Teaching: Inside Numbers

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Each year more U.S. parents find that their children's mathematics home work is vastly different from what math was when they went to school. This is the "new math," and the change goes back to 1952, when Mathematician Max Beberman and others became alarmed that math teaching in U.S. schools had not changed essentially in 150 years. In pioneering new methods at the University of Illinois, Beberman sparked a movement that has now influenced about 10% of U.S. elementary schools and 60% of high schools. This year Texas assigned 30,000 teachers to learn new math. This month California decided to spend almost $10 million for new math texts.

What is really new about new math is the teaching; it is basically old math taught in a far better new way. The purpose is to replace numb learning of rote computation with a confident understanding of the structure and relation of numbers—the why of the drills. Rules and formulas are still vital tools, but new math aims to go back to the sources of the rules to show why they are valid, rather than blindly prescribing them.

The Wonder of Zero. Math is the study of patterns; numerals symbolize real things—the size of collections, the length of lines, the position of points. New math thus begins on the concrete level and only later moves to the abstract. Math is also a unified system; new math thus shows the interrelation of all branches, such as algebra and geometry, rather than teaching them as separate topics. The stress is on "discovery"—the artful question that sparks a child's desire to see patterns and find answers. The idea is to get children inside the structure of numbers by means of a "spiral curriculum"—constant re-translation of concepts at higher orders of sophistication.

In laying out the floor plan—arithmetic—new math begins not with the names of numbers but with real objects, such as beads, stones, sticks. By manipulating objects in collections (or "sets") the child learns crucial ideas. He may be asked to remove pairs of objects from two collections, for example. When both collections run out at the same time, he begins to grasp the idea of equality. When one runs out first, he learns about inequalities.

Equal collections of different things bring up the idea of number as a common property of the sets; then the child can move on to grasp the symbolism of numbers expressed as numerals. He sees that for convenience the first ten symbols may be recombined for numbers greater than nine. He may also learn that each digit (say in 326) has a "place value" ten times that of its neighbor to the right (three hundreds, two tens, six ones). He discovers the wonder of that great ancient invention, zero, the "place holder" that allows infinite expansions (606 would be simply 66 without it).