Date: Mar 21, 1995 12:02 AM
Author: Ronald A Ward
Subject: Follow up--Chapter 3 Everybody Counts

1.  The definition given in Everybody Counts for "mathematical power" is:

"a capacity of mind of increasing value in this technological
age that enables one to read critically, to identify fallacies, to detect
bias, to assess risk, and to suggest alternatives."

It is an interesting exercise to compare the definition above with those
given in the Curriculum and Evaluation Standards as well as the
Professional Standards.

2. I used the expression "invisible culture" because Lynn Arthur Steen
argues that mathematics IS the invisible culture of our age. "Although
frequently hidden from public view, mathematical and statistical ideas
are embedded in the environment of technology that permeates our lives as
citizens." He discusses in some detail how the ideas of mathematics
influence the way we live and the way we work on the following different
levels:
Practical--knowledge that can be put to immediate use in
improving basic living standards.
Civic--concepts that enhance understanding of public policy issues.
Professional--skill and power necessary to use mathematics as a tool.
Leisure--disposition to enjoy mathematical and logical challenges.
Cultural--the role of mathematics as a major intellectual
tradition, as a subject appreciated as much for its
beauty as for its power.

I encourage readers to check out his detailed support in each of these
areas--it provides good answers to the question "When are we ever going
to use this stuff?" Steen concludes:

"These layers of mathematical experience form a matrix of
mathematical literacy for the economic and political fabric of society.
Although this matrix is generally hidden from public view, it changes
regularly in response to challenges arising in science and society. We
are now in one of the periods of most active change."

3. As a number of you pointed out, the statement "As computers become
more powerful, the need for mathematics will decline" is clearly false.
This is one of many MYTHS that are explored in Everybody Counts. After
each such myth, a discussion of reality occurs. I find these interesting
because there are lots of people who believe each of the myths reported.
And as mathematics educators, we need to be prepared to respond properly
when we encounter them.

4. Rather than give the author's explanation to why mathematics
education resists change--which you can all easily find and read for
yourselves--I'd like to refer you to another article, written by Zalman
Usiskin, which explores the nature of the "New Math" revolution, the
lessons we should learn from it, and some principles for the revolution
needed today. The article is entitled "We Need Another Revolution in
Secondary School Mathematics" and appears in the 1985 NCTM Yearbook. It
is a very well written article on a topic often mentioned but usually
discussed in ignorance.

On Wednesday, I'll post the questions for Chapter 4. Thanks to all who
have responded to this series. [No doubt you can tell that I think
Everybody Counts is a great book. It has generated more discussion and
controversy in my undergraduate and graduate classes in math education
than any other I've tried in the past five years.]

Ron Ward/Western Washington U/Bellingham, WA 98225
ronaward@henson.cc.wwu.edu