### A Hundred Years War

NCTM began publishing its Yearbooks in 1926. The very first one has been reprinted in 1955 and until a few years back was available at the NCTM store. My yesterday's search at the NCTM site for "First Yearbook" brought up only one item: Johnny W. Lott's (NCTM President 2002-2004) article A Static Mathematics Curriculum Is Unhealthy!

At the beginning of the twentieth century, E. H. Moore in his 1902 valedictory address as president of the American Mathematical Society characterized both the school and the college curriculum as in need of change. His picture of mathematics included integration, manipulatives, group learning, and technology. Moore recognized the need for change because he saw a curriculum steeped in the algorithms of arithmetic as unconnected to the real world and not designed to be studied by all.

Throughout the ensuing decades, similar messages calling for change echoed the underlying premise that including theory in the curriculum would greatly increase both mathematics skills and understanding. In the last decade of the twentieth century, the NCTM Standards documents and reform curriculum projects have come closer to the changes proposed by Moore 100 years ago.

The 1902 E. H. Moore's address *On the Foundations of Mathematics* has been included in the NCTM's First Yearbook which, by the way, was titled *A General Survey of Progress in the Last Twenty-Five Years*. Let me quote a few passages from Moore's address.

... I dare say you are all familiar with the surprisingly vigorous and effective agitation with respect to the teaching of elementary mathematics which is at present in progress in England. ...

One important purpose of English agitation is to relieve the English secondary school teachers from the burden of a too precise examination system.

In England, the Mathematical Association was established thirty years previously, with the primary goal of improvement of the teaching of geometry. Moore goes further and (among other suggestions) advocates a unified HS mathematics course:

Would it not be possible to organize algebra, geometry and physics of the secondary school into a thoroughly coherent four years' course, comparable in strength and closeness of structure with the four years' course in Latin?

Looking back at the century since Moore's speech, one cannot fail to observe changes in the educational system. Notably, Latin has disappeared from the curriculum, at least, as a reference point. As to the math education, this is still in a state of flux, with regular testing growing in significance. And, of course, with the ascendancy of algebra in the curriculum, Moore's hope for unified math instruction has never been in the cards.

I cannot say how much the NCTM's Standards brought us closer to Moore's vision; I doubt that they have. Here's another remarkable quote from Moore's speech:

Every result of importance should be obtained by at least two distinct methods, and every result of especial importance by two essentially distinct methods. This is possible in mathematics and the physical sciences, and thus the student is made thoroughly independent of all authority.

I may be terribly wrong but it seems to me that the question of making students independent of all authority was never considered seriously as a guiding principle of education. Moore also cautioned that

In contemplating this reform in secondary school instruction we must be careful to remember that it is to be accomplished as an evolution from the present system, and not as a revolution of that system.

This advice I believe went unheeded. If I am allowed to have a chuckle, the evolutionists never had as prominent a role in math education as the creationists who, as real revolutionaries, act on a sense of urgency for change. And you know what? We are regularly told that it is especially urgent now that we moved into the 21st century.

Judging by the intensity of the conflict between different views on math education that seldom subsided during the past century, this is what we may expect for the next few decades: continuation of the struggle. The change will come gradually from the bottom up as more students will begin getting more information and practice from the web. The authorities will eventually have to adjust to this irreversible process.