What Is Mathematics For?

Date: 2015-10-07; view: 492.

Finance 1 ENG

Akimbay Alibek

Underwood Dudley

A more accurate title is “What is mathematics education for?” but the shorter one is more attention-getting and allows me more generality. My answer will become apparent soon, as will my answer to the subquestion of why the public supports mathematics education as much as it does. So that there is no confusion, let me say that by “mathematics” I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects arithmetic is for or why it is supported. Society cannot proceed without it. Addition, subtraction, multiplication, division, percentages: though not all citizens can deal fluently with all of them, we make the assumption that they can when necessary. Those who cannot are sometimes at a disadvantage. Algebra, though, is another matter. Almost all citizens can and do get through life very well without it, after their schooling is over. Nevertheless it becomes more and more pervasive, seeping down into more and more eighth-grade classrooms and being required by more and more states for graduation from high school. There is unspoken agreement that everyone should be exposed to algebra. We live in an era of universal mathematical education.

This is something new in the world. Mathematics has not always loomed so large in the education of the rising generation. There is no telling how many children in ancient Egypt and Babylon received training in numbers, but there were not many. Of course, in ancient civilizations education was not for everyone, much less mathematical education. Literacy was not universal, and I suspect that many who could read and write could not subtract or multiply numbers. The ancient Greeks, to their glory, originated real mathematics, but they did not do it to fill classrooms with students learning how to prove theorems. Compared to them, the ancient Romans were a mathematical blank. The Arab scholars who started to develop algebra after the fall of Rome were doing it for their own pleasure and not as something intended for the masses. When Brahmagupta was solving Pell's equation a millennium before Pell was born, he did not have students in mind. Of course, you may think, those were the ancients; in modern times we have learned better, and arithmetic at least has always been part of everyone's schooling. Not so. It may come as a surprise to you, as it did to me, that arithmetic was not part of elementary education in the United States in the colonial period. In A History of Mathematics Education in the United States and Canada (National Council of Teachers of Mathematics, 1970) we read “ Until within a few years no studies have been permitted in the day school but spelling, reading, and writing. Arithmetic was taught by a few instructors one or two evenings a week. But in spite of the most determined opposition, arithmetic is now being permitted in the day school”.

Opposition to arithmetic! Determined opposition! How could such a thing be? How could society function without a population competent in arithmetic? Well, it did, and it even thrived. Arithmetic was indeed needed in many occupations, but those who needed it learned it on the job. It was a system that worked with arithmetic then and that can work with algebra today.

Arithmetic did make it into the curriculum, but, then as now, employers were not happy with what the schools were turning out. Patricia Cline Cohen, in her estimable A Calculating People: The Spread of Numeracy in Early America (U. of Chicago Press, 1983; Routledge paperback, 1999) tells us that 608 Notices of the AMS Volume 57, Number 5Prior to this act [1789] arithmetic had not been required in the Boston schools at all. Within a few years a group of Boston businessmen protested to the School committee that the pupils taught by the method of arithmetic instruction then in use were totally unprepared for business. Unfortunately, the educators in this case insisted that they were doing an adequate job and refused to make changes in the program. Both sides were right. It is impossible to prepare everyone for every possible occupation and it is foolish to try. Hence many school leavers will be unprepared for many businesses. But mathematics teachers, then as now, were doing an adequate job. A few years ago I was at a meeting that had on its program a talk on the mathematics used by the Florida Department of Transportation. There is quite a bit. For example, the Florida DoT uses Riemann sums to determine the area of irregular plots of land, though it does not call the sums that. After the talk I asked the speaker what mathematical preparation the DoT expects in its new hires. The answer was, none at all. The DoT has determined that it is best for all concerned to assume that the background of its employees includes nothing beyond elementary arithmetic. What employees need, they can learn on the job. There seems to be abroad in the land the delusion that skill in algebra is necessary in the world of work and in everyday life.

Underwood Dudley is a mathematician, retired from DePauw University. His email address is ddunx46135@ yahoo.com.