From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.edu
Subject: Re: teaching concepts?
Date: 29 Sep 92 18:51:40 GMT
Article-I.D.: mentor.BvCsE5.5wB
Distribution: na
Organization: Purdue University Statistics Department

In article <1a4ssnINNq50@bigboote.WPI.EDU> phillies@wpi.WPI.EDU (George D. Phillies) writes:
>In <Bv1uo4.6s2@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin)
>advocates

>>Teach the ideas, not the easily-forgotten details!  

>This is the oft-heard notion that one should teach concepts, not procedures.
>If the students have been taught that details are important, as opposed to the 
>modern American approach in which sign errors are treated as trivial, they will 
>tend to become meticulous in their study and understand the details.

>After several decades of teaching (and research in my field) I am gradually 
>convinced that evidence for the existence of concepts in the sense the word is 
>usually understood here, let alone evidence for the utility or possibility of 
>teaching concepts, is markedly absent.  So far as I can tell, the "concept" is 
>basically a mnemonic for a set of problem-solving procedures, which are more or 
>less generalizable, if one has had concrete practice generalizing them.  
>Observe that the successful approach to doing physics at the graduate and 
>research levels is not based on vague invocations of concepts, it is based on 
>successful implementation of successful procedures, e.g. Hamiltonian and 
>Lagrangian mechanics, solution of Maxwell's equations via orthogonal 
>polynomials, etc.  

Those who have not really used the concepts, or have used them only in too
restricted a class of examples, often confuse them with a set of procedures.
This does not mean that details are unimportant, but that they do not lead
to understanding.  And it is reaslly top-level research to extract concepts
out of details; when Dedekind published, "Wie sind und was sollen die Zahlen,"
he had finally distilled out the structure of the integers.

The "new math" was an attempt to teach the concepts of the number system to
children, and was pushed forward from the observation that total arithmetic
skill contributed nothing to understanding, nor to the ability to apply the
skill in different problems.  To simplify, learning how to add did not 
contribute to learning when to add.  Nor does the other hold.  Learning
concepts does enable people to know when to apply them, but will not get
the answers.  Merely knowing the arithmetic concepts will not enable one
to become a number theorist, but it will cut the time needed to learn how
to use a calculator to almost nothing.  It will also enable someone to 
apply arithmetic to previously unforeseen situations.

The problem may be most evident in such areas as grammar, mathematics, and
statistics.  Certainly few researchers will use their knowledge of the 
concepts to propose something new almost out of whole cloth.  But the
use of concepts by itself can show that even well-established traditional
procedures are not answers to reasonable questions; statistical testing is
an excellent case here, where misunderstanding has led to the systematic 
use of unjustifiable procedures.

-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)