Xref: utzoo comp.edu:1690 sci.math:5248 sci.physics:5329
Path: utzoo!utgpu!attcan!uunet!ncrlnk!ncr-sd!hp-sdd!ucsdhub!ucrmath!marek
From: marek@ucrmath.EDU (Marek Chrobak)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student preparedness
Message-ID: <605@ucrmath.EDU>
Date: 25 Dec 88 23:28:07 GMT
References: <4893@phoenix.Princeton.EDU> <6435@killer.DALLAS.TX.US> <9238@ihlpb.ATT.COM> <1077@l.cc.purdue.edu>
Reply-To: marek@ucrmath.UUCP (Marek Chrobak)
Organization: University of California, Riverside
Lines: 62

In article <1077@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes:
>
>Teaching means presenting the WHY, not the HOW.  It is very difficult to teach
>the why to students who are not research caliber who already know the how.

>A lecture has been defined as material going from the lecturer's notes to
>the auditors' notes, without passing through the minds of either.  I once
>made the mistake of asking a question with such a lecturer.  He could not
>teach, he could only present.  Too many students want such garbage.  We
>should not oblige them.
>-- 
>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907

How true and how sad. I have once tried to do something with
this habit of "xeroxing" a lecture, by following very closely
a textbook, so that the students do not have to take too
much notes, and may have more time to think in class. Once they
noted that I follow the book, half of them stopped to come to
class at all. In the other half this xeroxing habit was yet
stronger than I thought, they were still copying every word
I said. 

What I find quite irritiating, is when the students at the
beginning of a course, ask whether I will do proofs. I remember
the first time it happened to me, I simply did not understand
the question. How can one teach math without proofs at all?
Mathematics is more in proofs than theorems. But what the math
education here seems to accomplish is to reverse this completely.
Math is taught as a set of magic rules, which have to be followed
with precision and veneration. Of course, this is all "true",
because the professors say so. And it's in the book, anyway. They
would not lie in print would they? The students know that the
proofs, these scary complicated things, exist somewhere but
they are just some technical and messy explanations of what 
everybody knows anyway, so why to bother at all. They not just
don't understand the proofs, they do not even feel the NEED of
a proof. In Herman's terms, the question WHY does not cross
their mind. They just want to know HOW.

It would be silly to blame the students for this. This is the
way they have been taught in school, it's no wonder this is
what they expect from college. 

My daughter is in the second grade now. All math she has been
taught so far is addition and subtraction, for numbers smaller
than 100 of course. This is already a year and a half of
addition and subtraction. She is studying also from second-grade
textbooks we received from Poland. At her age children there have
already some understanding of elementary notions in set theory:
sets and operations on sets. In the second grade, they are already
taugth solving linear equations. Arithmetic is taught on a way,
it's derived, in a way, from sets, and is regarded rather as a
necessary tool, not the goal. Every exercise in a book is a real
pearl, requires a little bit of thinking, just enough for a kid,
but also enough to live a trace and teach something.  And still,
this is all entertaining enough, so that even if it's
not really fun, it's surely less boring that hundreds of additions
and subtractions. I wonder what will they cover in her school later
this year, will they teach numbers greater than 100, or start 
multiplication? 

Marek