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