Give me the good old time math.
in [Math]
|
From: Pfsszxt on 3 May 2010 10:05 On Mon, 3 May 2010 01:37:47 -0700, William Elliot <marsh(a)rdrop.remove.com> wrote: >The Corvallis school board is deciding upon a new math curriculum, one >that will focus on mathematical logic and reasoning instead of problem >solving. Is this happening elsewhere in the nation? That math will again >be taught in math classes? > >Unfortunately there's yet more emphasis on working in teams and in >collaborating. That I consider to be a mistake like cook book math has >been. What I've noticed is that team work students are unsure of >themselves, that they need group confirmation at a time when they >need to become self reliant. Is this alas, becoming a national fad? One wonders how many group gropes Euler or Cauchy or Riemann etc were involved in !!!
From: J. Clarke on 3 May 2010 10:42 On 5/3/2010 8:24 AM, William Hughes 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. For one thing, knowing how the theorems fit together helps recall. For another sometimes if you can't remember some necessary detail of the theorem and don't have a reference handy you can reconstruct the logic. Then there's the issue that one should as a matter of general knowledge know what a rigorous formal proof looks like, not just as something one saw once but as something that one has internalized to the point that one recognizes how far short of such proof most arguments presented the course of everyday life fall.
From: William Hughes on 3 May 2010 11:15 On May 3, 11:42 am, "J. Clarke" <jclarke.use...(a)cox.net> wrote: > On 5/3/2010 8:24 AM, William Hughes 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. > > For one thing, knowing how the theorems fit together helps recall. As a general principal, very very questionable. In any case simple mnemonics would be more effective and easier to learn > For another sometimes if you can't remember some > necessary detail of the theorem and don't have > a reference handy you can reconstruct the logic. Actually, I have grave doubts that this holds for most people. > Then there's the issue that one should as a matter of general knowledge I.e. you dont *need* to learn theorems but here is why I think it is a good idea. This argument can and has been made in support of the teaching of latin, including the idea that learning latin will enable you to debate more intelligently. I think the best analogy is the automobile. It is very necessary for most people to be able to drive. 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. - William Hughes
From: J. Clarke on 3 May 2010 12:23 On 5/3/2010 11:15 AM, William Hughes wrote: > On May 3, 11:42 am, "J. Clarke"<jclarke.use...(a)cox.net> wrote: >> On 5/3/2010 8:24 AM, William Hughes 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. >> >> For one thing, knowing how the theorems fit together helps recall. > > > As a general principal, very very questionable. In any case > simple mnemonics would be more effective and easier to learn Mnemonics for the entire structure of integral and differential calculus? Please do make them up and share them. >> For another sometimes if you can't remember some >> necessary detail of the theorem and don't have >> a reference handy you can reconstruct the logic. > > 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". >> Then there's the issue that one should as a matter of general knowledge > > I.e. you dont *need* to learn theorems but > here is why I think it is a good idea. This > argument can and has been made in support > of the teaching of latin, including the idea > that learning latin will enable you to debate > more intelligently. The argument with regard to Latin has also been made with regard to programming languages. > I think the best analogy is the automobile. > It is very necessary for most people to be able > to drive. 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. 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. Given what is happening politically in the world today, whatever we're doing now to educate people certainly isn't working.
From: William Hughes on 3 May 2010 13:17
On May 3, 1:23 pm, "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: > >> On 5/3/2010 8:24 AM, William Hughes 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. > > >> For one thing, knowing how the theorems fit together helps recall. > > > As a general principal, very very questionable. In any case > > simple mnemonics would be more effective and easier to learn > > Mnemonics for the entire structure of integral and differential > calculus? Please do make them up and share them. The OP talked about the "Corvallis school board". I assume we are talking about elementary and possible high school (The OP also talked about national without saying which nation he was talking about. This almost invariably means the United States). So I don't think we are talking about anything but basic integral and differential Calculus. When teaching an introductory Calculus class I give a short table of derivative/ integrals for the students to memorize. > > >> For another sometimes if you can't remember some > >> necessary detail of the theorem and don't have > >> a reference handy you can reconstruct the logic. > > > 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". > Actually we are talking about the needs of the people in the "nation" who attend school. - William Hughes |