Re: Japanese schools and math lessons

In article <[EMAIL PROTECTED]>,
K.M.Rowley <[EMAIL PROTECTED]> wrote:
>toto wrote:

                        .....................

        Japanese teachers generally start by tossing
>> out a problem and requiring students to grapple with it,
>> often in groups. Only after exploring different ways of
>> tackling the problem does the teacher help. The goal is
>> to foster thinking skills and problem-solving abilities.

>I've done some of this over the years - give the kids an
>assignment before we actually went over what they needed to know
>to do it.

Sorry, I would call this an absolute don't, unless they
have the background conceptual understanding to correctly
deduce a method.  What is likely to happen is that one
member of a group has heard of a method.

Problem-solving, in mathematics, at the pre-college level,
usually comes quickly if the underlying material is known,
or requires being lucky.  If you took 1000 high school
children and asked them to solve a cubic, using only what
is taught in algebra, many of them would consider reducing
the coefficient of x^2 to 0, but how many would consider
using the substitution x = y + q/y for some q to reduce
the problem to a quadratic for y^3, if they had not seen
this trick?
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
[EMAIL PROTECTED]         Phone: (765)494-6054   FAX: (765)494-0558