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<p>And what team would you assume that to be?</p>
<p>@ucba: One certainly does not need to know calculus to understand how percentages work! </p>
<p>@bogney: I wish I knew calculus because when my HS senior tries to explain it to me, I’m absolutely fascinated - and absolutely mystified. Like you, I’ve never “needed” to know math beyond simple algebra and geometry (maybe occasionally a bit of trig) and statistical concepts. But I’ve always regretted not knowing at least the basics of the language that scientists and engineers use to describe and manipulate their world. </p>
<p>I have over 65 years acquired an immense amount of totally useless knowledge - and am immeasurably richer for it. That’s why I agree fully with the quote from Andrew Sullivan that I posted at the top of the thread.</p>
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<p>So when someone is out studying medicine they don’t cite this paper: [Medical</a> researcher discovers integration, gets 75 citations An American Physics Student in England](<a href=“http://fliptomato.■■■■■■■■■■■■■/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/]Medical”>Medical researcher discovers integration, gets 75 citations | An American Physics Student in England)</p>
<p>Seriously though, when people hear reports of “The rate of illegal immigration is decreasing” and think that means illegal immigrants are going back to Mexico (or whatever their home country is) and support specific policies based off of that, you see the problem with the general population not knowing calculus. </p>
<p>And that was a real example… I tried to show them graphs but they didn’t get it. </p>
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<p>I don’t even… What are you trying to say? You’re saying in India engineering students take harder math classes than math majors? In which case I’m extremely doubtful but I’m not going to argue. You’re saying in the US engineering students take harder math classes than math majors? You’re dead wrong and I know because it’s common knowledge.</p>
<p>Once again, one hardly needs calculus to understand that the rate of illegal immigration decreasing doesn’t imply anything about people going or not going back to Mexico.</p>
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I’m surprised people are saying things like this. If anything, I have precisely the opposite view. Students at Harvard can major in art history, take a couple of econ classes, and go to work on Wall Street. That option is most certainly NOT available to art history majors at Northwest Kentucky State. The job prospects at the latter are best for those majoring in nursing, accounting, etc. </p>
<p>Note that the NY Times article criticizes the rigor of average business programs, not the job prospects, which actually seem to be pretty good.</p>
<p>Bogney, thank you for post#99. Most of the math that most of us use every day is fairly basic. We rush students through those basic concepts in the mistaken belief that calculas in high school is the gold standard. We end up with young adults who score a 5 on Calc AP exams, but are blissfully unaware of the ins and outs of loans, personal finance, and practical math. </p>
<p>We are all blind men describing an elephant. We bring our personal experience to these boards, and make broad proclaimations based on a very narrow perspective. (I’m guilty of that myself … Never went past Algebra II, and therefore don’t see the value of calc for all students, though I see the value of it for some students).</p>
<p>^^^^^^^good point</p>
<p>I have noticed that over the past decade, even the “lopsided students” who get into elite schools as undergrads have not been all that lopsided wrt to grades or tests scores, even if their interests and EC achievements have been lopsided. </p>
<p>If you want to go by who took and excelled at the first couple of calc courses - </p>
<p>I would keep in mind that at elite schools, at least these days and judging from the types of students from our high school who get into these schools, most art history or English majors probably ALSO took calc 1 and calc 2 (which is all that many pre-meds and bio majors who scoff at those who did not major in STEM have taken, let alone business majors who struggle through “business calc”) and scored decently on math SAT’s, generally well above the 75% for students at lower tier schools. </p>
<p>And, the elite tech schools also seem to be turning away students who have not done well in high school courses in humanities or scored well on the CR section, even if their standards in these areas are somewhat relaxed relative to other “most competitive” schools and expectations for math and science scores and grades are higher.</p>
<p>Having gone through eight semesters of math in Engineering school which were vital to me, I don’t feel the need for everyone to be taught Calculus; I feel statistics is far more important for the average person. </p>
<p>On the other side, while the theory is good that learning history and such will make us wiser in learning from our past mistakes, in practice no such thing happens. You can have the same set of people over hundreds of years and in scores of countries do the same thing, but political correctness will ensure it still continues. You can see Ponzi schemes and irresponsibility across the world but people will still continue to do the same.</p>
<p>"Most of the math that most of us use every day is fairly basic. We rush students through those basic concepts in the mistaken belief that calculas in high school is the gold standard. We end up with young adults who score a 5 on Calc AP exams, but are blissfully unaware of the ins and outs of loans, personal finance, and practical math. "</p>
<p>-the purpose of math in k -12 is completely lost. K - 12 has to develop critical thinking which is crucial in decision making and very basic pre-req. in science based proffessions. The only way to develop it is by teacing math correctly. Very easy concepts of loans and balancing checking book would not be such a hurdle either if math is taught properly, slowly, diligently and much earlier than High School. Pre-HS should not be even called math. Of course arithmetic is part of math, but just for the sake of understanding what k - 8 is devoted to in math, it should be called “arithmetic”. The other side of coin is most kids get so bored with arithmetic by the time they are 14, that they decided that they hate it, pay too little attention to it and end up not being prepared for college. I am not talking just about math here, many kids are faced with huge obstacles in college. Some realize it qucickly and seek help, others cannot bring themselves to ask, too proud or whatever. They end up falling out of their original dreams to become engineers, medical doctors, computer science majors (no math required in a last one at all, but great degree of critical logical thinking). Actually anything that is going on around us require ability to think logically, otherwise it is very easy to get lost. Specific knowledge of calc, stats, trig, geometry, algebra, etc. could be easily acqired at any level if one developes certain way of thinking in k -12. This is not just my opinion. Some college profs are pointing out that this specific skill has gone down considerably. It is not remembering facts and calc. formulas. Math is a language that requires conceptual understanding.</p>
<p>Maybe I am old fashion this way, but I have always believed that being an educated person is being a Renaissance Man, Dr. Johnsons idea that one should know something about everything and everything about something. Not understanding the basic concepts of science at the dawn of the 21st century is really stretching the meaning of being educated, and I dont know of any non-mathematical method of understanding them. Like it or not, these are the disciplines that brought us this far, not religion, not philosophy, not history, not arts.</p>
<p>I always advocate studying as much math as one is capable of handling. My siblings and children have obviously taken it to heart. Whatever they ended up doing, they all completed the math sequence to calculus by the end of high school, and a minimum of one more year in college not including statistics. When I asked two of my siblings for advice one year, their responses were so logically tight from assumption to conclusion that I had the urge to stand up and cheer the emails. I only come across this type of disciplined reasoning from those with a good math background. Does this make sense at all?</p>
<p>I took all the senior math courses I could in high school and a year and a half of calculus and linear algebra in college and stopped reluctantly because I reached my intellectual limit and I knew it. There is no shame in that. I did go on to take more statistics and philosophical logic though. They helped me to see through some of the nonsense I see and hear in life, and give me the tools to venture out on my own path.</p>
<p>My feeling is that disciplines like math can humble even the intellectually gifted and it does not make us feel very good. So, we avoid this discomfort by simply re-defining the meaning of being educated to sooth our ego. That is the type of critical thinking I see a lot these days in the humanities and I think its greatest failing; it gives us the tools to rationalize away anything we dont want to admit. </p>
<p>Ironically, the only public intellectual I know to openly admit his shortcomings with math is Charles Murray, a graduate of Harvard with a PHD from MIT. Double irony!</p>
<p>dad<em>of</em>3 - Can you explain what your 8 semesters of math covered? It looks like that much of math does not seem to be a requirement for engineering these days.</p>
<p>Thank yaou for being more clear about it, Canuckguy. I meant to express exactly the same.</p>
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<p>I agree with this. I used to be one of the kids mentioned - I got a 5 on my AP Calculus BC test, but still didn’t know how to balance a checkbook. So one day, I decided it was time to learn, and asked my dad how to balance a checkbook. It literally took me 5 minutes, and that was only because my dad likes to overexplain things. It really should not be a problem to learn these types of things.</p>
<p>Oh, now AP calculus is necessary to be able to figure out the deep, dark mysteries of balancing a checkbook? In addition to understanding the concepts of simple percentages?</p>
<p>Post #114 is a proof of what math is not about and what is missing in math education completely. You can teach a 5 years to balance checking book. You can skip all math classes, if you desire so, nobody will care.</p>
<p>I’m looking at the calc in high school issue through the lens of where I live, and where my kids attend/have attended high school: the Washington suburbs, where The Washington Post’s Jay Matthews writes about educational issues. He has published “Ranking America’s High Schools” in the paper every year since 1998, using “the Challenge Index, his measure of how effectively a school prepares its students for college. The formula is simple: Divide the number of Advanced Placement, International Baccalaureate or other college level tests a school gave in 2010 by its number of graduating seniors. While not a measure of the overall quality of the school, the rating can reveal the level of a high school’s committment to preparing average students for college.” </p>
<p>The fallout from this is that very competitive area schools actively push students into increasing numbers of AP classes, not out of concern for student achievement, but out of concern for the rankings. AP Calc BC is totally appropriate for some high school students, but not for all. (You could insert any other AP class in the point I’m making. Some are appropriate for some students, but not neccessarily all students.) </p>
<p>I do see kids pushed through a lot of earlier math or arithmetic or whatever term you’d like to use, by parents and the schools around here. With 3 children, I have one who tested into “GT Math”, skipped two years of math instruction in elementary school, self taught the stuff he missed, and never skipped a beat. He was one of the kids who really SHOULD be in AP Calc BC by his senior year. I have 2 others who could not handle just skipping a year or two of instruction in elementary school. Smart, but needed the sequential teaching. One tested into “GT math”, but even after working with a tutor (paid for by us) for a year, looked (as her teacher described her) like a deer in the headlights. She was doing OK, but was really uncomfortable with the speed of instruction and with the gaps in her own knowledge base. She passed the Algebra I state assessment in 7th grade, but even so, we dropped her down a level in 8th grade, which meant that she repeated Algebra I. She is not on track to be able to take calc BC in high school. It would have been inappropriate for us to have continued to push her into higher level math that she wasn’t ready for. (Passing a test, and actually knowing the subject matter are not one and the same thing, in my opinion.)</p>
<p>Having taken years of calculus in college that I never used despite working in a STEM field, I agree that calculus is far less useful in life than statistics. Here is an excerpted article from a Brown professor who would like to revamp high school math education to make it more useful:</p>
<p>Quote:
(from <a href=“Opinion | How to Fix Our Math Education - The New York Times”>Opinion | How to Fix Our Math Education - The New York Times)
"How to Fix Our Math EducationBy SOL GARFUNKEL and DAVID MUMFORD
Published: August 24, 2011 </p>
<p>…Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). … This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life. </p>
<p>For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood. </p>
<p>A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein’s famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light. </p>
<p>Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now. </p>
<p>Traditionalists will object that the standard curriculum teaches valuable abstract reasoning, even if the specific skills acquired are not immediately useful in later life. A generation ago, traditionalists were also arguing that studying Latin, though it had no practical application, helped students develop unique linguistic skills. We believe that studying applied math, like learning living languages, provides both useable knowledge and abstract skills. </p>
<p>In math, what we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car)… </p>
<p>It is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now. </p>
<p>Sol Garfunkel is the executive director of the Consortium for Mathematics and Its Applications. David Mumford is an emeritus professor of mathematics at Brown. "</p>
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I’m assuming this is from the article. I think the point of learning at least some of this stuff is that you don’t know whether you might become a mathematician, physicist, or engineer until you at least get to the point of learning the quadratic formula.</p>
<p>I haven’t used everything I learned in math in my career (I’m an engineer -with physics and EE degrees). But I have certainly used a lot of it. And since I now work in the energy sector and do some analysis of electrical power, protective relaying and electrical faults, I would certainly not have what I consider an adequate preparation without knowing complex numbers, matrices, and at least basic algebra. Maybe I could get a computer to work some stuff out for me, but since I’m sometimes an expert witness I need to be able to explain what the computer is doing, at least in a rudimentary sense.</p>
<p>One other thing I don’t understand is this love affair everyone has with learning statistics. Exactly what do people mean by the statement that every person needs to know statistics? Sure, people should know what the difference between average and median, and have some idea about the standard deviation. But beyond that, aside from folks doing research studies or polling, how often in daily life does a person need to know the z statistic, or ANOVA testing or the Chi square test?</p>
<p>And I’ve got to admit it’s a little bemusing to me when someone says, for example, it’s extremely valuable to learn about the z-statistic, but that even a conceptual knowledge of calculus is sort of useless, since I believe that’s where those tables of z come from.</p>
<p>I learned how to do t tests and ANOVA, etc., 30 years ago in graduate school. Have I ever “used” it? No. Could I do the math today? No. But the in-depth knowledge I once had has served me very well in understanding the frequent references to surveys and other statistical matters I encounter in news reports and elsewhere (including here on CC, where the level of statistical ignorance is sometimes staggering.)</p>