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In article <1jv3k6INNlqa@uwm.edu>, radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
|> There is an article in the January 1, 1993 issue of Science which
|> compares the mathematics achievement of Chinese, Japanese, and 
|> American children.  The article finds that American students continue
|> to lag far behind their Asian peers.  Only 10% of Japanese fifth
|> graders and 8% of Japanese eleventh graders had scores which were
|> lower than the average score of their American counterparts.
|> 
|> Eleventh graders from each country were asked the following question:
|> "Here are some factors that may influence students' performance in
|> mathematics: a good teacher, innate intelligence, home environment,
|> and studying hard.  Only 27% of American students chose studying
|> hard, as opposed to 72% of Japanese students.  However, 54% of American
|> students selected "a good teacher", versus 14% of Japanese students.
|> 
|> The teachers of eleventh graders were asked the same question.
|> 93% of Japanese teachers chose "studying hard", and 7% chose "innate
|> intelligence".  However, only 26% of American teachers thought that
|> studying hard was the most important factor, while 41% selected
|> innate intelligence.

I think a good teacher can outweigh studying hard. However, students
really have to teach themselves a lot of the cirriculum (I'm not a
teacher so don't laugh if I mispell this word). Whatever the teacher
says in class might not make sense at first. There's some distraction
or noise or some damn reason. But a student has to make it make sense.
The student's best teacher may turn out to be (him)(her)self. I was
lucky enough to have teachers that could present with enough style for
me to pick up the idea of teaching myself. A really confident and
presentable teacher who makes good sense can get an interested student
going. I've found it hard going if a teacher begins with off-the-wall
ideas. Unless these ideas are clearly explained and justified,
students may gain false impressions on the class. They have to gain
some kind of impression to fill their blank slate, and it'd best be a
good one.

|> I think that these attitudes are very destructive.  In my limited
|> teaching experience, students have often told me that they are
|> not "math people".  When I try to emphasize concepts rather than
|> algorithms, students are resentful.  I think the reason for this
|> is that my students don't really believe that they can understand
|> mathematics, so they memorize procedures and hope to bluff their
|> way through the course.

They're "pulling Homers"!

People who want to learn algorithms should learn algorithms. But you
have to show them what computer programming is all about. It's really
neat.

|>  They are not necessarily lazy, but they
|> become frustrated easily; if they can't solve a problem in a few
|> minutes, then they give up.

It's ok to give up. But you show them how to do it (make it interesting,
make them appreciate the novel application of concepts) and give them a
harder one.

-- 

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie

radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
> There is an article in the January 1, 1993 issue of Science which
> compares the mathematics achievement of Chinese, Japanese, and 
> American children.  The article finds that American students continue
> to lag far behind their Asian peers.
[part deleted]
> 
> The teachers of eleventh graders were asked the same question.
> 93% of Japanese teachers chose "studying hard", and 7% chose "innate
> intelligence".  However, only 26% of American teachers thought that
> studying hard was the most important factor, while 41% selected
> innate intelligence.
[more deleted]

> 
> I think that these attitudes are very destructive.

[more deleted]

I completely agree with you.  As someone very much into Piagetian
psychology, it seems to me that, in some sense, everyone needs construct
mathematics for themselves.  I've always wished that there were no word
'teach' in the English language, and like Spanish, we would use a word
with the implication of 'show,' instead.  When people lack
the belief that they can understand mathematics, they simply won't.

By the way, for an outstanding article on the same general subject, see
the December 1992 Scientific American.  It presents results similar to the
Science article you cite, and it also explores the differences in teaching
style, societal support, school structure, etc., that account for the
differences in math/science learning. For me, it was amazingly clear and it
also exploded some stereotypes and mis-impressions I had had about Asian
schools.

Paul MacFarlane
Danville, California
pmacfar@eis.calstate.edu