NetNews Usenet Archive 1992 #26/NN_1992_26.iso/spool/sci/math/14592

Internet Message Format | 1992-11-08 | 3.5 KB

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Newsgroups: sci.math,misc.education
Path: sparky!uunet!zaphod.mps.ohio-state.edu!cs.utexas.edu!sun-barr!ames!purdue!mentor.cc.purdue.edu!hrubin
From: [e-mail] (Herman Rubin)
Subject: Teaching mathematics  Was: Re: group theory for HS students
Message-ID: <[e-mail]>
Organization: Purdue University Statistics Department
References: <[e-mail]> <[e-mail]> <[e-mail]>
Distribution: sci
Date: Sun, 8 Nov 1992 13:09:02 GMT
Lines: 57

In article <[e-mail]> [e-mail] (Dan Prener) writes:
>In article <[e-mail]> [e-mail] (Randolph Gregory Brown) writes:

>   [ ... ]

>>            Math teaching suffers from a chronalogical problem -- just
>>because calculus was invented (discovered if you really want) before
>>group theory doesn't mean that it should be learned beforehand.

>The conventional order of the mathematics curriculum isn't based on the
>history of mathematics.  It is a compromise to accomodate a heterogeneous
>audience.

It is not just a compromise, it is a surrender to the fact that the "students"
are now brainwashed into routine.  A substantial majority of those taking
college mathematics do not even know what a proof is, nor can they formulate
word problems.

>If math courses had the training of mathematicians as their only purpose,
>then the ordering would be more like what you suggest.  On the other hand,
>there is an urgent need to provide, say, physics students, with calculus
>at an even faster rate than is usually done.

>So the compromise gives everyone a quick jolt of calculus, then gets on
>with other stuff.  Real analysis courses are an explicit recognition that
>that first jolt of calculus wasn't really part of the orderly training
>of mathematicians.

This was done right after WWII, with the calculus course usually being
done in 1 year, including multivariate.  Then the student went directly
into abstract algebra and real analysis.  But it did not take long for
the dumbing to set in.

But the chonological order even was abandoned in favor of computation
against concepts.  Axiomatic geometry is no longer required, and many
cannot even get it.  Nor are the universities willing to consider this
as something to be remedied, nor are they willing to assume this anywhere.

I doubt that any student is in a better position to understand "abstract"
mathematics after calculus than before.  The general concept of measure
and integration is about 5000 years old, although only formulated a
century ago.  It can be taught to someone who understands algebraic
notation, but is very difficult for those who have had a calculus course.

At this time, there is little, if any, logic in the mathematics curriculum.
Learning to compute, unless it is presented as merely this, makes learning
even what the computations mean more difficult.  If we must teach arithmetic
without concepts, make it clear that this is what is being done.  If we must
teach calculus manipulations without understanding, make this clear also.
And point out explicitly that learning to compute may very well make it
much harder to understand, and remove the computing from the prerequisites
for the conceptual courses.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: [phone]
[e-mail] (Internet, bitnet)
{purdue,pur-ee}!snap.stat!hrubin(UUCP)