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Re: Learning and Mathematics: Hiebert & Wearne, Teaching
Posted:
Feb 22, 1996 11:10 AM


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 levelswe 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 "inservicing" 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 highschool > 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 highschool. > > 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 highschool 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



