From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Summary: One needs to learn how to learn.
Date: 10 Nov 92 00:41:59 GMT
Followup-To: sci.math,misc.education
Organization: University of Hawaii (Mathematics Dept)

In article <ccDyTB3w164w@allen.com> carolyn@allen.com (Carolyn Allen) writes:
>> 	(P. S. I'm not complaining... I like Michigan State.  I am,
>> however, rather jaded from the years of school for which I have nothing
>> useful to show.  Also, while I haven't done disastrously, my grades
>> here don't reflect my ability well because my high school did NOTHING
>> to teach me the study skills I would need here, so I am trying to
>> teach myself, as usual.)
>
>...excuse me, but what class is supposed to teach you study skills? I 
>thought every kid knows how to learn, some better than others, but if a 
>child learns to talk, walk and potty in the right place, that child has 
>study skills.  Applying them in complex ways is up to the motivation of 
>the individual and you are sitting on a pitty pot, my young man.

Well, I think that this brings us to the very crux of this whole
discussion on math education.  

One can have a hypothesis that the reason some students do better in
mathematics than others is because they have faster, more high powered
processors in their skulls.  Or more disk drive capacity, as it were.  If
that's true, then there's not much we as teachers can do about the
situation.  I personally don't believe it, though.  I think the problem
is not in the hardware (or wetware, if you will) but in the software.  I
think that some people learn mathematics more efficiently than others
because they use a different strategy for learning.  And that if we want
to actually accomplish something in terms of improving math education
instead of just sitting around and saying "Ain't it awful?" then we
need to realize that the real problem is not what subject matter we
should be teaching, or the best approach for teaching arithmetic or
algebra or whatever.  What's really important is figuring out how to
teach students how to learn.  Once a student has a good strategy for
learning mathematics, he'll manage to figure out a way to learn whatever
he wants/need to.  

As things stand now, you're right in that nobody teaches you how to
learn.  (Or when they do, it's usually by accident.)  A teacher simply
starts teaching the subject matter and students have to figure out for
themselves how to learn it.  Since they're not aware that they're
learning a skill, they assume that whatever strategy they develop for
learning is the same one everyone uses.  And the ones who are good at it
are usually the ones who are least aware of what their strategy is.  

One thing I think we can be fairly sure of is that learning is not
primarily a matter of effort.  Students who are the best at mathematics
typically put far less apparent time and effort into studying than
students who do less well.  (This doesn't count, however, the time that a
good mathematics student spends just walking across campus or sitting at
the lunch table with some friends, lost in a trance as he works out the
implications of something that was said in class that day.)  

Unfortunately, the psychologists don't seem to have much to offer us to
help figure out the difference between those who learn efficiently and
those who don't.  Until about 20 years ago psychology was in the grips of
a religion called Behaviorism.  Behavioral learning theory produced a lot
of useful things, especially for those interested in training pigeons and
goldfish -- or even dolphins.  But to the behaviorists concepts like
"understanding" were out of bounds.  It seems that the education
establishment today is still large committed to seeing education in terms
of teaching behaviors -- skills.  They like this because the learning of
skills can be measured quantitatively -- "objectively" -- unlike
understanding.  Like the rest of what Richard Feynman referred to as the
"cargo cult sciences," the educationists often consider the trappings
of science -- especially statistics -- more important than actually
producing good results.


If one wants to teach skills, I think one ought to be realistic and
acknowledge that one of the most important skills for success in the
educational world is that of taking tests.  Over and over again while
grading a set of exams I notice students whose grade clearly does not
reflect their understanding of the course material because they are
simply not good test takers.  At the very least, I think that a
student needs to realize that test taking is a skill that needs to be
learned, like any other skill.

A person who is having trouble with his golf or tennis game can go to a
pro who can show him how to correct his obvious errors.  A student who
fails to get full credit for his mastery of course materials because of
his lack of skill at taking tests has no one to turn to.  


Finally, I would like to say that if I were in Eric Green's situation (in
which I would be much less successful than he is) I would start having my
students measure things.  I suspect that they would learn more
mathematics in wood shop than in arithmetic class.  

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet