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Topic: Learning and Mathematics: Hiebert and Wearne, Teaching
Replies: 40   Last Post: Jan 21, 2004 3:45 AM

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Jim LaCasse

Posts: 48
Registered: 12/3/04
Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Posted: Feb 22, 1996 11:10 AM
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On Thu, 22 Feb 1996, John Conway wrote:

>
>
> On Thu, 22 Feb 1996, J. Wendell Wyatt wrote:
>

> > > I agree with Dana, it seems that it just make too much since to tell
> > >students why they are learning a subject. Usually, when students ask why
> > >they are learning a subject, the teacher would say because you have to and
> > >that it will help us in the future. That is not good enough, because it
> > >would be very easy to say that I am going into a profession that does not
> > >need math or sciences. If teachers would incorporate some real life
> > >applications to a subject, then students would be more receptive to the idea
> > >of learning that subject.

> >
> > I feel that this is one of the greatest needs/deficiencies of teachers at
> > all levels--we do not know where/how the mathematics that we are teaching is
> > used. Too many of us have been in school all of our lives and have very
> > limited experience in using mathematics in the workplace. Our primary
> > application of mathematics is that of an ordinary consumer.
> > One answer to this need could be highlighted boxes in textbooks (or
> > teachers' eds.), like historical notes, that would give some of this info.
> > Or it could be included in supplemental textbook materials written for
> > teachers. Regardless, we need "in-servicing" re: applications of the
> > content that we teach.
> >
> >

> I have rather deliberately refrained from entering this discussion
> so far, but there's something I really feel should be said, that is
> brought up by the above question.
>
> Namely, NOBODY knows just how the mathematics that we are teaching
> our children will be useful later in their lives; but I for one am
> very sure indeed that it WILL be.
>
> Already in my own life, I have seen an enormous number of very
> valuable applications of bits of mathematics that were of purely
> theoretical interest when I learned them at school.
>
> For example, I would never have dreamed that the US government (and
> many commercial organizations) would find it worthwhile to spend millions
> of dollars on the problem of factorizing large numbers. When I learned
> this stuff, it had essentially no application at all; now the computers
> used by banks and other financial organizations make millions of
> calculations every day (indeed, probably every second!) that depend
> vitally on the assumption that factorizing large numbers is hard.
>
> Again, the theory of finite fields was a theoretical backwater
> when I learned it; but a few years later it acquired many valuable uses
> in the telephone industry and elsewhere. Not quite a high-school
> topic, that; but it illustrates the same point, and made use of
> the small amount of number theory that WAS taught to me in my high-school.
>
> From my own mathematical experience I take a third example. I
> have long been interested in what I always thought was PURE geometry;
> but some stuff I did about the best way to pack spheres in a big box
> (in 8 dimensions, would you believe, but that's irrelevant here) was
> eagerly patented by the Bell Telephone Labs, for use in the digital
> transmission of numerical information from space satellites (and maybe
> transatlantic telephone conversations soon).
>
> The big message here is that I think teachers should NOT try to
> find out too much about particular applications of known mathematics.
> As I said before, following the practical applications tends to be
> more boring than following the mathematics. [I recall again that
> the high-school teachers who attended a talk I heard a few months
> ago were very lively and interested until one of them asked "but
> what is this used for?", the answer to which effectively put them
> to sleep!]
>
> The world is changing even faster now than it has over my lifetime,
> and it's important that kids learn mathematics because it's interesting
> and will help them to think up answers to NEW problems rather than OLD
> ones.
>
> John Conway
>
>

Right on the point, 100%. Beauty should be admired for its beauty, not
how well it covers the hole in the wall.

Jim LaCasse





Date Subject Author
2/14/96
Read Learning and Mathematics: Hiebert and Wearne, Teaching
K. Ann Renninger
2/15/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Nette Witgert
2/16/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Johanna K. Peters-Burton
2/16/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Stephen Weimar
2/16/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Kristin E. Waugh
2/16/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Laurie Gerber
2/16/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Jim LaCasse
2/17/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Lyndsley Wilkerson
2/19/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Emily Mott
2/19/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Emily Mott
2/21/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Jane Ehrenfeld
2/21/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Shawn R. Beckett
2/22/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
J. Wendell Wyatt
2/22/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Lou Talman
2/22/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
John Conway
2/22/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Will Craig
2/22/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Jim LaCasse
2/23/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
John Conway
2/23/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
andrew@plan9.att.com
2/24/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Johnny Hamilton
2/25/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Mara Landers
2/26/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Nette Witgert
2/26/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Stephen Weimar
2/27/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Will Craig
2/27/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Emily Mott
2/27/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
NiYa N. Costley
2/28/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Tony Thrall
2/29/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Mara Landers
2/29/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Marksaul@aol.com
2/29/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Laurie Gerber
2/29/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
W Gary Martin
3/1/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Brian Hutchings
3/1/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Brian Hutchings
3/6/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Liza Ortiz
3/9/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Judith Haemmerle
3/13/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Richard Tchen
3/17/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Richard Tchen
3/17/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Richard Tchen
3/20/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Kristin E. Waugh
3/27/96
Read Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Richard Tchen
1/21/04
Read calclus
zaheer

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