What Is Mathematics For
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Abstract
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 beyond arithmetic. There is no question about what 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