<p>My son, the humanities guy, always loved math and physics. His problem – and this started early on – was that he couldn’t find a class that was at the right level for his interest and ability. </p>
<p>He’d do well and get but into the advanced class with the mathaholics. He couldn’t keep up with these kids so he’d do poorly and get put into the regular class where he’d do well, etc. There never seemed to be a class for kids who could grasp the concepts, loved the “abstract poetry of numbers” but weren’t brainiac math-kids. </p>
<p>At Williams one of the distribution requirements is a class that uses quantitative, non-verbal thinking due, I think, to the administration believing along with Dadguy that it’s not okay to be mathematically ignorant.</p>
<p>“Does it seem crazy, then, to make future engineers and physicists to take AP english? Or AP spanish? Top colleges look for that stuff too, you know.” I agree with the (implied) idea here that just as it is good for a math student to be well-rounded by taking advanced english and foreign language courses, it is equally important for liberal arts students to become more well-rounded by learning calculus. I do not see why anyone would want to put it off until college. In my opinion it is very important for an educated person to take at least one course in calculus.</p>
<p>Without calculus one cannot learn much science from a fundamental basis. The most revolutionary aspect of Isaac Newton was that he realized you could look at the world by DERIVING the physical laws from a few basic principles and math (calculus). I am an interviewer for MIT, and many students I interview indicate that they do not really like high school physics, because it is taught using memorization (rather than by using calculus and deriving the results from basic principles). Marite suggested learning statistics instead of calculus, but even statistics cannot be understood without calculus. Without calculus, science or statistics is just a bunch of memorized formulas. Obviously not everyone needs to be a scientist, but a well-rounded educated person should at least try to understand what was so revolutionary about the approach of Isaac Newton to physics compared to the approach of Aristotle.</p>
<p>And I think for some kids, using math in a “real world” way…to balance a checkbook, figure out a tip or sales price, etc., is about as far as they will go mathematically. I have seen high school kids so busy memorizing (without any understanding of underlying algorithms) in higher level math, when they can’t even manage simple every day math. </p>
<p>There are plenty of kids at both extremes, but seems to me that strict memorization, without understanding and application, doesn’t serve anyone that well.</p>
<p>In most schools, the basis for AP-Stats is Algebra II. Not Precalc, not calc. As a result, some colleges do not give math credit for AP-Stats. I think that for the layman, an understanding of statistics is more important than an understanding of calculus. At non-techie schools, the proportion of math/science majors is 1/3. The other 2/3 should be well served by stats is they cannot or do not wish to master calculus.</p>
<p>Learning statistics without calculus is analogous to learning physics without calculus. You might be able to handle a certain set of problems, but you will not have a rigorous understanding of how to determine which types of problems the approach applies to and why. For example, without calculus a student could never understand WHY so many processes appear to have a normal distribution (and under which circumstances they would be expected to have this type of distribution). They could not even have an understanding of the relationship between a probability density function and a probability distribution function. Anyone can learn to use a calculator and to compute standard deviation, mean, median, and mode of a data set. This can be learned in about an hour. But you cannot understand statistics without calculus.</p>
<p>I have no argument that you cannot do well on an AP exam for statistics without taking calculus, just as I would not argue that you cannot do well on the SAT-II physics test without calculus. As a matter of fact, if you have learned physics with calculus such as taught at the university level, you may have to relearn and restudy to do well on the SAT-II physics exam. But without taking calculus, you can never FUNDAMENTALLY UNDERSTAND the material.</p>
<p>I have no dispute with your argument. But my question is how deeply should people who are not going to be statisticians or scientists go into the study of statistics. I would submit that most people do not. Most people need some understanding of statistics to be educated citizens; most people need to know some history to be educated citizens as well. They also need to some biology, some chemistry, some physics, and so on and so forth. There’s only that much one can study at either the high school or the college level. There will always be students who have far more aptitude for one subject than others and they should be allowed to proceed at a more advanced level.<br>
But just because we think "our* own field of interest is vital does not mean that everybody should follow the same regimen.</p>
<p>This does not come from a mathophobe. As I’ve said, I have one who does not like math and one who aced calculus in 8th grade. I would not subject my math-averse student to his brother’s set of course, nor would I subject my math-loving student to his brother’s. To quote Karl Marx wildly out of context: “From each according to his abilities, to each according to his needs.” Educationally speaking, that’s my motto.</p>
<p>I like the way my d’s very competitive hs handles calculus. Every girl’s needs are met. Five levels are offered: College Prep Pre-Calc, Honors Pre-Calc, High Honors PreCalc, High Honors Calculus, and Calc AB - AP.
They also offer both College Prep Prob & Stat and Statistics- AP. Every girl must take a year each of Biology, Chemsitry, and Physics in order to graduate.</p>
<p>“Does it seem crazy, then, to make future engineers and physicists to take AP english?” Not at all. In fact, to attain success in these fields, you must be an excellent writer.</p>
<p>A student who decides he doesnt like science before he has taken calculus would be like someone who decides he doesnt enjoy studying literature after reading only primary school literature. Much of real science and engineering is not at all similar to high school science. The typical high school science sequence (biology, then chemistry, then physics concurrent with calculus) tends to reinforce in students minds that science is fundamentally based on memorization and/or getting to know many rules and formulas. One can definitely succeed in this world financially without thoroughly understanding calculus, and could even, for example, obtain an MD at Harvard Medical School with good grades without a good grasp of calculus (I have spoken to MIT faculty who have taught courses to Harvard Med students and have mentioned that few students could handle calculus well). However, once you accept the mode of ASSUMING that most (if not nearly all) phenomena are too complex to be understood, you have lost something very important to the scientific discovery process. </p>
<p>A friend of mine (and office-mate for a year when I was a grad student) was the chairman of his universitys physical therapy department and in his late 30s when he participated in an NIH program that allowed him to better himself by getting involved in research and courses at MIT. He decided to take introductory mechanics (statics) in the mechanical engineering department. He came to me after about two weeks into the course and humbly told me that he had just realized that he had previously always just tried to MEMORIZE the various complex behaviors of muscles, ligaments, joint motions, etc. The emphasis in this course of starting with the most basic assumptions and then slowly building up from there was a Eureka moment for my friend. He now understood that most of the various complex phenomena he had previously memorized could very likely be derived and explained.</p>
<p>But if you study statistics, biology, chemistry, or another science or engineering subject without mastering calculus, then you should recognize that you have significantly limited yourself in terms of basic understanding, and you will never experience what it is like to conceptually understand science.</p>
<p>Not everyone must necessarily study calculus, just as not everyone must necessarily study Shakespeare. But students who would like to LEAVE OPEN THE POSSIBILITY of rigorously understanding any scientific field should not opt out of math before studying calculus. If this has to wait until college, that is fine.</p>
<p>If you want to leave open the possibility of doing math and science, fine. But there are lots of students who knew, in 7th or 8th grade, that they loved the humanities and social studies and that, although they did fairly well in math and science, that was not going to be their destiny. That happened to S1. There was no point in pushing him into calculus. Choice is what this is all about.</p>
<p>Just speaking from a student’s perspective. Math has never been an interest of mine, I could care less for it. However, as I’ve always been pretty good at it, I have signed up for AP Calc BC next year. A class known for being excruciatingly hard.</p>
<p>Although I guess it seems like “small potatos” compared to the stuff people talk about on college confidential (namely in the “what are my chances?” board), I only did it because I know its going to look a hell of a lot better to college than AP Stat, a class known for being a fairly easy class at my school. Of course the reality is that I am FAR more interested in Statistics than I am in Calculus. I also consider Statistics to be something that I could actually use a later date in my life once I am done with education (and hopefully math).</p>
<p>I think one of the most interesting points made by the OP is that in our society it does seem to be excused more readily the inability or disinterest in math than in language or the like. I have been guilty of it myself especially since starting college. In high school I was always in math and science classes, and I always did very well, but now that I’m an English majorin college, and I’m not taking those classes anymore (except for the math/sci requirement for graduation), I found myself making jokes about a math inability that never existed before. When dividing up the tab at a restaurant with friends I would say, “don’t look at me, I’m an English major.” With anything slightly mechanical, “let’s get an engineer in here.” I didn’t even notice what I was doing until, in an English class, we read an essay by Walker Percy “The Loss of Creature” (it’s a good read for any English people out there, jk), and it expressed an idea similar to that of the OP. </p>
<p>I know I’ve also gotten the same idea thrust upon me from the other side, the math/science people, some of whom have said that they can handle English courses and history courses, but that humanities people are hopelessly adrift in science or math courses. I think culturally that idea is reinforced, that the humanities are the easier majors. The core curriculum at my school is chock full of literature, history, philosophy, and a negligible science requirement that one can curtail with courses such as “Physics for Poets” and the like. There is no literature for the illiterate or the like. I don’t know where this idea started, but it’s turned into a self-perpetuating stereotype.</p>
<p>I think all of the “humanities people” out there should push themselves by taking that extra math course or science course, not necessarily Calc BC but something. I’m fulfilling my math/science requirement with Calc 2 and I’m deciding between physics or calc-based physics for next semester, because I’m not just an English major, and no one else should be either.</p>
<p>Why not pick math that is educational AND challenging? Why is it that we are so stuck it having to be Calculas? </p>
<p>From what I have read, many students are terrible writers, can’t analyze a story, don’t understand how statitics are created, don’t get the concept of one man one vote, don’t understand interest rates, inflation, recession, etc</p>
<p>Why are we soooo stuck on Calculas as the barametor for learning math? Are we so close minded we can’t see another way?</p>
<p>Boy, now the question is about Calculus in high school. A few months ago we were discussing whether Alg II should be a requirement for hs graduation since some may never pass the class.</p>
<p>Since when is calculUS not educational and challenging? Do you even know what calculUS is? It’s a major branch of mathematics that underlies many, many natural phenomena, and it’s not difficult for a reasonably smart student to pick up. By reasonably smart, I mean anyone considering a school that would expect to see a student with calculUS on his or her transcript.</p>
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<p>These are all things to be covered in other classes or on the student’s own time. I’ve picked up a lot of nuggets of knowledge just by opening up the newspaper. Other things I’ve learned at school in classes like economics.</p>
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<p>It’s not a “barametor”[sic] for learning math. It’s the next progression in the series of algebra/function based math that students learn in high school. We’re not closed minded. Maybe you’re the one who should try to understand the field of mathematics a bit more before baselessly denouncing its subdisciplines.</p>
<p>And for the last time, it’s calculUS, not calculAS.</p>
<p>Great points, thank you. Good luck with you studies. Conversely, I think Math and Science majors could do with more humanities classes as well.</p>
<p>cgm,</p>
<p>The fact that “many students are terrible writers, can’t analyze a story, don’t understand how statitics are created, don’t get the concept of one man one vote, don’t understand interest rates, inflation, recession, etc” has nothing to do with the presence of Calculus in the high school ciriculum. You can take Calculus and learn about those other things. They’re not mutually exclusive. I have to believe that the human brain can take hold of both the things you think should be taught and Calculus. I can not concede that one should be taught INSTEAD of the other.</p>
<p>I’m sorry you don’t appeciate the value of calculus. The various posts on this thread by pafather (on page 2, I think) lay out the argument for this as well as anyone could, I think.</p>
<p>oh and cgm, as a recently graduated high school student, i can say that all of those things you mentioned were taught in classes such as government and english. both required for graduation. so, if “many students are terrible writers, can’t analyze a story, don’t understand how statitics are created, don’t get the concept of one man one vote, don’t understand interest rates, inflation, recession, etc” then they either didn’t try to understand the concept in school or it was inadequately taught to them. and just as dadguy said, this has nothing to do with the presence of calculus in the curriculum.</p>
<p>I guess there is something good about being a “brainwashed soviet kid” . We started algebra in 6th grade concurrently with geometry. Math sequence ended with calc in the last grade( 10th) . Everything was mandatory. Physics, chemistry, bio( and before that botany, zoology and human anatomy) . Geography was taught extensively. History( starting with the Ancient World) , literature( Russian and foreign) , foreign language. Kids in magnet schools( I was one of them, music) had to study all sorts of things on top of that. And somehow everybody survived. I am glad that my S could CHOOSE his high school classes, but find it hard to belive that “some kids are incapable” . They just need the right kind of brainwashing( JK,JK) . :-)</p>
I am glad that my S could CHOOSE his high school classes, but find it hard to belive that “some kids are incapable” . They just need the right kind of brainwashing( JK,JK) . :-)</p>