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WBraun
climber
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Nov 11, 2014 - 02:56pm PT
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All these so called math guys who think they're smart are actually stooopid.
They all have to hire guys that know no math to do all their work for them since all they know is one dimensional ....
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JEleazarian
Trad climber
Fresno CA
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Nov 11, 2014 - 03:12pm PT
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Now wait a minute, Werner! Just because mere arithmetic differs from "real" math is no reason to criticize mathematicians.
I must admit, though, that one undergraduate linear algebra midterm at Berkeley had four numeric answers, all of which I got wrong because I was too hasty and sloppy in my arithmetic, and the prof still gave me 100% because my methods were right.
John
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Lorenzo
Trad climber
Oregon
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Nov 11, 2014 - 04:06pm PT
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Big controversy here in Oregon this week because kids are being traumatized by taking tests.
It seems they are expected to actually know some math.
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neebee
Social climber
calif/texas
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Nov 11, 2014 - 04:19pm PT
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hey there say johnEleazarian and all...
i just recently got curious, about an abacus... as, i had seen one at someones house, as a kid...
somehow, i 'ran' into one, one the web and looked up more about it, to read-up on them...
such an old time, 'always been around' hardy thing, :) as to basics, :))
so, i practiced a bit online and then went and got one from amazon...
for me, that goes 'blank' at math, and transposes various combo letters or numbers... THIS was just beads... so i thought i'd give a go...
oddly, it is working out nice (though i HAD to put a few markers, scratches, on it, so i do not 'flip' my vision of it)...
well, it is helping me sort the thoughts in my head... expecailly when i have to subtract... i need to REDO the beads...
have to take out ONE pretty bead and put back TWO pretty beads on the other stick, so that i will have ENOUGH neat little beads to subtract with ...
once in a while i get stuck on which pole to adjust, but, i reckon, so far, as FAR left, as you need to...
i practice on my check book, which is already figured out, as to what i have taken out, etc... for to see if i get the beads right...
onward and upward, ... not sure how much it is helping my MATH but it sure is helping my brain and i do see in pictures, anyway, so i 'don't panic' at the numbers... :O
wish my daddy was still alive, somehow, i think he'd have enjoyed this
adventure of mine... :)
:(
edit:
http://www.alcula.com/suanpan.php
oh, there is also this one, too:
http://www.alcula.com/soroban.php
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crankster
Trad climber
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Nov 11, 2014 - 05:06pm PT
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All these so called math guys who think they're smart are actually stooopid. ^^^
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rgold
Trad climber
Poughkeepsie, NY
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Nov 11, 2014 - 06:21pm PT
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Neebee's story about the abacus reminds me about the origins of calculus. Not the subject, the name. All you medical types know that a calculus is a stone (usually or perhaps always a kidney stone). And that is the original meaning of the word, stone or pebble.
Although Asians were clever enough to put beads on a stick, Greek and Roman merchants reckoned with pebbles manipulated in grooves in the dirt in the same way as the abacus is used. The same fundamental concepts of place value that eventually led to Arabic numeration were present in those pebble systems. And the manipulation of pebbles, of calculi, became associated with having a system for obtaining mathematical results, so much so that it seems only the medical world continues to use calculus in something like its original sense. For the rest of us, calculus and its associated term calculate are mathematical notions.
In the spirit of a return to ancient times, one apparently embraced by the American electorate, I propose that henceforward the Stonemasters be referred to as the Calculusmasters.
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yanqui
climber
Balcarce, Argentina
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Nov 11, 2014 - 06:45pm PT
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All these so called math guys who think they're smart are actually stooopid. Blah blah ... all they know is one dimensional
Mathematicians may be stooopid, but at least they're smart enough to know that some of the most interesting questions in analysis actually occur in infinitely many dimensions.
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Nov 11, 2014 - 07:00pm PT
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When teachers organize to promote better teaching, rather than to oppose burdensome or insulting requirements, we can hope for real progress.
I'm not a big union guy, but when teachers organize to oppose burdensome requirements, don't you think that might just be because burdensome requirements hinder better teaching? Your statement makes very little sense, and wreaks of the typical arrogance that many other professionals such as lawyers or investors have towards teachers. I got news for you: we're not all idiots.
The letter written by the teacher in Syracuse hits the nail on the head. I think what he is trying to say is that for his entire working life he has dedicated himself to being the best teacher he can, and because people perceive that ALL education in the US sucks, he's being forced teach a poorly designed curriculum (Common Core) that is 100% owned and operated by Pearson, Prentice-Hall (which is true), in the name of educational reform.
The Common Core demands that I teach more content in my classes than ever before. (Even though advocates that don't actually know will claim otherwise.) The kids I teach are missing more class than ever for these stupid tests such as CMAS and PARCC, and its all technology-based testing. They are getting tested to death, when they would rather be in a classroom with one of the many excellent teachers at my school.
With the new evaluation system here in CO, I am definitely spending more time proving my worth as a teacher by documenting inane aspects of my job, and it is taking valuable time away from the time I spend trying to actually improve my craft. All the serious, good teachers at my school feel this way.
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JEleazarian
Trad climber
Fresno CA
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Nov 11, 2014 - 07:14pm PT
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wbw, my daughter and son-in-law both teach high school math, and they're no idiots. What they think of some of their particularly gung-ho-union colleagues is a different matter entirely.
Of course burdensome requirements can get in the way of teaching. What I ask, however, is that the union-types offer something else that actually helps deal with the problem the rest of the world sees, viz. poorly-trained students with diplomas.
John
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Nov 11, 2014 - 07:27pm PT
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http://educationnext.org/the-common-core-math-standards/
For those wondering what is wrong with the Common Core, there are some very interesting comments made in this article by a math professor who sat on the Governors' Advisory Board for the Common Core.
WSW: When you are so far behind, comparing the United States with better-performing countries through the incredibly narrow lens of standards doesn’t make a lot of sense. I think Common Core is in the same ball park, certainly not up there with the best of countries, but Common Core isn’t up there with the best state standards either, and what does that mean? Look at California’s standards for example. They are great standards and have been unchanged for over a decade, but many in math education hate them. They think they are all about rote mathematics, but I think such people have little understanding of mathematics.
So, let’s just pretend for a moment that Common Core is just as good as the very best. Who, in education circles, will agree with that enough to put it all in practice? The standard algorithm deniers will teach multiple ways to multiply numbers and mention the standard algorithm one day in passing. Korea will say “no calculators” in K–12, a little extreme perhaps, but some in the U.S. will say “appropriate tools” means calculators in 4th grade. We, in this country, are still not on the same page about what content is most important, even if everyone says they’ll take Common Core. Without a unified, concerted effort to teach real mathematics, there isn’t much chance of catching up.[
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Ed Hartouni
Trad climber
Livermore, CA
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Nov 11, 2014 - 08:20pm PT
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John wrote: ...In particular, employers outside (and, I suspect, even inside to a certain extent) academia find educational credentials meaningless. A high school or college diploma carries with it no reasonable expectation of any particular knowledge or skill.
Frustrated employers started demanding some evidence that graduates demonstrate certain minimum skills and knowledge. Those same employers concluded that neither grades nor graduation gave the desired assurance. The standardized tests and curricula were a ham-handed attempt to convey the desired assurance.
I don't recall when education became a certification process for the private sector. In particular, given the general reluctance to pay local taxes to support the education system, why would the concerns of the private sector be relevant to the discussion?
As I've said many times in the past, the four years I spent as an undergraduate, and eight years at graduate school was not an "investment" in my future, at least I didn't see it as such at the time and I had little belief that I would be stamped "certified" and then accepted in some private sector job. I didn't quite know what job I would do, but certainly those 12 years were an intellectual adventure for me. It turns out that I did make a career in science, and I'm lucky that it was a very good career, at least as successful as some others I might have pursued.
I do understand the standpoint of the value proposition implied by investment in education, but as others have pointed out in this discussion, going to school isn't the only path to a successful life.
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rottingjohnny
Sport climber
mammoth lakes ca
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Nov 11, 2014 - 08:39pm PT
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Can compund interest be computed via slide rule...?
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Ed Hartouni
Trad climber
Livermore, CA
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Nov 11, 2014 - 09:05pm PT
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Can compund interest be computed via slide rule...?
maybe define "compund"? then we can talk about the computation... what part of the new curriculum has spelling in it?
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rgold
Trad climber
Poughkeepsie, NY
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Nov 11, 2014 - 11:25pm PT
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In particular, employers outside (and, I suspect, even inside to a certain extent) academia find educational credentials meaningless. A high school or college diploma carries with it no reasonable expectation of any particular knowledge or skill.
Wow, John, that's quite an overstatement.
Frustrated employers started demanding some evidence that graduates demonstrate certain minimum skills and knowledge. Those same employers concluded that neither grades nor graduation gave the desired assurance. The standardized tests and curricula were a ham-handed attempt to convey the desired assurance.
I'm not at all sure efforts at reform were driven by employers, though they may have piled on after the fact. Indeed, if the point of education is to train the citizenry for employment, then why isn't education funded by the industries that benefit from the training? Why are we paying tax dollars to fund employee training programs?
I don't think employee training was ever supposed to be the point of public education.
I'm sure the educational world has been swept by reform movements from its inception. The first one I was aware of is probably Plato's Academy, which said on the entrance, "Let no one ignorant of geometry enter here." It is worth thinking about this a bit, because Plato was not in the geometry business at all, and no doubt he had some students who said, "we never use geometry here, so why did I waste all that time learning it?" Three thousand years later we hear the same echo today from people who don't seem to realize how their education may have shaped their abilities.
The first reform I experienced was the Sputnik crisis, when the USSR put the first satellite into space. Life magazine ran an article purporting to compare the lives of typical students in the US and the USSR. The US students were cheering for football teams and preparing for proms, while the USSR students were staying up all night studying.
Government, not private, money flowed into what are now called the STEM fields, and presto, we landed first on the moon. The mathematics reform at the time was called New Math. Tom Lehrer wrote a funny song about it. It was part of an educational enterprise that created a generation of scientists who fueled American primacy in science and engineering for years, but it was deemed a failure and is still referred to as an example of bad educational reform. Many of the complaints were the same: the parents didn't understand it and some of the teachers didn't either, features which, if you think about it for moment, might just as well be signs of quality too.
I'm willing to wager many of the principles of the New Math can be found in the Core Curriculum Standards. The difference then and now is that having promulgated the ideas, the reformers trusted the teachers to implement them. The current system seems to begin with an implicit assumption of teacher incompetence and then tries to make those benighted souls support standards the system implicitly assumes they are too incompetent to implement. Is it really any great surprise that this is not working well?
I find it particularly interesting that many professions with demanding postgraduate educational requirments still administer tests outside of those administered in school. Lawyers must deal with bar exams, physicians with board certifications, etc. Why don't I hear law or medical faculty decrying the influence of those tests?
I'd guess there are several reasons. One is that the tests are administered once at the end of years of education, rather than the current moment-to-moment intrusions that distort the everyday fabric of the classroom. The content of those tests is made available to students to study, and it is the responsibility of the students to learn the material on the test. In particular, the material on the test may not be what was taught in those postgraduate courses, it being assumed that the courses provided the skills and knowledge that would enable the students to master new material of importance. This is particularly true of Bar exams, which are tailored to state law. The whole situation is about as far from the testing programs in elementary and secondary education as it is possible to get.
Another is that, at least for now, faculty in these demanding postgraduate fields are not held personally responsible for their student's performance on the exams (although this might change). The role of student effort and preparation in passing the exams is recognized as a primary ingredient in success, and no one thinks that the faculty is somehow responsible for forcing or motivating those efforts.
And another is, I think, that by and large the faculty are either in charge of designing the exam questions or at least have considerable trust in those who do.
I don't think any of these conditions apply in the case of elementary and secondary educational testing.
When teachers organize to promote better teaching, rather than to oppose burdensome or insulting requirements, we can hope for real progress. Until then, I'm not holding my breath for better American performance in math, or in education generally.
I think teachers have been organizing to promote better teaching for years. In mathematics, there is, for instance the NCTM, the National Council of Teachers of Mathematics and I'm pretty sure there are analogous very active groups in most of the major fields. I'm also pretty sure that the unions have invested many resources into improving teaching. I know this to be true in New York State and assume it to be the case elsewhere.
But I also think it fair to point out that the US system, in marked contrast to at least some of the Asian systems, makes it almost impossible for teachers to meet and collaborate and so advance their professional standards and abilities. US teachers are almost prisoners in their classrooms with little or no ability to interact on a professional basis with other teachers, and little if any useful mentoring. New teachers are basically thrown into the deep end to see if they sink or swim, in a system that devises ever more ways of sinking while providing inadequate support for swimming.
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Degaine
climber
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Nov 12, 2014 - 12:10am PT
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Binks wrote:
I took math up to Vector Calculus. I rarely even use algebra. I use recursion every now and then in programming. Why do we need to learn all this math anyway? If I need to use it, I look it up on the internet. College isn't even necessary these days. Skip the debt, learn what you need to know on the job or taking online classes. I'm way ahead of my friends who went all in for the phd. They are still living in grass huts and complaining about privilege.
Tone is difficult to express on the two-dimensional Internet, so I'll take your post as tongue-in-cheek.
In the event that you are actually serious, math contributes to developing your brain muscle (analytic skills), doesn't matter if you don't use specific calculus equations in your daily life.
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Degaine
climber
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Nov 12, 2014 - 12:13am PT
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rgold wrote:
only the medical world continues to use calculus in something like its original sense.
Indeed. In French "calcul" can mean "stone" as in "kidney stone/gall stone".
Also, thanks for the other in-depth posts - an interesting read and perspective.
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Andrew Barnes
Ice climber
Albany, NY
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Nov 12, 2014 - 03:15am PT
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I think it was Yvon Chouinard who said something to the effect that he never had any use for algebra. I see other comments like this in this thread and hear them all the time. I don't say much to these people, because it's pointless - they don't like math, there is no point trying to convince them that they should like it. Needless to say, selling overpriced garments is not rocket science, and Patagonia is never going to resemble Google.
On the original subject of this thread, "why Americans Stink at Math" - it is not just an American problem. There are many other countries which do not do well in math. Economic wealth is not related to strength in math. You cannot buy mathematics, you have to earn it by hard work. The situation is similar to climbing. You can have all the newest, most expensive climbing gear, but this does not propel you up an El Cap route - you have to earn it with patience, blood, sweat and tears. There is no royal road to geometry.
In my opinion, most pedagogical problems in math stem from lack of knowledge and enthusiasm of teachers (at the high school and lower levels). If I had my way, teachers of math would be required to have PhDs and would be paid accordingly. I would drop a lot of the purely pedagogical training (education departments) because it is largely BS.
Doing math seriously is akin to climbing El Cap or climbing a difficult alpine route. There is no room for mediocrity here. On an alpine route, you will die if you are incompetent. The same thing happens in mathematics - the laws of logic are as immutable in mathematics as the law of gravity is in climbing. Quacks and posers are quickly weeded out in math, so they typically migrate to easier subjects. This is okay. Climbers make up a very small fraction of the overall population, so do mathematicians.
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Nov 12, 2014 - 05:35am PT
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In the event that you are actually serious, math contributes to developing your brain muscle (analytic skills), doesn't matter if you don't use specific calculus equations in your daily life. Excellent comment. Question: "How am I going to use this?" Honest answer: "You're going to use it everyday because it's gonna make you smarter. Duh." I don't know why so many people don't get this.
Andrew, you make some great comments.
I can just hear John thinking to himself about his children that are teachers. . . that's such a cute career for kids, teaching. Maybe when they grow up they'll get a real career like law. Again, typical arrogance from a profession that takes people to the hoop every chance that they get.
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rgold
Trad climber
Poughkeepsie, NY
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Nov 12, 2014 - 06:05am PT
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One hears the "I never needed to use this" complaint at all levels of education right through grad school. And of course it is true in some cases, in other cases not, although I'd guess that it is very rare that someone "needs" (whatever that really means) anywhere near everything they learned in any field. But mostly the claim misunderstands the point of education, perhaps even highly vocational training, and tries to impose a strictly individual perspective on an enterprise that is obligated to look well past individual pathways.
Here's an imperfect analogy: I start a rock-climbing school. Naturally, I intend that my degree certifies that a student is competent in all climbing genres, so I teach them about everything. Now someone graduates, moves to NYC, and has a long climbing career consisting primarily of weekends in the Gunks, with trips to the Tetons, Wind Rivers, Tuolumne Meadows, Red Rocks, etc. Now it happens that during this long and productive career, the graduate never has to do any real offwidth climbing and certainly nothing technical requiring either refined technique or just the applications of more basic techniques to a very sustained pitch. And so they complain that the very substantial amount of time in my program devoted to offwidth was wasted, because they never had to use any of that stuff.
So how does my school respond to this criticism? Naturally, we say we could not peer into the future of any one of our students and figure out what types of climbs they were going to choose, that our program was intended to make its graduates competent to confront any and all of the difficulties they might encounter in a climbing life, and the fact that this or that individual never used some of the skills we taught is actually irrelevant. We prepared them. They sought us out precisely because we would prepare them. What they eventually did with that preparation is their business, but does not reflect on the appropriateness of what we did.
And let's say our graduate moves on to some other outdoor sport and never really does any climbing. Then of course they say the never needed any of what we taught, and point to people in their newly-chosen field who have done well without any climbing education. Why exactly are those observations relevant to what we do in our climbing school?
Now the analogy is imperfect, as I'm sure people will be quick to point out. I do think it works pretty well as the collegiate level, where people choose majors and degree programs. My hypothetical climbing students also choose to go to a climbing school. But in our primary and secondary system we require students to go to school and learn certain subjects, so in some sense we are now teaching climbing to everyone, whether they have any inclination to do it or not.
Surely this has drawbacks and benefits. Among the benefits, we get some climbers who would never have known about it or engaged in it otherwise. Among the drawbacks, we get people who hate everything about climbing and were forced to endure a lot of instruction they found distasteful and irrelevant.
Now to continue the analogy, we would have to stipulate that climbing is actually a basis for a wide spectrum of life pursuits, so that failing to teach young people to climb would close them out of many modern opportunities. This would be bad public policy and a bad approach to the development of the highest possible potential in our population, and most authorities, going back thousands of years, have understood that some dissatisfied customers are a price that has to be paid in the pursuit of an ultimately greater good. This does not make the dissatisfied customers feel any better, but it also doesn't mean that their afflicted cries should be taken as a call to stop preparing everyone equally for the future.
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