The New Mathematics

At least 35 of the students who gathered for the special class at Benson Polytechnic High School in Portland, Ore. last week had reason to feel a little ill at ease. They were all local high-school teachers, and there they were with 45 of the brightest boys and girls in town, taking a course as if they were still in their teens. "Let us not let our blood pressure go up." said Instructor William Matson soothingly. "Let us not let our hearts beat too fast." Then he began his lecture on the complexities of modern mathematics.

100 Years Old. With the help of Reed College, Portland has been holding such classes for its gifted pupils since 1952. The program is so successful that last fall some teachers finally asked Math Supervisor Lesta Hoel: "Why can't we have a class in modern math for teachers too?" The teachers decided that they and some youngsters should learn together under five Reed-trained instructors, and Supervisor Hoel even joined the class herself. Research in mathematics, she explains, has advanced so rapidly that today's teachers are now way out of date. "We're using in geometry and trigonometry the texts of 100 years ago."

For many of the teachers, the course is anything but a snap. While the pupils grasp the latest teaching with ease, the teachers must first discard much of what they were taught, master such new (to them) terms as Cartesian products, null sets and strict inequalities. "In trigonometry, for instance," says Supervisor Hoel, "the emphasis used to be on surveying and navigation. Now the emphasis is on vectors, the theory of sets, probability, statistics and symbolic logic."

Casehardened with Tradition. Teacher Genevieve Simpson (B.A.1922) was surprised to find that the algebra taught in the ordinary classroom is "not a part of modern algebra at all." Teacher Edgar Arnold (B.E. 1930) found that "this is all new to me. I have to unlearn old symbols and learn new ones. We are casehardened with tradition." "In modern math," adds Teacher Helene Lannon, who got her master's degree as late as 1948, "we have had to learn a new vocabulary. In the traditional mathematics we would say 'cancel out numbers.' Now you say 'divide.' Traditional algebra was taught as real numbers, and it was taught by rote. In the set theory, you can prove it logically."

After only three sessions, some of the teachers have already begun to expose their own pupils to the new things they have learned. But the major lesson of the Portland project is that if more cities do not do something similar soon, U.S. teachers will find themselves dismally unprepared for a curriculum in which the barriers between algebra, geometry and analysis are crumbling, solid geometry and trigonometry may disappear as separate subjects, and algebra will deal with such topics as groups, rings and fields. As one Portland student put it: "Even the concept of the line has changed. In geometry you may have learned that a line is the shortest distance between two points. In the future you will learn that a line is a set of points."

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