What's So Great About Calculus?

Parents Forum
1

<p>Excerpting and combining some of my OT posts on the bad-accents thread:</p>

<p>
[quote]
A calculus requirement is at least as valuable as a "Great Books" one.

[/quote]
</p>

<p>I am still waiting for an explanation of why this statement could even possibly be true. I don't remember any of my calculus because I have never, ever encountered a situation where I needed it. I remember almost all of my algebra because I need it all the time. When I learned calculus, I took for granted that it was important as part of a general education, but life has not proved that out at all. I never got any idea there was anything at all intellectually interesting about it; it was just a series of rules someone told me I had to learn, so I did.</p>

<p>I agree that we need more rather than less scientific literacy, and a passing understanding of basic math. I have never understood the value of requiring calculus. It obviously was poorly communicated to me. I don't understand why everyone ought to know how to calculate how high the initial pull on a rollercoaster should be. I'm not saying it isn't useful for someone to be able to calculate that, but it doesn't impress me as a requirement for citizenship (unlike, say, understanding compound interest and present value, or probability, or the nature of scientific proof).</p>

<p>Furthermore, a year's basic calculus course, as far as I can tell, does not get students anywhere near the ability to perform any meaningful real-world task using calculus, and no one has been willing to propose that general education requirements extend beyond that level. With "Great Books", in contrast, fairly limited study does impart useful knowledge. A year of college study can give a student a tremendous store of shared cultural and philosophical reference points with educated people all over the world.</p>

<p>
[quote]
The math department has to teach introductory calculus to almost half the students; many of these have no intrinsic interests in math nor do they think will use it in their career. Thus, much of the course focuses operation proficiency rather than the interesting aspects behind simple calculus.

[/quote]
</p>

<p>This statement indicates something is terribly wrong to me. I recognize the "service work" problem. But if students have no intrinsic interest in calculus and don't plan to use it in their careers, why not emphasize what is intellectually interesting in math rather than focusing on unwanted and unuseful operational proficiency?</p>

2

<p>Because it is a lazy way of teaching "thinking" and "learning" and whatever else they think doing years of calculas is supposed to do</p>

<p>My D was told, MUST TAKE TWO YEARS OF CALCULUS...she took AP Stats and learned more real life stuff then she ever would have in calc class</p>

<p>There are many more ways of teaching logic, thinking skills, etc</p>

<p>And we need more kids who understand taxes, debt, IMF, Nafta, etc than we do who can do some formula</p>

3

<p>JHS- I have been complaining about this need of Calculus for non math majors for years</p>

<p>WHy should a really smart kid who wants to do Law be "forced" to take two years of Calc in HS? Wouldn't a year of "real world math" be so much better, with some logic puzzles, some stock market work, some complex banking, some information on loans, debts</p>

<p>Throw in some puzzles, some games, and whatever else can "teach" thinking, analyisis, etc</p>

<p>How about some LSAT questions? </p>

<p>Again, its laziness and no imagination that pushes this "need" for calculas for people that will never ever use it</p>

4

<p>I think the theory is that calculus requires learning a certain way of thinking, of problem solving, of doing logic, that is helpful brain food for tackling other learning situations. OTOH, some kids aren't ready to learn calculus until they are older, because it does mean a different kind of thinking.</p>

<p>The only kids in high school who "must" take calculus are those who are either going into scientific areas, or who are applying to highly selective schools. The vast majority of colleges couldn't care less if you take calculus in high school.</p>

<p>A friend of mine recently told me she didn't appreciate calculus until she started taking economics in college, when she realized why it was important to measure the area under a curve.</p>

<p>I took calculus twice, in high school and in college, and I remember nothing. I don't think I've ever used it. It definitely was easier in college than high school, so I think being older helped. </p>

<p>We agonized over whether my daughter should take calculus in high school. She was interested in selective schools, and worried it would hurt her if she didn't take it. OTOH, we knew that getting a C in calculus would hurt just as much (and the HS calculus teacher assumes that her whole class is destined to major in engineering -- not a good situation for non-science types). We managed to figure out a way for her to study calculus in a different setting -- and sure enough, she got the C. I know she remembers none of it. Was it a waste of time? Perhaps -- although calculus proponents would argue that she benefited from the problem solving skills.</p>

5

<p>I loved calculus, it stretched my brain, it made math seem beautiful. But like JHS I sometimes wonder why it was required. All statics in architecture school was taught without it. I've never, ever used it in the real world and I don't remember a thing. Algebra and trig I use pretty regularly. I'd encourage people to take calculus because I think it's the mathematical equivalent of being well read, but I don't know that I think it should be required.</p>

<p>OTOH, while I wouldn't use it in my work, I think an argument could be made that everyone should take a statistics course so that, if nothing else you could understand how they get misused and misunderstood. My husband complains all the time that too many of his fellow scientists don't really understand statistics, event though they are quite handy with calculus. :eek:</p>

6

<p>You cannot describe a dynamic world without calculus, period.</p>

<p>Things move? Calculus is involved.</p>

<p>Of course, it also requires a totally different approach to problem solving, and since the point of a liberal arts education is to obtain various lenses through which you can explore a problem, any expansion into an uncomfortable, uninviting, and unique form of thought is a tremendous benefit to you.</p>

<p>Citygirlsmom-- I'd argue that you can't understand true probability and stats without calculus. Non-discrete options (continuous options...like say, where someone is-- it doesn't have to be 1m or 2m it can be anything of an infinite number in between) requires calculus.</p>

<p>If you want to move beyond dice and cards, or be able to more accurately describe things than making arbitrary integer cut offs, you need calculus.</p>

<p>I'd argue that the design of most pre-calculus courses is what fails students, not their calculus courses.</p>

7

<p>(I like what the last three posts said....)</p>

<p>I suppose an English major doesn't need math beyond high school algebra any more than an engineering needs English beyond high school composition. These are both examples of a somewhat narrow education, though. I have great respect for people I know who are smart on both sides of their cranium (and I don't claim to be a member of their club!) I think we all need to be forced to excercise both sides of our brains, even those of us who don't want to. Some schools (or some majors) expect more stretching than others.</p>

<p>An elementary understanding of calculus, however, can change the way one perceives those parts of the world that can be described mathematically--motion, slopes, areas, volumes, population growth, economics, chemical reactions, drug absorption, heat transfer, probability, and even JHS's example of compound interest.</p>

<p>As for how it is taught, I found all of the courses in the math department in college to be rather dry and difficult as they were usually taught without regard to applications. Fortunately I was motivated by the physics and engineering courses I was taking concurrently. My son's Calculus book at least tried to bring in some real-world examples from different disciplines.</p>

<p>I can imaging my son asking the same kind of questions that citygirlsmom asked. Why would a really smart kid who wants to do Engineering should be "forced" to take two years of English and American Literature. Wouldn't a year of "real-world English" be so much better, with some recreational reading, technical writing, science fiction, maybe watch some movies? He would argue that he'll never use Jane Austin and Dostoevsky again. As for foreign languages, he would claim that the lingua franca of the world is now English. </p>

<p>However, all that complaining aside, he did choose to take AP English Lit, English Comp, US History, and European History because he wanted the top courses in everything (he didn't exactly kill himself on these, though, and got B's and 4's). I'm sure a lot of really smart pre-law high school students do the same with the science and math courses. </p>

<p>Random questions from the left side of the brain:</p>

<p>Why is it that...</p>

<p>at my college they had a special class: "Calculus for Biology and Social Science Majors" but they didn't have "Walt Whitman for Engineers?"</p>

<p>Why is it that...</p>

<p>The St. Johns Great Books Program reads Newtons Principia? Have there been no better Calculus textbooks written in the last 300 years, or is it a copyright thing?</p>

<p>Why is it that...</p>

<p>from high school (many years ago), I can still remember that the Battle of Hastings in 1066 resulted in the "Great Vowel Shift" and I can recite almost all of The Raven, but I can't remember the the law of cosines?</p>

<p>Why is it that...</p>

<p>I still don't buy any of the reasons they give for studying Latin in high school?</p>

<p>Anybody want to add to my "Why is it list?"</p>

8

<p>I appreciate the points about a different way of problem-solving, and modestmelody's accurate statement that non-discrete outcome probability requires calculus. However, nothing I remember in the calculus courses I took generalized any kind of problem-solving method, so I am completely ignorant about what this different way is, and how it differs from, say, algebra (the value of which I don't dispute at all). </p>

<p>Also, the point about probability and statistics goes a little flat if (a) basic calculus courses don't address that kind of application, and (b) basic statistics courses don't either. Is that the case?</p>

<p>It is pretty confusing to me, as a non-science person, to hear about calculus classes full of uninterested pre-meds. I would have thought they needed calculus to do advanced work in hard sciences. Why are they all there?</p>

9

<p>JHS, does a year of sociology qualify one to do a "meaningful, real-world task" in sociology? does a year of history qualify someone to be a historian?</p>

<p>does the fact that I had no "instinsic interests" in literature as an undegrad (much less poetry...) mean that I should have been able to do something else instead?</p>

<p>In fact, that you actually remember the rollercoaster example tells me the course was a success.</p>

10

<p>I never understand why premeds are premeds when they don't like science. It's ridiculous, it's stupid, and it's why I hope most of them don't get into med school because I don't want that person to be my doctor.</p>

<p>There are a ton of things that could be addressed, but I can tell you that Calc 1 can be taught with a ton of explanations, and students who are not into science should have the option to take a different version of Calc II which is all applications of calculus.</p>

<p>I'm pretty sure all but the most basic Prob/Stat course at Brown which most people skip use calculus, btw.</p>

<p>I use calculus daily, but then again, I'm a chemistry student. That being said, even in high school calculus, to me, was like physics-- it opens up a whole new description of the world around you.</p>

<p>It's unfortunate that more people don't have the right teacher to present the material that way (problem #1 in my opinion), because learning calculus can be as mind-blowing as reading Joyce for the first time-- you need to take the time, dig deep, pull out all it's meanings and develop advanced skills to do that, but when you do, there's a seemingly infinite amount of power in simple statements.</p>

<p>And to get back to the original post-- a year of calculus, if not blown off by someone who thinks they're too good for it, can give the exact same level of proficiency in math and at least getting an idea as to how to solve some of the complex real world issues with calculus as one year of a history or political science course can give you.</p>

11

<p>But do you need TWO years of calculas to understand stats,....NO</p>

<p>and you can darn well explain the world without years of calculus, for heavens sake</p>

<p>oh, my, how did poets do it!!!</p>

<p>this defense of years of calc is really quite amusing</p>

<p>How did the founding fathers get it done without it</p>

<p>How does my H work as a contractor without it</p>

<p>If you think you can't imagine without calculus, can't deduce without calculus, can't talk about the world without caluculas, you are sadly mistaken</p>

<p>As for WHY an engineer should take English and Literature, is because that is how people in the real world communicate </p>

<p>They are not equally needed by human beings for getting along</p>

<p>An engineer should know about the world- </p>

<p>Yes at a dinner party table or with our kids, lets just discuss formulas, and not know about politics or current events</p>

<p>Calculus is narrow, its not enlightening in a human way and to equate that with reading The Odessy is funny</p>

<p>How does a person learn to interact with the world? Through literature, history, social justice</p>

<p>Somehow for centuries, mankind moved forward...why, not because everyone spent years studying math, sure some did and we have lots of beneifts from that, but because others studied history and wrote constitutions so it wouldn't be repeated, others wrote about slavery, so others would know how horrid it was</p>

<p>I wouldn't want an engineer who knew little about humanity designing a building</p>

<p>I wouldn't want a doctor who knew little about human nature to diagnose me</p>

<p>I wouldn't want an computer programmer who doesn't see the impact of their inventions</p>

<p>I would rather a good lawyer who never took Calc but studied philosophy</p>

<p>I would rather a banker who had some social justice background than who knew about calc</p>

<p>This need to defend calc as if its some sort of track to understanding the world is a joke</p>

<p>DeVinci knew his math, of course he did, but he ALSO knew about battles, history, farming, literature, he was well read, imagine that</p>

<p>But most of his inventions came from knowing the world and the people in it</p>

12

<p>nothing!!!</p>

13

<p>I don't know about other probability/stats classes, but I sure couldn't have done the one I had to take without calculus.</p>

<p>
[quote]
WHy should a really smart kid who wants to do Law be "forced" to take two years of Calc in HS?

[/quote]
</p>

<p>Using that logic, why should that smart kid be forced to take science classes, either? Why should a really smart kid who wants to be an engineer be forced to take humanities classes outside of non-creative writing? At some point, either you believe in a well-rounded education regardless of intended professional field, or you don't (I do). In high school, especially, I think it's important, because most kids don't know what they want to major in in college at that point, or they think that they want to major in something and change their minds later.</p>

<p>The modern world is interdisciplinary. A lawyer could have engineers, or pharmaceutical companies (or people suing them) as clients, and needs to have the basic knowledge to communicate with the client and understand the client's work. Anyone who needs rigorous stats (probably all the social sciences) needs calculus, because you can't understand the theoretical framework of the stats without it, and the theoretical framework helps you make intelligent decisions about what tools to use, etc. An engineer needs to be able to write, and communicate with others in their or other cultures. A microbiologist who doesn't use calculus or diffeq in their usual work might end up collaborating with a mechanical, electrical, or software engineer - bioengineering's a growing field - and they need to understand each other's languages. A nuclear engineer designing imaging tools needs to understand something of the science of the people using those tools. A fiction author could have a scientist or engineer protagonist and need to be able to write realistically, and a software or hardware engineer needs some psych to understand human-computer interaction.</p>

<p>Obviously we can't mandate everything everyone might ever need, but we can provide a basic toolbox. Depending on the person, they might end up using all of the tools, or a subset, but it's nice to have them just in case.</p>

14

<p>I'd respond to citysgirlmom, but honestly, what you just wrote speaks for itself. No need to defend what I said any further.</p>

<p>For what it's worth, I'm at an institution that requires no courses.</p>

15

<p>calculus is also necessary for many social sciences, such as econ or psychology (at least in some colleges).</p>

<p>I can understand why Lit major would not like it. But, OTOH JHS, I can also understand why a science major would not like a Great Books-writing sequence. If one is required, why not the other?</p>

<p>Yes, </p>

<p>
[quote]
A year of college study can give a student a tremendous store of shared cultural and philosophical reference points with educated people all over the world.

[/quote]
</p>

<p>I concur, but that is OUR value (and the value of the academicians at the college that require it). No different than saying Calculus is necessary by other academicians. That's the beauty of our higher ed system with over 3,000 colleges from which to choose. We have core colleges like UChicago and Columbia and those 180 degrees opposite, like Brown and Sarah Lawrence.</p>

<p>One reason I think parents should encourage calculus is that a LOT of all college classes require it. At $200k for an education, I would prefer that my child have the necessary background to take any class that the college offers.</p>

16

<p>I don't find any of Dad'o'2's questions (cross-posted with my last) very puzzling at all:</p>

<p>Why study English and American lit? (1) Common culture (a perfectly good argument for math, too). Jane Austen comes up all the time. So does Shakespeare. Dostoyevsky not so much, but it tends to constitute a sort of Philosophy Lite. (2) The courses do triple-duty -- teaching basic writing and grammar, etc., and analysis of written texts, as well as the underlying subject matter, and they are explicitly designed that way. (3) I doubt most high-school lit classes or college Freshman Comp required classes are so different from what he proposes as "real-world" English. It certainly describes classes my kids took.</p>

<p>Why don't they have Whitman for Engineers? They probably should. My English-major daughter certainly wished they did. I think lots of places do have courses like that. I didn't know any prospective English majors who didn't place out of English 10 when I was in college. Also, read last weekend's NYT Magazine re teaching poetry at West Point.</p>

<p>Why does St. John's still read Newton? Because the "Great Books" concept kind of has its head up its you-know-what. And because it proceeds historically, and emphasizes the correspondences among various things happening at the same time. And because, if I understand correctly, most basic calculus courses don't go beyond Newton anyway. (And Leibnitz is in German.)</p>

<p>Why do they study Latin in high school? It's not required in so many places anymore; generally the students are volunteers. I appreciated my kids' Latin classes because traditionally Latin is taught with a high degree of systematicity, so that you actually learn the grammar and structure of the language early on. Living languages emphasize inane conversations, not structure, and English grammar instruction seems to be catch-as-catch-can. Traditional Latin instruction gives you a way to understand lots of languages, including English. Any language could be taught that way, but for some reason only Latin is, at least in high school. Finally, because there's no need for inane conversations, Latin students encounter real literature and real historical material at a much earlier stage of their studies than students of living languages do. In third-year Latin, my kids read Virgil, Catullus, Caesar, Livy. In third-year French, my daughter's class spent three months on Le Petit Prince.</p>

17

<p>I think some of this conversation is also stemming from people who think that all education should be directly practical and that non-directly practical education is as worthwhile, which is a whole can of worms and completely different framework than that adapted by myself and colleges that value liberal education (i.e. nearly all).</p>

18

<p>
[quote]
I wouldn't want an engineer who knew little about humanity designing a building?</p>

<p>I wouldn't want a doctor who knew little about human nature to diagnose me</p>

<p>I wouldn't want an computer programmer who doesn't see the impact of their inventions

[/quote]
</p>

<p>I agree with you on all these points, but apparently you think the need for a well-rounded education applies only to science/engineering people. See my previous comment for a refutation.</p>

<p>Also, science and engineering are increasingly a part of general life. You like philosophy? There are whole subfields of the philosophy of artificial intelligence, and the philosophy of quantum physics, and you'd better understand these fields a bit if you're going to understand the philosophy of them. Bioethics is a big issue right now, between stem-cell research debates, cloning debates, many others...it rather helps if you understand the bio part as well as the ethics part. Debates about climate change and alternate forms of energy are also rather big right now, and you need to understand some science and engineering to fully understand and consider those debates.</p>

19

<p>jessiehl-- the thought that science is not an integral part of our lives is very "old" thinking and misses the point. Show me a criminal lawyer that doesn't need to have a grasp of biotech? Heck, an ambulance chaser who needs to understand medicine? A real estate attorney who needs to understand engineering issues?</p>

<p>JHS-- you so wonderfully understand and explain why Latin (which I wish we offered in my HS), it surprises me you can't supply the same strong argument for calculus...</p>

20

<p>OH, so in order to understand climate change, you need three years of Calculus....really?</p>

<p>Oh my, and to understand Ethics, you need it as well</p>

<p>Oh gosh, my opinions on stem cell research are tainted because I only took one year of Calc in college, the horror!!!!</p>

<p>Many very smart people can understnad those topics without years of math, thank you very much</p>

<p>It is that VERY attitude that if you are't a math whiz, you are too stupid to "get" complex life issues that blows me away</p>