Give me the good old time math.
in [Math]
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From: J. Clarke on 3 May 2010 22:00 On 5/3/2010 8:15 PM, Ray Vickson wrote: > On May 3, 12:29 pm, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >> On 5/3/2010 2:32 PM, Frederick Williams wrote: >> >>> "J. Clarke" wrote: >> >>>> However knowing how to fix a car does not help you to detect that a >>>> politician or lawyer's "proof" is anything but. Knowing what real proof >>>> looks like does. >> >>> That's irrelevant, lawyers are not required to prove things >>> mathematically. >> >> So what? Are you saying that the public should be trained to be easily >> bamboozled for the benefit of lawyers? > > Since when have _logical_ arguments prevailed in court? Are you saying that they shouldn't? > Evidence > sufficient to convict murderers may be tossed out (and has been more > than once in the past) because it was gathered as a result of stopping > a car without sufficient reason; never mind what the evidence shows! How is this not logical? The police know the rules and know that if they do not follow those rules then any evidence they gather will be inadmissible. The judge found that they had not followed the rules, so he applied the prescribed penalty under the law, which is to throw out the evidence. However a judge is not a member of the lay public from which the jury pool is selected. > A > few years ago in the province of Alberta a person's dismissal from a > parole-board job was overturned by an appeal court. The person was > dismissed because they were proved to be incompetent, but the court > ruled that the necessity of being competent was not stated anywhere in > the hiring criteria. If only courts _did_ operate on the basis of > logic, but this is not necessarily so, at least in Canada, and > probably also in the U.S. This is hardly an argument against the general public being taught what "proof" looks like.
From: J. Clarke on 3 May 2010 22:29 On 5/3/2010 9:36 PM, porky_pig_jr(a)my-deja.com wrote: > On May 3, 7:37 am, Pubkeybreaker<pubkeybrea...(a)aol.com> wrote: > >> I disagree. Strongly. If one knows how to prove theorems, then one >> knows >> how to solve problems. > > So, suppose you dilligently studied Rudin's Principles of Analysis, > through integration and differentiation, so you can rigorously prove > FTC, integration by substitution and integration by parts. Cool. Now > take the Calculus book, the one that contains real tricky expressions > to integrate. Like sometime you need to use trig substitution. Or > combination of several techniques. Now how do you think knowledge of > Rudin will help you? Answer: not a bit. Exercise for anybody who thinks they know how to solve problems in calculus. Get the Schaums Outline "Mathematical Handbook". Start with expression 14.1, and work through to 14.677.
From: J. Clarke on 3 May 2010 22:11 On 5/3/2010 6:50 PM, Transfer Principle wrote: > On May 3, 9:23 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >> On 5/3/2010 11:15 AM, William Hughes wrote: >>> On May 3, 11:42 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >>>>>> A balance is needed--students need to know how to prove theorems, but >>>>>> they also need to be able to solve problems, and knowing how to do one >>>>>> does not necessarily enable one to do the other. > > This is the second thread I've seen on the topic in the past > few weeks about this topic. The other thread asked when most > American students learned about proofs, and the answer was > that while they were traditionally taught this in the > high school geometry class, this is now on the decline. One > would have to go to Asia to learn math fully rigorously. I can't see any high school teaching math "fully rigorously". One generally doesn't get exposed to "full rigor" until the sophomore analysis class. One does learn proofs in geometry but it's an introduction to proofs. >>> Actually, I have grave doubts that this holds for most >>> people. >> Most people don't need any math beyond arithmetic anyway, so we aren't >> talking about "most people". > > Bingo! There lies the dilemma. Since most people don't use > math beyond arithmetic, many people believe that math > shouldn't be taught past elementary school at all. In > particular, _no_ math should be required to graduate from > middle or high school or enter college. One should only > have to learn the bare minimum of math required to survive > in the real world and that's it. And therein lies the problem. The justification for teaching math in the public schools has to lie beyond practical utility. But at the same time, if students come out not being able to solve problems then they have been short changed. > Then whenever anyone asks why more math should be taught in > school and more rigorously, the answer inevitably goes back > to "Asia." Math classes need to be made more rigorous in > order to keep up with Asia, and the US will keep falling > behind unless the curriculum is changed. Which is silly because the success of "Asia" has never relied on their public knowing anything about math. Their success in consumer markets has not been because they know more math, it has been because they are willing to try new ideas like that crazy "transistor" stuff and because they have a cheap workforce with a solid work ethic. If the Chinese go to the moon before the US goes back, it won't be because the Chinese know something special about math, it will be because their politicians decided to do it and ours didn't. > So there are two philosophies on how much math should be > taught in school -- the minimalist idea that students need > only to learn as much math to survive in the real world and > not one iota more, and the competitive idea that one needs > to learn as much math as they do in Asia. And never the > twain shall meet. > > An argument could be made that the status quo is in fact a > compromise between the two philosophies -- so one has to > learn more math than is needed in the real world in order to > get into college, but less math than Asians do. > > The one question that I have never seen answered is why don't > the _Asians_ complain that they are required to learn more > math than is required in the real world. Complaining is detrimental to one's future prospects in many Asian societies. > If Americans don't > like that the little math that they are forced to learn isn't > used in the real world, then Asians, who have to learn much > more math than Americans, have more right to complain -- and > yet we don't hear about such complaints. If Asians only had > to learn as much math as they need in the real world and not > one iota more, then there would no longer be a gap between the > math curricula of the two continents. The question is why anyone should care if there is a "gap between the math curricula of the two continents". The simple fact is that most people with technical degrees in the US do not work in technical fields. When that workforce is entirely utilized doing what it was trained to do, _then_ we have cause to worry about whether our math instruction is inferior to that of some other country.
From: William Elliot on 4 May 2010 04:40 On Mon, 3 May 2010, Transfer Principle wrote: > The one question that I have never seen answered is why don't > the _Asians_ complain that they are required to learn more > math than is required in the real world. If Americans don't > like that the little math that they are forced to learn isn't > used in the real world, then Asians, who have to learn much > more math than Americans, have more right to complain -- and > yet we don't hear about such complaints. If Asians only had > to learn as much math as they need in the real world and not > one iota more, then there would no longer be a gap between the > math curricula of the two continents. > Because the Asians know that the real world is scientific and that math, real math instead of USA play at math (as stated by a Vietnamese immigrant) is science. The America view of real world is media myopic commercialism. In short, Asians don't complain because they're not lazy and fat like Americans.
From: William Elliot on 4 May 2010 04:48
On Mon, 3 May 2010, William Hughes wrote: > It is not necessary for any but a very small minority to be able to > repair cars, and a very very very small minority to be able to design > cars. For the vast majority, being able to repair cars does not improve > driving skill. And while it may be a "good thing" to have a general > understanding of automobiles, it is ludicrous to suggest that such an > understanding is needed. > Of course you don't have to know how to fix a car. In fact there is much effort in American, and now world wide, to design things that can't be fixed. Fixable or not, an understanding of the equipment you use is essential to maintaining the equipment, it's safety and affordability. > - William Hughes > > |