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From: tiwasawa@netxcom.UUCP (Takashi Iwasawa)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student and Course Integrity  (was Rising cost of textbooks)
Message-ID: <1121@netxcom.UUCP>
Date: 3 Jan 89 18:54:50 GMT
References: <1131@osupyr.mast.ohio-state.edu> <1887@sun.soe.clarkson.edu> <1057@l.cc.purdue.edu> <484@ur-cc.UUCP> <15561@joyce.istc.sri.com>
Reply-To: tiwasawa@netxcom.UUCP (Takashi Iwasawa)
Organization: NetExpress Communications, Inc., Vienna, VA
Lines: 72

In article <15561@joyce.istc.sri.com> gds@spam.istc.sri.com (Greg Skinner) writes:
>In article <484@ur-cc.UUCP> bjal_ltd@uhura.cc.rochester.edu (Benjamin Alexander) writes:
>>It is EXCEEDINGLY important for an average person to learn how to add.
>>Recognizing addition in daily life makes living that much easier.  If adding
>>is some kind of mystery black box machine (push the buttons for the first
>>number; push the holy and sacred Plus sign; push the buttons of the second
>>number; push the almighty Equals key) then ordinary people like Johnny will
>>be deceived by clever people throughout his entire life.  [...]
>
>Granted, but there is a limit to how much rote manipulations should be
>taught.  Case in point:  in the eighth grade (!!) my math teacher put
>long division and addition problems on his exams and homeworks.  (I
>got in trouble because I didn't do the homeworks, but I thought they
>were silly.)  I should think that after the fifth grade useful
>mathematical concepts, such as logic, should be taught.
>

Many years ago (nearly twenty!) I was a poor graduate student, and took a job
with a nearby university as a teaching assistant.  I had two sections of a
math course for non-science majors (Mathematics for Non-Mathematicians, or
some such title).  Thinking as Greg Skinner did, I intended to focus on logic
and other concepts rather than calculus;  after all, these kids were not going
to become engineers or scientists, let alone mathematicians!  I had been given
a text by the Chairman of the Math Department, which had lots of pictures and
skimmed lightly over history of mathematics, geometry, logic, calculus, etc.
So I plunged ahead into logic and truth tables as explained in the book, and
tried to explain that the same logic can be generated from different sets of
operators (you know, inclusive-OR versus exclusive-OR;  I think I even tried
to explain how the NAND operator suffices to generate NOT, AND, and OR).  I
got complete expressions of non-comprehension.  I went back to the book and
gave them problem sets (after working some out in detail in class).  Out of
40-50 students in my sections, 4 or 5 turned in excellent to good solutions
(say 80% to 100% correct).  The rest had garbage, or simply did not turn in
any solutions.  I worked out more problems in class and assigned simpler
problem sets, with the same result.  The students complained that the 
problems were too hard; they had been promised (!!!) that they wouldn't
have to know mathematics.  In desperation I gave a problem set of long
addition and division.  With the same result;  the 4 or 5 who had done well
before turned in near perfect scores, the rest of the sections could not
add ten 5 digit numbers together consistently, and a sizable number did not
turn in their work at all.  It was the end of the term, and I calculated
the grades from the students' scores on tests and problem sets (I had told
them how I was going to grade at the beginning).  A large number of the
students had failing grades.  I was called in by the Dean of Students (the
Chairman had died during the term).  The Dean said I couldn't fail so many
students;  their parents were complaining.  I explained that the students
could not add properly, let alone divide, understand logic, Venn diagrams,
or anything in the required text.  The Dean said "You are wrong!  These
students aren't stupid;  here, look at this one...565 (I no longer remember
the exact number, but it was in the 500-600 range.  T.I.) on the math SAT!"
I explained again that regardless of their SAT scores, they could not add;
perhaps I should have told him that when I had been taking SAT's, 650 was
the rough dividing line between a good score and a mediocre one.  The Dean
tried to get me to change the grades;  I refused.  I was reassigned, and
my contract was not renewed.

So there it is.  I agree with Greg that in the ideal world, rote training
with addition, subtraction etc. should not be necessary at eight grade level.
In practical terms, these (mostly freshmen) students at a mid-level (not
top-notch, but not exceptionally bad academically) small university needed
rote training.  And they had been cheated out of one of the essentials of
intelligent thinking by parents who insisted that their children get good
grades regardless of what they didn't know, and advisors who told them that
they didn't have to know mathematics, and Deans and faculty who would rather
keep parents happy (and students in school paying tuition) than teaching
them essential skills.  Are secondary schools any better about teaching the
simple arithmetical skills now than they were 20 years ago?

					Takashi Iwasawa
					(Obviously my company has no opinion
					 on mathematics;  if they did they
					 should be paying me more!)