Re: Why is math so difficult for some people?

In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
>I have taught math for many years, both in a classroom setting and one
>on one, and more often than not, the main problem lies in students not
>understanding the basic ideas behind the formulas, rather than just
>memorizing the formulas. For many students, there is the mistaken
>belief that "knowing" the formulas is enough.

This is not surprising, considering that this is essentially
how everything is taught in the elementary and high schools,
and also in the courses through calculus.

As just about all textbooks take that approach, and the great
bulk of teachers believe in teaching that way, it is hard to
see what can be done.  We are NOT going to be able to teach
the teachers; this failed for the new math, and it was very
definitely tried.

It is not even learning the basic ideas behind the formulas;
this might get through to a percentage of the teachers.  It
is knowing the properties and the concepts of the mathematical
objects used, and these are not going to be learned by the
mistaken methods of the educationists.

We can teach variables in the general sense (do NOT limit 
them to numbers) as linguistic entities with beginning 
reading.  We can teach sound mathematical logic to at least
half of those in elementary school; it has been done.  

But we cannot succeed if "learning mathematics" is measured
by the multiple choice computational stuff on the exams now
being mandated.  Nobody learns what multiplication means by
memorizing the tables, and one can understand what it means
without having any facility in computing answers.
-- 
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