Give me the good old time math.
in [Math]
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From: Phil Carmody on 7 May 2010 02:40 "J. Clarke" <jclarke.usenet(a)cox.net> writes: > On 5/3/2010 7:37 AM, Pubkeybreaker wrote: >> On May 3, 7:00 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >>> On 5/3/2010 4:37 AM, William Elliot wrote: >> >>> The big question is what the math curriculum is supposed to accomplish. >>> 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. >> >> I disagree. Strongly. If one knows how to prove theorems, then one >> knows >> how to solve problems. The converse, of course, is not necessarily >> true. > > Then you disagree with Apostol. We all know what he's done for the > teaching of calculus. What have _you_ done? He's been one of the world's foremost resources for number theory. What have _you_ done? And before you ask what I've done - I've read a lot of what pubkeybreaker's published. Phil -- I find the easiest thing to do is to k/f myself and just troll away -- David Melville on r.a.s.f1
From: Hagen on 7 May 2010 00:06 > "J. Clarke" <jclarke.usenet(a)cox.net> writes: > > On 5/3/2010 7:37 AM, Pubkeybreaker wrote: > >> On May 3, 7:00 am, "J. > Clarke"<jclarke.use...(a)cox.net> wrote: > >>> On 5/3/2010 4:37 AM, William Elliot wrote: > >> > >>> The big question is what the math curriculum is > supposed to accomplish. > >>> 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. > >> > >> I disagree. Strongly. If one knows how to prove > theorems, then one > >> knows > >> how to solve problems. The converse, of course, > is not necessarily > >> true. This kind of statement is too rough to capture the reality: being good in proving mathematical facts requires skills of creative working that are surely helpful in solving real world problems using mathematics. However solving real world problems requires to handle all kinds of disturbing side effects like noise in data, imprecise knowedge etc. approprietly. This is an additional skill component that one does not learn by doing just theoretical mathematics. H > > Then you disagree with Apostol. We all know what > he's done for the > > teaching of calculus. What have _you_ done? > > He's been one of the world's foremost resources for > number theory. > What have _you_ done? > > And before you ask what I've done - I've read a lot > of what > pubkeybreaker's published. > > Phil > -- > I find the easiest thing to do is to k/f myself and > just troll away > -- David Melville on r.a.s.f1
From: J. Clarke on 7 May 2010 07:50 On 5/7/2010 2:40 AM, Phil Carmody wrote: > "J. Clarke"<jclarke.usenet(a)cox.net> writes: >> On 5/3/2010 7:37 AM, Pubkeybreaker wrote: >>> On May 3, 7:00 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >>>> On 5/3/2010 4:37 AM, William Elliot wrote: >>> >>>> The big question is what the math curriculum is supposed to accomplish. >>>> 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. >>> >>> I disagree. Strongly. If one knows how to prove theorems, then one >>> knows >>> how to solve problems. The converse, of course, is not necessarily >>> true. >> >> Then you disagree with Apostol. We all know what he's done for the >> teaching of calculus. What have _you_ done? > > He's been one of the world's foremost resources for number theory. > What have _you_ done? > > And before you ask what I've done - I've read a lot of what > pubkeybreaker's published. In othe words neither of you has done squat for the teaching of calculus.
From: rich burge on 8 May 2010 21:53
On May 3, 5:24 am, William Hughes <wpihug...(a)hotmail.com> wrote: > On May 3, 8:00 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > > <snip> > > > 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. > > Certainly students need to know how to solve problems, but > why do they *need* to know how to prove theorems, the overwhelming > majority will never need to prove a theorem is their lifetime. > Math teaches us to carefully distinguish between belief and certainty. Proving a few theorems is part of the program. Solving problems, even simple ones, allows the technician to make statements with complete certainty that the uninitiated can only guess at. Ever what to be a magician? Consider mathematics. rich |