Among the Educationaloids/Bring Back the Old Math
Nelson, Caleb
AMONG THE EDUCATIONALOIDS BRING BACK THE OLD MATH I t is no longer news that American 1 children know little about mathematics. One 1986 national study, for instance, found that more than...
...As far as math is concerned, Americans tend to neglect this fact...
...nfortunately, it also represents a curious but familiar mixture of trendy relativism and trendy absolutism...
...Except when political orthodoxies dictate otherwise, New Age education deliberately attacks the idea of the black-and-white answer, and Standards is no exception: even as it condemns "questions that require only yes, no, or a number as responses," it urges teachers to present the idea of ratios by asking, "If 245 of a company's 398 employees are women, how many of its 26 executives would you expect to be women...
...If I don't agree The American Senti• nel is Washington's best watchdog of the radical left, I can get a full refund—no ^ ^ questions asked...
...In fact, the NCTM baldly asserts that in the calculator age, students "should not be expected to become proficient with paper-and-pencil computations with [numbers of] several digits...
...American youngsters do relatively well on tests of "set theory," an abstract topic that New Math programs introduced to help students see the connections between traditional mathematical subjects...
...Standards rejects the "demeaning" institution of failure: "No student should be denied access to the study of one topic because he or she has yet to master another...
...Like the rest of today's education establishment, the NCTM can think only in terms of appeasement...
...But students do much worse on tests of algebra, geometry, and calculus—the subjects that set theory was supposed to make more accessible...
...Each of the two players has a calculator...
...Every two weeks we break stories the Establishment media ignore or bury, like...
...Thus they routinely speak of mathematical "geniuses," a hyperbole that they never apply to students who excel in other subjects...
...NCTM students are not to learn calculus, but "it is important that they develop an awareness of, and appreciation for, the historical origins and the cultural contributions of the calculus...
...Along the way, their studies might be complemented by serious courses in computer programming, instead of the NCTM's fluffy computer "applications...
...Mathematics instruction, the group insists, must be "consistently positive...
...Instead, it recommends presenting each mathematical topic at a wide range of levels,to accommodate children who have failed to grasp earlier material...
...Charge my...
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...Inevitably, in each of the NCTM's examples only the students at the top level might actually learn any math...
...Lest students be bored, games and experiments replace lectures...
...They might collect information about the pulse rates of their classmates, analyzing how the rates go up during exercise and down during relaxation...
...A game played to ten points takes ten minutes or less...
...Activities should be designed to "help students clarify feelings about mathematics," and there should be "discussions about any negative feelings and [about] ways to deal with unpleasant experiences...
...In the Second International Mathematics Study, for example, the average score of the top five percent of American calculus students was below that of all Japanese calculus students...
...Indeed, to judge from appearances, the proposal's principal aim is to extend this selective assault on certainty from the humanities to mathematics...
...Similarly, Standards calls for students to "formulate problems themselves," as in this sample exam question: "Four by Caleb Nelson of every five dentists interviewed recommended Yukky Gum...
...Students must master arithmetic sooner in order to get to algebra and geometry sooner...
...As these test results suggest, most modern American math curricula are incoherent blends of New Math and traditional math...
...The media, too, have been receptive...
...Visa C:3 Mastercard ^ American Express 1 Card # Exp...
...That is why your publication is so valuable...
...lest students be discouraged by failure, certainty disappears...
...As in the New Math, which NCTM publications helped popularize in the 1960s, Standards students are to "construct their own meanings" for mathematics...
...The NCTM consequently touts problems that "have no [single] right answer," such as the following exercise for middle school students: "A national magazine surveyed teenagers to determine the number of hours of TV they watched every day...
...They use the calculators to find the discounted price, and the player who comes closest to the actual discounted price earns one point...
...High school students are not to study how factoring techniques can solve polynomial equations (an impor'Students can approach this "problem" in a variety of ways: "[They] can discuss their predictions in small groups, write summaries of their group work or of their own ideas, share their predictions with the class, discuss their reasoning, and compare their predictions with the magazine's report...
...Some of the foremost mathematicians and educators in America have issued a report (egregiously titled "Everybody Counts") urging parents to "demand that schools meet the new NCTM Standards...
...today most American students do not begin the serious study of algebra until ninth grade...
...Of all the traditional staples of mathematics instruction, computation drills have the highest concentration of clear-cut answers, so the NCTM reserves special scorn for them...
...By seventh grade, American students should have moved from arithmetic to algebra, as have their counterparts across the globe...
...At the same time that Standards introduces the uncertainties of sociology and psychology to math class, it strives to transform math itself into an active experimental science, filled with uncertainties of its own...
...They regard math as an elite subject, in which success is determined more by aptitude than by effort...
...Thus the programs emphasized unusual mathematical systems, so that children could make discoveries for themselves about the structure of more familiar systems...
...One 1986 national study, for instance, found that more than one-fourth of our 13-year-olds are unable to perform consistently such calculations as "Subtract: 604 - 207" and "Find the product: 21 x 3." Only six percent of 17-year-old students, and hardly any 13-year-olds, can answer such questions as: The number of tomato plants (t) is twice the number of pepper plants (p...
...Solve the problem...
...the others, who lack the prerequisites, spend much of their time plugging numbers into computer programs that they have not written and do not understand...
...They might use computers or dice to simulate various experiments in probability...
...Standards cares deeply for students' "sense of mathematical competency," and accordingly urges that examinations give "decreased attention" to "assessing what students do not know," as opposed to "assessing what students know and how they think about mathematics...
...By all accounts, Standards represents the wave of the future in education reform...
...students had to justify even simple arithmetical identities by reference to forbiddingly named Laws, such as those of association, commutativity, and distribution...
...At every grade, math students should be expected to succeed, and therefore be required to work hard at their homework...
...But as children learned that 2 + 2 = 11 in base three, that a line is best thought of as the illustration of a particular set of points, and that a circle is topologically identical to a triangle, they made only one discovery: that they were extremely confused...
...Math students, the NCTM suggests, might study traffic congestion near their school, assembling statistics from which to draw subjective conclusions...
...In keeping with its overriding concern for students' self-esteem, the NCTM would dramatically reduce the importance of grades...
...And any time you don't THE AMERICAN SPECTATOR NOVEMBER 1989 think The American Sentinel is worth every penny, I'll refund your money—no questions asked...
...t = 2p 0 2t = p lilt= 2 +p 0 2 +t=p 41Fis between which of the following pairs of numbers...
...of late, it simply has not been tried...
...How many hours do you think the magazine reported...
...Despite a limited return to basics in the early 1970s, the continuing influence of the New Math is evident in test scores...
...Though this system gives all but the best students no more than the illusion of mathematical knowledge, the NCTM asserts that "further efforts toward mastering computational skills" may be "counterproductive" because of "the effect of failure on students' attitudes...
...One player turns over a card to reveal a price and a discount...
...Sign up for a full year subscription at the special introductory rate of only $49—that's 45% off our regular subscription price...
...49 check enclosed...
...Youngsters are not to be drilled on computation but "might draw pictures and then tell or write stories about the equation . . . 18 + 6 = 0...
...the Washington Post, for instance, hailed Standards as a "bold and comprehensive program" that will replace the "outmoded" current curricula with "patterns of active, creative learning...
...0 4 and 5 0 8 and 9 ^ 16 and 18 ^ 288 and 290 As a result, American math students at all levels invariably rank near the bottom in international comparisons...
...36 THE AMERICAN SPECTATOR NOVEMBER 1989 tant topic in algebra...
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...Such exercises, not incidentally, involve very few definite answers...
...the time freed by this and similar reforms will let them "keep journals describing their mathematical experiences, including reflections on their problem-solving thought processes...
...Date Signature I I i m milowww — No mm om im^ASI2 m =1 37 Editor & Publisher P.S...
...In the real world, perseverance and accomplishment—not lowered standards—are what is "personally empowering...
...It urges that drills be replaced with "fun" exercises: A set of cards is prepared, each one bearing the price of an object and a particular discount in percentages (e.g., $10.95, 15...
...they must master precalculus sooner in order to get to calculus...
...Reporting like that made the Washington Post call me "the right wing's answer to Abbie Hoffman...
...Subscribe now and I'll send you a FREE copy of an 83-page expose of the radical left in Congress—"What's Left of Bipartisan Foreign Policy...
...in addition, they should learn "about other countries and cultures" in math class...
...Congressman Phil Crane The best intelligence network in Washington for anybody who wants to keep track of the radical left—that's what The American Sentinel has been for 18 years...
...Old-style math education has not failed our children...
...Though American schoolchildren already lead the world in thinking themselves good at math, the NCTM's paramount goal is to boost that inflated self-confidence even more: "What matters is that students experience mathematics in situations in which they come to view it as personally empowering...
...encouraged children to use their own creativity rather than rely on teachers...
...It has assembled solidly behind the recent Curriculum and Evaluation Standards for School Mathematics, published by the National Council of Teachers of Mathematics (NCTM...
...Most observers agree that the spread of the "New Math" in the 1960s is at least partly responsible for this state of affairs...
...But in order to downplay certainty, Standards carefully blurs this distinction by stressing other disciplines at least as much as math...
...School mathematics has traditionally been distinguished from the humanities by its exactitude...
...Since we began as "The Pink Sheet on the Left" back in 1971, the best informed Conservatives in America have relied on us as a watchdog of the left wing...
...In traditional curricula, teachers showed their pupils how to solve a particular problem, and then assigned similar problems as homework...
...The back-to-basics movement of the 1970s, though it halted the spread of the New Math, never inspired the necessary changes in curricula and attitudes...
...In an effort to make grade-schoolers think like research mathematicians, the new programs also Caleb Nelson (B.A., Mathematics Harvard) is assistant managing editor of the Public Interest...
...the teacher must become a "facilitator of learning" rather than a "dispenser of knowledge," and ought to "suspend judgment" so that students learn to "guess courageously...
...Discover how Liberals in Congress have made their own foreign policy—and how it conflicts with America's...
...According to the NCTM, "Measurement situations should continually be part of the program," to such an extent that "parents who expect students to do mathematics homework on paper at a desk rather than by gathering real data to solve a problem will be surprised...
...Write a question to go with this statement to make a problem...
...Then both players estimate the final, discounted price...
...The education establishment is therefore lumbering toward further reform...
...American MIAs—still alive in Vietnam • How one defense contractor "lost" over 1,000 classified documents on the Stealth bomber • House Armed Services Committee invites Soviet Marshal Sergei Akhromeyev to testify against the Bush Defense Budget...
...At the same time, curricula must pick up speed...
...The new programs, which professional mathematicians helped educators devise, linked diverse mathematical topics with a new stress on abstract proof...
...in this way students progressed, with little overlap, from arithmetic to algebra to geometry to trigonometry...
...they must master algebra and geometry sooner in order to get to precalculus sooner...
...ne of the NCTM's biggest fears V is for the psyches of childrenwhose math homework might be labeled "wrong...
...This elitism should be overcome...
...Plug into the network today...
...As Senator Jesse Helms said, "the average American would be appalled if he were suddenly to discover what is being done to his country and its principles by extreme left-wing forces...
...Which equation best describes the sentence above...
...The NCTM's book has also been endorsed by the nation's two largest teachers' unions and a number of other distinguished groups, some of which are expected to release similar books of their own...
...Unfortunately, this prescription marks no less severe a departure from present practice than the NCTM's...
...one of the most authoritative and informative newsletters on the activities of our adversaries on the let't...
...But though the NCTM can banish drudgery and failure from school, it cannot banish them from life...
Vol. 22 • November 1989 • No. 11
