>As far as statistics - sure, nearly everybody should know what the mean, median, standard deviation, and generally what the percentage breakdown is for the bell curve. And if you are going to be a researcher of some kind you probably need to know something about hypothesis testing and what those little charts and tables at the end of research studies mean.</p>
<p>But I also think that you would probably at least want to know the symbols for the differential and integral in case you run across them, and basically that the derivatve represents a slope or rate of change, and that the integral basically represents a sum or an area under a curve - and that they are related in some way. I think maybe people take for granted that they were at least introduced to these concepts.</p>
<p>Now I’m done, I’ll just read what others say and resist the temptation to repeat myself anymore.</p>
<p>LOL JHS, we are so similar sometimes. I skipped out of Physics in order to take AP Art. I did take Calculus BC as a high school senior one of only four in my class (plus one junior). I took Physics (real Physics not for poets) in college so I did get it eventually.</p>
<p>The observation about physics is true. The honors track at our school has kids taking AP Physics B (no calculus) in 10th grade, and many kids who only have room for two more AP sciences and I think there’s only one section that takes Physics C. (About 5% of the class.)</p>
<p>“Today, all students encounter some sort of dumbed-down version of Physics”</p>
<ul>
<li>Comment in regard to college Physics. In college, there are calc-based and non-calc based Physics. It is free choice for some, and requirement based choice for others. For example, I believe that most engineering majors probably require calc-based Physics. On the other hand, to complete Med. school requirements, pre-meds do not need to take calc-based, they can take non-calc-based Physics. Unless they are interested in Physics, most pre-meds are taking non-calc based Physics. But do not kid yourself, it is very challenging even for very top, straight A students at state schools. There are no dummied down version of Physics in college as far as I know. D’s HS Physics was not dummied down either, although they did not have time to cover all material. But this is another concern with HS curriculum.</li>
</ul>
<p>It is based on my D’s comment who is college senior pre-med and who so far has never had any Bs in her life.</p>
<p>I think JHS just meant there are non-calculus based physics courses offered. Yes these courses are still a challenge, and in fact contain much of the same material as the General Physics sequence, but the fundamental connections to calculus are not made there. If one intends to pursue physics or engineering as a major, sooner or later those connections have to be made, simply because that is where the foundations of physics lie. In a way, it is similar to having theory based calculus vs. non-theory based calculus. In one, you learn to drive, in the other you learn how the car works. Which course is appropriate depends on what you need to do with the car next.</p>
<p>For my kids, at least there was no comparison between non-calculus-based physics courses and calculus-based ones.</p>
<p>I am completely puzzled why medical schools require applicants to have taken a year of calculus, but permit them to take non-calculus-based physics, and don’t require them to take any stats, with or without calculus. My former neighbor is a biophysicist who teaches in a medical school, and he is in a perpetual state of dudgeon over how little the medical students know about physics (and how little they care to learn more).</p>
I’m with you there, but I don’t think the current medical education establishment has really caught up with the fact that the future of medicine is so physics-focused. If you think about it, in a very simplified sense, at one time medicine was biology centered, then it became chemistry centered, and now it is becoming physics centered. Aspiring doctors have to know more and more stuff to keep up with the base.</p>
<p>My husband (cancer researcher PhD not MD) is in a constant state of dudgeon about how little his grad students know about statistics. Interestingly he actually double majored in biology and physics and his PhD is in Biophysics. I’ve never heard complaints about the lack of physics in his students, but that may be because his research work no longer requires as much of it.</p>
<p>^^S2 decided to take AP Stat instead of BC Calc senior year because he figured the stat will be more useful for what he wants to do (had Calc AB as a junior) and will give him at least a rudimentary background for more stat courses. True, but if he wants to take more Econ as well (which he does), he’s now realizing he’ll need more calc, too.</p>
<p>He is starting to think that a humanities guy with good number-crunching skills might have better job prospects, and in what he wants to do, being able to handle data and statistical analysis is the way the field is trending anyway.</p>
<p>Among my kids’ classmates who are of the science persuasion, there is a distinct division between the bio/chem folks and those physics/math people. Different parts of the brain?</p>
<p>My son took Calc BC because he felt that he’d get a better statistics course in college. Mind you he originally planned to take both because he adored the AP Stats professor. Unfortunately there was a scheduling conflict with AP Euro which has the reputation of being the best course in the school. </p>
<p>My older son did fine in biology and chemistry, but no question that he enjoyed physics and math far more. Younger son loved biology, hated chemistry, and enjoyed physics though he didn’t necessarily excel in it. (He did take AP Physics C though.)</p>
<p>I loved chemistry and math - physics less so, though I did like my statics courses which is just the physics of stuff that doesn’t move.</p>
<p>I would think that the future of medicine is a lot more statistics-focused than physics-focused, at least at the practitioner level. Sure, physics is extremely important for research and for understanding the cellular processes involved in diseases and pharmaceuticals. But an internist doesn’t necessarily need to understand all of that at a deep level. What an internist DOES need to understand is how to think critically about drug studies.</p>
<p>To correct JHS’ post #49: ParentofIvyHope made the connection between physics and calculus in his post #45, not me.</p>
<p>And I completely agree that a doctor needs to be able to think critically about drug studies, which necessitates an understanding of statistics, alpha vs beta, power, statistical significance testing, and so forth. I’d also submit, however, that the skills that are developed in learning statistics and to a lesser extent probability are useful to most people in their lives. Look at how many people can’t interpret a poll result correctly, or mix up percentage changes and point changes, and so forth. It’s sort of the classic “Did you know 1/4 of all robberies take place between Memorial Day and Labor Day?” question – well, the person who knows how to think recognizes that 1/4 of the year takes place between Mem Day and Labor Day. It’s that kind of sloppy thinking that is all too common and which I think would be of more use to the average person than knowing the symbols for the differential and integral.</p>