<p>Honestly, I would appreciate that argument more if you gave me an example of something I can't understand without knowing how to perform basic calculus. I have only a very limited idea what anyone does with basic calculus, except perhaps to figure out how much water you need to fill odd-sized pools, and how to aim guns and rockets. </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. If knowing how to do calculus, as opposed to having a basic idea of the concepts and of the logic of math proofs, has anything to do with my life, I've never noticed it. I can, and do, sometimes read papers in science or economics. I don't check the math. I assume the reviewers did.</p>
<p>(This is a little bit facetious, of course.)</p>
<p>JHS, Introductory calculus is taken by almost all pre-meds, and many of them have little interest in it. </p>
<p>Calculus was developed originally to transform natural phenomena described by non-linear functions into linear forms, which we can better visualize or extrapolate (becoming simple algebra). Take the simple case of acceleration (a non-linear function) is transformed into velocity (a linear function). Of course it gets a bit harder if you have more dimensions (multivariable calculus) but it is essentially the same in transforming nonlienar equations into linear ones. What mostly left out now in courses are proofs behind such transformations, the approximations, and their practical usages. Introductory courses should be taught by the most seasoned experts with a wide ranging understanding of mathematics. Unfortunately, calculus teaching at larger universities has become the means of unseasoned graduate students to earn their stipends.</p>
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Students in the United States are getting a good education if their undergraduate instruction comes from people who were born all over the world.
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Not if the prof is unintelligible in which case the student gets NO education from that prof. I'm not talking about foreign or accented but rather, so heavily accented as to be virtually unintelligible.</p>
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I'll hazard this guess: Every one of the foreign-born profs and TAs people are complaining about here speak English better than 99% of the American-born students could handle any language other than English not spoken in their homes.
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This is true but not relevant to the topic since those students aren't trying to lead a class in the other language. If they were, then the same issues would exist for them.</p>
<p>Another example: Car commercials describe cars as achieving a speed of 60 miles/h in 4 seconds. Here we have transformed a nonlinear phenomenon into a linear form so that you can compare cars with a linear function. The engineers deal with the nonlinear part with calculus.</p>
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Of course it gets a bit harder if you have more dimensions (multivariable calculus)
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Unfortunately, one of the profs I was referring to is my D's multivariable calculus prof and it looks like she'll not glean much from the lectures.</p>
<p>uc's_dad, that is unfortunate as the multidimensional world is hard enough for all students already. Is she proficient in Mathematica? Can she just attend lectures from another section (I presume the tests are equivalent if not identical)?</p>
<p>She's very good in math so I think she'll manage to get through it. She has a pretty full schedule and at this level there aren't so many classes even at her large uni so I don't think she'll be able to go to other lectures. She'll have to manage by gleaning what she can from the prof lectures (mostly what he writes on the board), TAs in the discussion section, other students she might know who have already taken the course, and probably mostly from herself studying the textbook and self-teaching. It's just a shame that she couldn't have a more understandable prof in this subject that on the one hand is difficult for many but on the other hand is one that she might enjoy.</p>
<p>padad: Of course, what you have said is about exactly what I understand about calculus. I don't have any trouble appreciating the concept without remembering how to perform any of the calculations.</p>
<p>I also know, of course, that pre-meds must take calculus, and that at my kids' college EVERYBODY must take calculus, essentially. I always assumed that, in the case of the pre-meds, there was some valid reason for that, and that they would need it to do other things (like biophysics) they ought to know about. If that is the case, why aren't they interested? (And in the case of my kids' college, the basic course is very proof-centric.)</p>
<p>Finally, as to "basic competence . . . to convey information in English": I am pretty sure all of the profs under discussion have such basic competence. I think people are demanding a level of fluency and easy intelligibility way beyond basic competence.</p>
<p>JHS " I am pretty sure all of the profs under discussion have such basic competence. I think people are demanding a level of fluency and easy intelligibility way beyond basic competence."</p>
<p>JHS... hmm... I dunno... I've heard perfectly competently & grammatically spoken English which was also completely un-understandable (is that a word?) due to the heavy accent. Often this was by native English speakers! Ever hear a New Zealander or an Aussie or even an Englishman from certain parts of UK get going really fast??? I have. And I often failed to understand a single word they said.</p>
<p>Son is a math major at Berkeley. He doesn't seem to mind accents, but this semester he signed up for an honors math class taught by a prof with an advanced stage of MS (or some other neurological condition) who he heard was pretty unintelligible. He also heard he was brilliant and put all the notes online so he gave it a shot. He ended up switching to the non-honors version of the class because he couldn't understand him and felt like he would be teaching himself the material.</p>
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I am pretty sure all of the profs under discussion have such basic competence. I think people are demanding a level of fluency and easy intelligibility way beyond basic competence.
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Not the ones I'm talking about. I'm talking about those extreme cases where the profs are unintelligible and there are some out there. Again, I'm not simply talking about accents. Most profs with accents can be understood even if one must 'listen closely'. Fortunately it's not a huge number but it's enough that both Ds have had the experience.</p>
<p>In this globalized world it would serve a very useful purpose for our children to learn how to understand accents from all over the world. It is really a skill that will place our kids at a competitive advantage- to be comfortable with English as spoken by the English, Australians, Indians, Chinese, Japanese..and also the folks from Cape Cod, New Joisey and Alabama! If you can converse with them you can do business (or negotiate nuclear peace agreements) with them later in life. </p>
<p>College is a good time for our kids to be exposed to all these accents- whether coming at them from other students, teachers or teaching assistants. </p>
<p>OTOH, if besides the accent, there is limited language proficiency to the extent that the prof cannot express himself or herself, then of course it is a problem, no matter how brilliant the prof.</p>
<p>JHS, Have you wondered how Rollercoaster designer figured out how high the initial pull should be? Actually at the time when Calculus was first invented, people were interested in using gravity as a source of energy for travelling long distances, say from Paris to London. Using Newton's Second Theorem on Gravity, you can actually show it is quite worthwhile to dig a tunnel down until midpoint and then a rising tunnel toward the destination. All you would need is a little bit of fuel at the end to compensate for friction. What they couldn't figure out how to do at that time was building the tunnel.</p>
<p>How long does it take to go from Paris to London? A relatively easy problem for anyone who still remembers elementary calculus.</p>
<p>padad: I recognize these things as calculations that use basic calculus. What I don't understand is why everyone ought to know how to calculate how high the initial pull on a rollercoaster should be, or the best gradient on a Paris-London tunnel. 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>Anyway, we are sort of far afield from the original issue in this thread.</p>
<p>Trying to decipher common accents from all over the world would be like learning that many foreign languages- you would be performing some kind of translation every time you listened to the accented speaker. Also, there can be many accents from a single language or country- I have proof of that in my inlaws, the accent depends on which school they went to when they learned English. The target audience is in the US, speaking American English; the burden is on the teacher (TA/prof..) to communicate effectively. This would occur in the perfect world, people here are giving information and expressing opinions on how far apart the ideal and reality are.</p>
<p>A mathematical aside- with the use of computers many more fields are making use of calculus than in the past, a better understanding of more math principles isn't as esoteric as it was years ago. Just think of economics and business, for example. Given the retention rate of material learned one needs to learn a lot to retain a little. I could easily make a point of all the useless knowledge I have been required to learn in other fields, especially those where the "facts" change with political/philosophical changes. Years later the precise knowledge may fade but the understanding that it exists and the principles- the how to think aspects- enrich one's knowledge base. A calculus requirement is at least as valuable as a "Great Books" one.</p>
<p>I don't underestimate the problem of incomprehensible foreign profs and TAs. And it is not just a matter of accent, but unidiomatic, ungrammatical English. But the problem is easy to identify and decry, much harder to address. The reason is simply that not enough Americans are going into the fields in which the foreign born profs and graduate students are represented in great numbers. I looked at the list of profs in a math department, and more than half of the names were from Asia.</p>
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A calculus requirement is at least as valuable as a "Great Books" one.
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</p>
<p>This really deserves its own thread. But 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.</p>
<p>And, to some extent, computers have made it less so. I don't know how to do regressions, but now, at least for simple ones, I don't really have to know.</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>BAck to the original issue -- My belief that everyone may not need to study calculus does not mean that the many students who do need to learn calculus shouldn't be able to understand their teachers. The relevance of this side-trip is that if we stopped trying to teach calculus to everyone, and taught it only to those who wanted and needed to understand it (and who were planning to pursue it beyond a basic level), we could be much more selective in who was teaching it.</p>