Date: Mar 23, 1995 3:11 PM
Author: CHAPMAN@APSICC.APS.EDU
Subject: Ron's Questions

I'd like to respond to "What should be the principal goal of elementary
mathematics?" I think elementary school is where it is CRUCIAL that
students get the idea that mathematics is MUCH MUCH more than
arithmetic. They need basic understandings and skills but they must
go beyond. They need to be involved in genuine problem solving. They
must be asked to explain and justify their thinking. They must see
that there are many ways to solve problems. Please notice that I did
not exclude basic understandings and skills--they ought to be able to
perform all four operations, they ought to be at least familiar with the
standard algorithms, (by the time they leave elementary school) although
they may not choose to compute with standard algorithms. They need to
have learned to listen to other students' ways of solving problems.
They should have worked with negative numbers--they should have
flexibility in their thinking, not stuck in the "one right way/
one right answer" mentality. I think that kind of thinking (that I
just described at the end of that sentence) makes further learning of
mathematics difficult for students and difficult for secondary teachers
to teach.
A middle school teacher once told me (very politely and appropriately
by the way!) that it made her job harder when students told her that
it was impossible to subtract 9 from 7, as they had been taught in
elementary school. They'd be much more ready for middle school and
further math if they knew math was more than rules and procedures.
Cindy Chapman@apsicc.aps.edu