<p>pkay, please tell me what Calculus teaches that can never ever be taught in another way- and I am not talking minutia here, I am talking big picture</p>
<p>I think it's dumb, by the way, to require science students to take "a year of history". I'm not generally big on requirements anyway, but if I were going to require something it would be a course on historical methods, not a course on The Ante-Bellum South. Ditto all social sciences, and literature, too, although at least with literature methodological questions seem to be more in the forefront on a regular basis, at least in college.</p>
<p>I think everyone should know basic science and math; the question is what math that is. I also think everyone should know some common cultural and historical touchpoints, and understand the basic methodological differences among categories of disciplines. I think high school is probably where they should learn that, but I don't think it happens uniformly.</p>
<p>No one is saying you're too stupid, no one is saying that it requires three years of calculus even.</p>
<p>All I'm saying is you're far better equipped to tackle dynamic problems having had at least an introduction to the concepts of calculus provided you are intelligent enough to link those concepts to the larger picture (or have a teacher gifted enough to do that for you) the same way that introduction to the basic concepts of philosophy and logic can make you far better equipped to tackle problems provided you can link them to concepts to the larger picture (or have a professor/teacher who can do that for you).</p>
<p>Oh, so I can't understand right from wrong without doing complex truth tables and semantic word games?</p>
<p>That's the equivalent statement.</p>
<p>
[quote]
jessiehl-- the thought that science is not an integral part of our lives is very "old" thinking and misses the point.
[/quote]
</p>
<p>And you misunderstood mine, apparently. The whole point of my post is that science IS an integral part of our lives.</p>
<p>Methodological thinking and course work is exactly what most introductory courses WISH they were doing. There are a lot of problems with establishing these courses from a pedagogical sense though and it's a major issue faced by all of higher ed. For starters, methodological based introductory courses, without any content to ground these methods in, are often seen as being banal by students and too abstract to grasp. They also do a poor job of preparing students who are interested in that discipline who will be expected to amass some level of content. The difficulty is framing content within a clear, independently structured, "mode of thought" type course such that it engages students, presents enough of a picture of how this discipline thinks to actually prepare a student to tackle problems outside of course content in this way, as well as satisfy the needs of those who actually need to learn a certain amount of content.</p>
<p>It's that very challenge and balance that top institutions are frantically struggling with each year a course is offered in an attempt to create a better liberal arts education.</p>
<p>
[quote]
And you misunderstood mine, apparently. The whole point of my post is that science IS an integral part of our lives.
[/quote]
</p>
<p>I was agreeing.</p>
<p>I think our comparisons here are false and unfair to mathematics. Asking “Why Calculus?” is to me like asking “Why language?” or “Why sounds and letters?”. I don’t know a lick of Calculus. In fact, I have never taken it. The algebra I know I learned on my own. So I am not even close to being an expert. Math is all Greek to me. But it seems to me Calculus is just a rudimentary tool in mathematics that ought not be compared with “The Illiad” or “The Odyssey”. As language helped produce The Illiad”, mathematics helped produce, say, “Relativity”. I do not think anyone should make the case that they would prefer one over the other.</p>
<p>The question, then, is “Why math, in addition to language?” to which my answer would be they are both the same thing (i.e. language) existing on the same continuum of human understanding. Both tools can and do help us understand the world in which we live. Math, philosophically speaking, ought even to be able to explain art and aesthetics. Currently, however, it seems we need a combination of math and language to do this. In some areas math is perhaps far less efficient than English, or music, or some other form of language. Either of these can be more efficient than the others in conducting knowledge depending on the context involved.</p>
<p>The same way allusions to the Bible, Homer, and Shakespeare appear throughout literature, much of higher level math uses calculus-based examples and definitions time and time again as a means for understanding.</p>
<p>@citygirlsmom,
You can understand them, really? Or do you only understand the digests and media coverage that people have given you to read? Without being able to understand the math and the numbers behind an argument in favor of human causation of climate change, you are stuck relying on what other people have told you.
Pick up any academic science journal, in any sort of chemistry, biology, physics, environmental science, math, engineering field, and you will need a basic grasp of calculus to understand it, citygirlsmom, from reading your posts disparaging understanding of math, i would say you understand those issues about as well as someone understand shakespeare who has only ever read the cliffnotes.</p>
<p>To respond to the OP, I think the way you take the value of a Great Books course for granted is telling.</p>
<p>
[QUOTE]
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.
[/QUOTE]
</p>
<p>Part of the problem is that the way we define 'educated' implies that one has a grasp of the classics and of history, but not necessarily any understanding at all of chemistry, physics, biology, or math. Kristof had a column in the Times a while back called the Hubris of the Humanities, <a href="http://select.nytimes.com/2005/12/06/opinion/06kristof.html%5B/url%5D">http://select.nytimes.com/2005/12/06/opinion/06kristof.html</a> , where I think he does a fairly good job of illustrating that, and of course there's the classic C.P. Snow essay The Two Cultures.
Of course, if the circles you move in don't assume a basic understanding of math and science, neither will appear to have much use to you, and really too many people move in circles where it's not assumed.
Science literacy is just in a terrible state in this country. If you've ever read or tried to write any sort of mass media article about science or related to science, you should realize that they are all incredibly dumbed down to be understandable to the average American.</p>
<p>modestmelody:</p>
<p>No one is disputing that people who encounter higher-level math should understand calculus. The question is whether people who don't encounter higher-level math should understand it. By the same token, the fact that the Bible or Shakespeare get name-checked in contemporary literature is not really sufficient reason to study them. The reason is that they get name-checked in a wide range of literary, political, social, psychological, historical debates.</p>
<p>Phat: </p>
<p>If you think I like "Great Books" programs, you're not paying attention. My only argument was that a year of Great Books wouldn't be completely useless in the way that, in my experience, a year of calculus was. I'm also sure that, hypthetically, I could have had a great calculus class that would not have been completely useless. But that doesn't seem like the norm in the world.</p>
<p>Citygirlsmom, you might find "John Adams" by David McCullough an interesting read. Calculus was considered to be part of a well-rounded education during the 18th century, along with Greek, Latin, etc. John Adams had a working understanding of calculus and was able to help the teenaged John Quincy learn it when they traveled to Europe together.</p>
<p>I really struggled with calculus freshman year (8 am class 5 days a week, and I had never had to work at learning math before). I dropped calc after 2 quarters, which is probably the equivalent of Calc AB in hs, and I can't say that I was terribly well-versed in it. That being said, I took Econ I in summer school, when there were also hs students in the class. Because the teacher couldn't assume that everyone in the class knew some calculus, he taught the class completely without it. It was so convoluted and difficult to understand - I would sit through an entire lecture and then go talk to him afterwards. In about 5 minutes he would summarize his presentation using calculus, and it would be crystal clear. Calculus provides a vocabulary for talking about change, and change is what our lives are all about. I don't think that people need a lot of calc, but anyone in the sciences or social sciences, or in business and finance, needs to understand the vocabulary.</p>
<p>i'm a few years out of college and all of my friends from a extraordinary range of schools WISH that we had some formal lessons on "real world" things like how to do taxes, insurance issues, mortages, etc. now that would have been useful! (i'd also like to learn how to program my tv, but thats a whole different issue..)</p>
<p>@JHS,</p>
<p>Apologies for misreading you, I just seized on that idea because it's so hard to defend the absolute value of any particular bit of understanding. Enough people go through life as complete dolts, that you clearly don't need any understanding of either science or humanities to get by.
I think what I'm trying to say, is that an understanding of the social, natural, and physical sciences at the calculus level, is at least as valuable as an understanding of the literary classics at a primary sources level.</p>
<p>
[quote]
I was agreeing.
[/quote]
</p>
<p>Oh, my apologies! I misunderstood your tone!</p>
<p>CGM,</p>
<p>
[quote]
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
[/quote]
</p>
<p>I never said that. Many very intelligent people struggle with math, and many people who are more than smart enough to understand math never took it, possibly because the weird pedestal of imagined difficulty that we put math on in this country sadly intimidated them. But I do think that if you understand higher math (whether you learned it slowly or quickly, whether it was in or out of school, whether it came easily to you or you fought your way through it) and basic science, you will be able to understand the complex issues that I mention both more easily and more thoroughly, as well as possibly open doors in your professional life.</p>
<p>I'm better at math than most people, but I'm certainly not a "whiz" - I got Cs in most of my college math classes. I'm glad I took them, though, even the ones that I wasn't required to take (most of them), because I learned useful tools from them. Also, contrary to stereotypes about scientists and engineers, I love the humanities and social sciences! I almost minored in political science (thanks to scheduling issues, I didn't quite get enough classes). I'm a bit of a history buff, and a huge bookworm, and took AP Art History for fun in high school. I think I am better off for having had all that humanities/soc sciences training, and was glad to do it. I just think it goes both directions.</p>
<p>I find a good understanding of stats, geometry and basic algebra most useful in the real world of business.</p>
<p>Goodness--I can't keep up with the posts!</p>
<p>JHS--</p>
<p>In case it wasn't clear, I was trying to be amusing with my list of questions. :) I think your kids have a better Latin program than mine, but I think my kids have a better calculus classes than you must have had! My D's Latin teacher came back from a summer workshop, and lo and behold, they are starting the mundane conversation approach in Latin IV! </p>
<p>citygirlsmom--</p>
<p>No, understanding climate change only requires Calc I ;). Seriously, I think that is an excellent example of a topic that people will interpret differently if they have been exposed to elementary calculus: "Look at the second derivitive of that CO2 concentration curve!" Or a good stats course: "So the evidence indicates the increase is due to human activity with a 95% confidence level?" </p>
<p>As for your quote:
[quote]
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
[/quote]
I certainly don't hold that attitude and I don't see any of this in this conversation. I see people here who find beauty in the way that calculus provide a way to describe certain aspects of the world. </p>
<p>In college, I majored in engineering and avoided as many of the humanities and social science classes as possible. My English, Political Science, and Sociology friends avoided as many math and science courses as they could. I don't think that qualified any of us as being "too stupid to 'get' complex life issues." Should I intepret your comments to say that the mathematicians and engineers are too stupid to "get" complex life issues if they haven't read Homer, Marx, and Durkheim? If so, should I take offense at the VERY attitude?</p>
<p>Different strokes for different folks.</p>
<p>CGM,</p>
<p>
[quote]
I would rather a good lawyer who never took Calc but studied philosophy
[/quote]
</p>
<p>Before the 20th century most of the great philosophers were mathematicians. A number of examples</p>
<ul>
<li><p>Rene DesCartes, know for saying "cogito ergo sum" (common but inaccurate translation, I think therefore I am). He is also the person for which "Cartesian Coordinates" are named.</p></li>
<li><p>Pythagorus</p></li>
<li><p>Blaise Pascal, philosophically he said "the heart has a reason that reason does not know" but is also known at the father of Pascal's triangle.</p></li>
</ul>
<p>There are many reasons to get a liberal arts education and that education should require mathematics and advanced mathematics. Fundamentally math is the language of science and calculus is the most applicable to any advanced study of science.</p>
<p>Considering that St. John's, probably the premier "Great Books" school, requires reading Newton on calculus I would think it must be an important part of a liberal education. However, I do agree that 2 years of calculus should not be required, I would think it is more important to take advanced algebra or probability and statistics instead.</p>
<p>A slight diversion, but related...</p>
<p>I keep getting confused when people talk about calculus experience in terms of "years" of calculus, or using arbitrary levels, and I can't imagine I'm the only one. In undergrad, we all (unless we placed out) took two semesters of calculus - the first semester was single-variable (which is what AP Calc BC is), and the second was multi-variable. Is "Calc I" single-variable? Or Calc I + Calc II? What does "2 years of calculus" mean in knowledge terms to most people on this board?</p>
<p>To get myself back on track ;), I'd say everyone should take single-variable calculus, which will teach the basics that one needs to use calculus as an effective tool in life. A full multi-variable course is probably not necessary unless you're in science or engineering or at a tech school - if you want elective math after that I'd probably recommend prob/stats or linear algebra instead.</p>
<p>There are scores of courses and choices for how a math, engineering or science student might pursue Humanities in college, but not so in reverse. </p>
<p>During high school, for me, I perceived a narrow funnel called "Calculus" and it was the only way up to any higher level course in Math.</p>
<p>This is sad, because I recall having a love affair with l0th grade Geometry. Then, in the slide-rule days, I couldn't "get" 11th grade Trig. What a lame place to meet one's Waterloo; I'm not stupid.</p>
<p>If only I could have chosen between an advanced Geometry class versus precalc in 12th grade, I'd have continued Math at that moment.</p>
<p>Was it something about my brain being more responsive to visual learning (right side brain) than analytical (left side brain)? Or the bad luck of having an alcoholic Trig teacher who came in and yelled crazily at the class daily such that we hid behind our books?</p>
<p>I did take a required college algebra course as a refresher, and later a Statistics course during my Masters degree in Regional Planning, but that's all I know about Math. It makes me feel downright stupid. </p>
<p>My D took precalc in 11th grade, but then discontinued so no 12th grade calc. In college, she could still choose from courses named: Musical Acoustics, The Geometry of Architecture, Logic, Computer Programming...She could handle these, enjoyed them a wee bit (as much as some engineers muster enthusiasm for their required poetry class). </p>
<p>Unlike me, she doesn't feel she has to flee from anything mathematical in a conversation.</p>
<p>I will drive over the bridge you build if you are the engineer, but I wouldn't have the audacity to tell you you're not allowed to study the Iimpressionists unless and until you took coursework in Greco-Roman Art. Of course it would be better to know both, but does it all have to be a prerequisite, one thing for the next?</p>
<p>I agree with the calculus confusion. I think citygirlsmom was upset about a two-year calculus requirement for her D in high school, but I'm not sure.</p>
<p>My S had a two years of HS calculus. The first year was AB. The second year was BC plus some supplemental. At his university, he got AP credit for two 4-credit courses, Calc I and II. He had to take Calc III (multivariate) and elected to sign up for a more theoretical version, rather than the standard Calc III for scientists and engineers. It was a big change for him. To quote him, "...ewww....proofs...evil, vector proofs..." After that is a one-semester course in differential equations.</p>
<p>@paying3tuitions,</p>
<p>I think Droseelmeier's analogy of math to language(post #26) is a great explanation for why there are so many choices for how to study humanities but not for math and the sciences. Having calculus under your belt is really the prerequisite to studying any other math or science, just like being able to read and write english is the prerequisite to any other humanities course.</p>
<p>@jessiehl,
Yes, I agree. I think if someone a calculus requirement should just be up through single variable calculus, and then definitely a primer on linear algebra. It's shocking how many people can't do simple matrix operations.</p>