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 firstname.lastname@example.org