Third R

Mathematics, the schoolboy's horror, is perking up again after a long sabbatical in the educational doghouse. During the '30s the proportion of high-school pupils taking math dropped a third in six years, and many an educator dismissed algebra, to the vast relief of pupils, as a useless subject. But last week there were signs aplenty that U.S. schools were returning to the view that there is much to be said for the third R.

> Private-school headmasters learned that too many boys knew too little math to qualify as officer material for the Army and Navy, decided to teach them more of it.

> New York City published a revolutionary new course of study for its huge public-school system, dedicated to the proposition that mathematics, as taught in school, should have more to do with the price of eggs. So doing, New York followed the example of public schools in Los Angeles, St. Louis, Detroit, Providence, Rochester, many another city.

>Many colleges are going in for survey courses, which explain and link together quickly all the branches of math.

> Even in Progressive schools teachers have found that math cannot be properly taught as an incident in storekeeping, needs to be studied in its own right.

Mathematicians have long been haunted by a paradox: although most U.S. citizens profess to dread the study of mathematics, they are suckers for mathematical puzzles, made a best-seller of Lancelot Hogben's Mathematics for the Million. The mathematicians' conclusion: the trouble is not with mathematics but with the way it is taught. Most math teachers emphasize computation to the point of drudgery. A prime example (from an old U.S. arithmetic textbook -- Greenleaf 's) : "Required the contents of the earth, supposing its circumference to be 25,000 miles. Ans. 263,858,149,120.06886875 cubic miles."

Such exercises are worse than useless, many modern teachers believe, because 1) in real life most computations involve numbers under 100, 2) pupils can spend their time more profitably checking simpler computations, learning how to trace and correct their errors, 3) they need to learn the principle of "approximation": i.e., that perfect accuracy in any measurement is an unattainable ideal. Heaviest charge modern teachers lay against traditional math teaching is that its artificial exercises fail to teach pupils how to solve practical problems.

New York City's new math course, ten years a-making, is for junior high school pupils, will eventually be extended to higher grades. Some of its innovations:

> Study of arithmetic, algebra and geometry is combined, relations between them explained.

> Pupils get less computation, more problem-solving.

> Lessons are based on such practical problems as meter reading, map reading, timetable reading, floorplan drawing, computing the cost of a trip, profit & loss, interest, taxes, budgets, insurance.

> Decimal fractions get more attention than common ones.

> Pupils are taught the functions of banks, the dangers of reckless speculation.

> All this requires sweeping revision of the famed old standard textbooks (e.g., Robinson's Practical Arithmetic, Wentworth's New School Algebra, the Schultze & Sevenoak's Plane and Solid Geometry).

Despite these changes, the principles of math teaching remain the same: virtually all modern teaching is still based on Euclidean mathematics (founded 300 B.C.). But a few scholars today are experimenting with a system of teaching influenced by Descartes: algebraic treatment of geometry. This method stresses algebraic proofs of familiar geometric problems such as the Pythagorean theorem--the square of the hypotenuse of a right triangle equals the sum of the squares of its legs. One advantage claimed for this method of teaching: it trains pupils in the analytical method of reasoning, which is the one used in science. New York City's new math course makes a start toward this system by combining algebra and geometry.

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