<p>QuickAg, Master cellular automato and you can solve the unified field theory and rule the world. Just ask Stephen Wolfram.</p>
<p>no it is NOT the same as trying to understand history</p>
<p>as for a sieve, that is such a lazy way at looking at very smart students</p>
<p>there is a difference between basic understanding of science and math, and the push to learn calculus, this only way of thinking to some peoples minds</p>
<p>again, hogwash</p>
<p>one lazy way to teach thinking imo- a cop out method and a short cut to finding worthy students</p>
<p>sure one year of calc is great, but if you think 2 or 3 years is necessary for the majority of students to study to understand the world, you are mistaken</p>
<p>I know some incredibly smart people who jsut took, gasp, one year of calc their whoolllleeeee lives and can talk circles around some math=smart people</p>
<p>How about some economics, some stats, some banking, some talks about budgets-national, state, city</p>
<p>I would rather a population that has some experience with all of those topics then a population that can do a bunch of proofs</p>
<p>and yes, you can learn about economics, etc without heavy math.....imagine that....learning REAL WORLD subjects is more useful than some proofs that actually don't mean didlly to most of us</p>
<p>Going over the congressional and presidential budgets would do us more good then anything else</p>
<p>Going over credit polciies and the law, going over bankrupty bills, learning about how the different tax proposals work, teaching about pricing, the global market, nafta, cafta, the world bank, the european market, the euro, the gold market, etc is how you educate people that can actually make life decisions</p>
<p>Sure calc is fine, but it is not the be all end all way of teaching thinking, and never will be, it is just that it has been built up to be that</p>
<p>Late to this thread...
a few comments:</p>
<p>(1) The ability to do higher math relies on brain growth spurts that happen in adolescence. Too much front-loading of complicated math <em>for all</em> ill-serves kids who need another year or two of brain growth.</p>
<p>(2) Paying3-- I was like you, VERY good at geometry and proofs; I loved Geometry. But I couldn't ever quite "get" Trig. I could memorize the things I was supposed to do and plug in the numbers, but it never had the appeal for me because I didn't really comprehend what I was doing. Was it a brain growth thing? Who knows, I got out of Dodge (math) as quickly as I could.</p>
<p>(3) mathmom, that you (and several others) found calculus "beautiful" seems like the best reason to try to teach it to all that I have heard so far!</p>
<p>Lately I have been thinking about trying again in math. Why? I know I'm not dumb and I suspect I could do better now if I am doing it for myself, to expand my mind, to understand how things work in our universe just a little bit better. </p>
<p>A week ago in the NY Times book review there was an ad for a College Calc course on DVD that I ripped out of the paper... still sitting on my desk. </p>
<p>However, I am going to go to the website and see what discrete math courses might also be available!</p>
<p>PS OF COURSE they would advertize in the book review!!</p>
<p>citysgirlmom:
Learning some abstract math is a good thing for everybody.</p>
<p>CGM, I don't think anyone here has been advocating two years of calculus, unless you think it takes two years for an introduction to integrals and differential equations. (Which maybe is what your high school was doing?) I think one year would be good for most college grads, but I find the arguments for discrete math and statistics compelling too. I certainly don't think you need two years of calc in high school.</p>
<p>CGM-- it's exactly the same way as understanding history. Just because you happen to think understanding history is more important doesn't mean thats true. Looking internationally, our k-12 system is a complete failure, an utter disaster. A lot of it comes from the attitude you're presenting, which basically says that it's ok to not be pushed, to not do things for the sake of the challenge, to only learn subject matter enough to be aware of it rather than to take part in the subject matter in a non-trivial fashion, and to strive towards, at best, mediocrity.</p>
<p>Our education system from k-12 is abysmal, and science and math education is particularly poor compared to the rest of the world.</p>
<p>Honestly, Canuckguy made the correct argument-- we settle for far too little when it comes to what the minimum standards should be for high schoolers, and to understand what should be hte minimum level of science calculus is necessary.</p>
<p>I believe we have the same problem with humanities/social science in HS, so this isn't a science major being self-righteous and self-important. It's the idea that it's ok to understand only a little bit about the subjects engaging the world around us that's scary to me.</p>
<p>As a general rule, when a math course is taken by mostly by non-math major student because that particular math course is required in their own major, the math course will be application oriented rather than proof based. Calculus can be proof based, however since most people taken Calculus are not math majors, it is seldom taught that way. It is also true of Linear Algebra.</p>
<p>Discrete math is one of the required first course for computer related major. So with the exceptions of a few colleges, discrete math is application oriented rather than heavy on proof, unless it is a upper division course or a seminar course.</p>
<p>On a separate topic, the last place you want to learn Calculus is to read Newton, there is very good reason that almost everyone follows Leibniz's approach.</p>
<p>The thread has been percolating nicely in my absence. Here are some links: </p>
<p>"The Calculus Trap" by Richard Rusczyk: </p>
<p><a href="http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php%5B/url%5D">http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php</a> </p>
<p>Knowing and Teaching Elementary Mathematics by Liping Ma: </p>
<p>and a review of that book by Richard Askey: </p>
<p><a href="http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf%5B/url%5D">http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf</a> </p>
<p>Hung-hsi Wu's website on teaching mathematics to elementary students: </p>
<p><a href="http://math.berkeley.edu/%7Ewu/%5B/url%5D">http://math.berkeley.edu/~wu/</a> </p>
<p>Undergraduate programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004: </p>
<p><a href="http://www.maa.org/cupm/curr_guide.html%5B/url%5D">http://www.maa.org/cupm/curr_guide.html</a> </p>
<p>How statistics is distinct from mathematics: </p>
<p><a href="http://statland.org/MAAFIXED.PDF%5B/url%5D">http://statland.org/MAAFIXED.PDF</a> </p>
<p>Lots of mathematicians are thinking about how to teach mathematics better. But the reform efforts take time.</p>
<p>Notice I use calculus versus specific books as the example- go ahead and substitute geometry... There are different calculus classes- the Honors sequence son is in prohibits getting later credit for a calc theory course- obviously this is a theory based sequence as opposed to the applications based one, or the "dead end" one that doesn't satisfy reqs for many majors. For those thinking of the AP calc class(es) their child took- consider this, like AP Language et al, there is only one specified set of materials to be learned so as to be able to offer a standardized test that colleges can relate to. It would be very hard to offer several types of calculus for most high schools, offering one requires many of their limited resources. Add it to the ideal world wish list.</p>
<p>The issue is why require a specific piece of literature to be considered well educated and yet not require some specific college level math courses, such as calculus. I get tired of people who have no experience in taking the math/science courses dismissing them while praising authors for whom there will always be substitutes. I doubt anyone will argue that a college level reading of some Shakespeare is a good idea, why not also agree it is a good idea to also have an understanding of the fundamentals of calculus? Either one can be considered totally irrevelent to one's future, both can be considered mind enriching. Maybe a problem is that so much literature does not require stretching one's ability to comprehend or a good teacher. I also know far more math/science types who also indulge in humanities than English majors who profess an interest in the physical or biological or abstract worlds.</p>
<p>if you don't think understanding history for the MAJORITY of people not going into math or science majors, that is really scary stuff</p>
<p>we go to WAR because we don't look at history, we don't go to war because someone doesn't know calculus</p>
<p>human interaction is more closely linked to shakepeare, literature, history, etc, than caluculus will ever be</p>
<p>yes, a year of calc is laudible in HS, but to force more than that for some lazy and antiquated idea that calc is the best path to crticial thinking and that if you can't do calc, you are stupid, is very narrow minded thinking when looking at the world and the people in it</p>
<p>we make life altering decisions for ourselves and others every day- right now there are major changes going on in Pakaistan, in a very volitale part of the world with nucluear weapons all around, unless you know how the got to that place can it be looked at in ways to make it better</p>
<p>yes, having SOME calc background is great, but believe me, it is not the only way to learn and stretch the mind</p>
<p>it takes more work for profs and schools to come up with different ways of teaching and approaches, falling back on good ole calc is easy</p>
<p>as for irrelevant, life is full of shakepearan drama, alluded to in art, movies, conversation, politics</p>
<p>I don't know many dinner conversation that discuss calc proofs, but I do know more about plays, books, speeches, etc</p>
<p>No, CGM, we do not go to war because we don't look at history. We go to war for other reasons.</p>
<p>m, yes we do...we don't look at what got those countries to those places very often</p>
<p>look, we may go to war with Iran...do we NOT look at what got them and us to this place? our leaders are using Irans HISTORY to justify current actions</p>
<p>If Iran, in some people's eyes, was a peaceful, non confrontational country, they couldn't use historic actions to justify current actions</p>
<p>For instance, we have Korea, who has a history of going to war and invading other countries, to this day, we are worried about them because of that history</p>
<p>In the middle east, each and every war is about history!!!!!</p>
<p>You can't talk about how to create peace in that region, without knowing history</p>
<p>World War 2 was all about history, us NOT going in right away was because of history, WW1</p>
<p>The civil war wa about history, and the constitution and what the constitution meant when it was written, each side took their interpretations of that HISTORIC yet living document to justify what they wanted</p>
<p>If you think we don't go to war because we don't look at history, that is really sad....we may turn it to our advantage and use history to go to war</p>
<p>I should have said, we use history to justify going to war, and unless you know history WELL, your actions can turn into a nightmare</p>
<p>My phrasing was poor</p>
<p>Korea has a history of going to war and invading other countries? Where can Korea invade? China? Japan?</p>
<p>mathmom, yes they are advocating it!!! that is what this is all about, and taking calc into college....</p>
<p>CGM:</p>
<p>I'm glad you're not a history teacher. You don't seem to be able to distinguish e
between knowing, using and abusing history.</p>
<p>And what going to war has to do with calculus is beyond me.</p>
<p>CGM, I don't know where you see anyone advocating TWO years of calculus. The question is whether any calculus is necessary to be considered well educated, or at least what level or what kind of math is necessary to be well educated. </p>
<p>I do think it's sad that we have created a nation where a large number of people feel that they aren't good at and don't like and don't need math.</p>
<p>now THAT looks interesting and more useful for most people than years of calc to prove you are smart</p>
<p>maritee, I said I didn't phrase it very well, oppsy</p>
<p>but I stand by what I said and still do</p>
<p>relying on calc as some sort of barameter of intelligence and capability of learning is pure laziiness on the the part of educators and it will indeed do more harm than good</p>
<p>when you force kids to take two years of calc in school, because of some warped idea that is the pathway to learning how to think and proof that you are capable causes those kids to MISS learning something that is more valuable to them and the world</p>
<p>as well, to equate learning more and more calc with learning hisotry or doing literature is doing a disservice to education and to students</p>
<p>and when taking that second year, or even that first, a student may be miissing out on ethics, morality, economics, stats, philosophy, world religions, criticial thinking, us government, civics, etc, real world math and anaylsis</p>
<p>we have a generation that is lazy when it comes to thinking, yet they are force fed the idea that calc is the be all end all way into college</p>
<p>we have students who can't write a decent paper or ask questions about something reported on the news, but can do some proof</p>
<p>we have students whp don't know how our government and budgets work and how it affects THEM, but can do some math problem that means nothing in the long term</p>
<p>we have students who don't know why the middle east is in such confusion, but are gung ho for war because they can't think for themselves, but regurgitate what they hear, because calc does not teach critical thinking in any real way that works in the world</p>
<p>we have students who couldn't tell you the names or inclinations of the supreme court justices and how their decisions affect their lives, but spend hours working on some math problems</p>
<p>we have students who don't understand the electoral college, or one man one vote, or how their taxes are used, but heaven forbid we don't push for that second year of calc in HS and even more in college, because, gee that is the best way to teach them how to think</p>
<p>it is laziness, little imagination, protecting the status quo to tell kids that they need two years of calc, or even one year in HS to prove they can think and learn</p>
<p>do some logic puzzles and your brain will indeed be stretched</p>
<p>play some chess</p>
<p>there is this defense of calc as some sort of tool of teaching thinking and analysis that only calc can teach</p>
<p>I don't believe that and that mindset is unfair to many, and simply habit</p>
<p>Ignorance is not bliss.</p>