theorv: “The federal government didrnnot ercate the states; the states ereatedrnthe federal government.” But, whilernpretending to be a deeentralist, Reaganrnmav have contributed more to the massiverneoncentration of power in Washingtonrnthan any other President with hisrnmultitrillion-dollar peacetime militaryrnbuild- up.rnWhen there is increasing agreementrnamong liberals and conservatives alikernthat the federal government has becomerntoo big, too powerful, too intrusive, toornbureaucratic, and too unresponsive tornthe needs of local communities everywhere,rndoes it make sense to continue indoctrinatingrnour youth with the misleadingrnview that the United States isrnindivisible? It is not; it never has been;rnand we cannot think of any good reasonrnwli’ it ever should be.rnDonald Livingston is a professor of philosophyrnat Emory University and ThomasrnH. Naylor is Professor Emeritus of Economicsrnat Duke University.rnEDUCATIONrnDumb and Numberrnby Marian Kester CoombsrnGirls mature physically and sociallyrnearlier than boys, God’s way of betteringrnthe survival odds for female children.rnThis accelerated maturation coupledrnwith the intrinsically femininernculture of public education, where thernideal student is a little woman, accountsrnfor the scholastic dominance of girls inrnthe earlv grades.rnBut as puberty strikes the old orderrnabruptly changes. Boys forge aheadrnphysically and intellectually, while girlsrnsometimes feel as though their veryrnseh’cs are dissolving. Many crash into arnmiserable pit of self-doubt, a slavish boycraziness,rna semihysteria not exactly conducivernto academic achievement. Also,rnat least until the recent past, the middlernand high school curriculum begins to invoKcrnsome serious math and science.rnHaving stoically endured years of a demasculinizingrnsystem, boys start to comerninto their own at last.rnBut not if Big Sister can help it. Thatrnpubescent female “crash” has become arncall to arms for feminists and their agentsrnthroughout the educational bureaucracy.rnSuch books as Mary Pipher’s RevivingrnOphelia, Colette Dowling’s The CinderellarnComplex, and Karen Blakcr’s Bornrnto Please, and such powerful policymakersrnas Donna Shalala and Ruth BaderrnGinsburg argue that this slough of femalerndespond is a crisis calling for fullscalernrevision of all our institutions, assumptions,rnvalues, customs, norms, andrnmethods, not least of which are ourrnmethods of teaching mathematics,rnwhich feminists correctly perceive as arnfortress of male excellence. Wheneverrnyou hear loud demands for “inclusion”rnin “unfairly exclusive” fields, you knowrnyou arc in the presence of those whornhave been utterly inessential to the establishmentrnor painstaking constructionrnof those fields.rnBut deconstruction of them—nowrnthat’s another matter! Having tried forrnyears with little success to boost girls’rnachievement and interest in math, therneducrats have finally concluded that thernbest way to close the gap is to cripplernboys, by making girls’ “learning style”rnmandatory for all. Mathematics, sornchivalrously called the queen of the sciences,rnis being neutered into “math appreciation.”rnA major explicit goal of the NationalrnCouncil of Teachers of Mathematicsrn(NCTM) is elimination of the “genderrnand non-Asian minority gaps” thatrnwiden as the math curriculum advances.rnRecent assessments, such as a 1996 studyrnof fourth-, eighth-, and twelfth-gradersrnin California, show that while overallrnperformance is at a standstill or slidingrnbackward, boys and girls have begun torndo equally badly in math. The N C T M ‘ Srn258-page “Curriculum and EvaluationrnStandards for School Mathematics,”rnwhich has been undergoing implementationrnsince its publication in 1989,rnmakes the tactics of this crippling strategyrnclear.rnVerbalization and visualization of problemrnsolving. Real mathematical thinkingrnmay be preverbal or postverbal or subverbalrnor supraverbal, but in any case it isrndefinitely not “word processing.” Teachersrnnow require pupils to write out inrnwords how they get their answers. Thernparents’ group Honest Open Logical Debatern(HOLD) reports that “teachers inrnmiddle and high school are actively discouragingrnthe use of mathematical symbolismrnand penalizing students whornwrite correct but short mathematical argumentsrnusing such notation.” This isrnequivalent to penalizing those with anyrngenuine mathematical gift, while rewardingrnthose without, especially giris,rnwho studies have shown process mathrnbetter verbally than abstractly, i.e., directly.rnSimilarly, using pictures insteadrnof numbers also sidesteps the basic abstractionrnof mathematics.rnA parent named Charles L.rnBeavers (on the Internet at http://rnwww.intres.eom/math/) recently confrontedrnan educrat named Ruth Parkerrnwho came before her school district withrna “New New Math” trick called thern”Turkey Problem.” Briefly, the problemrncould be, and in the past would havernbeen, solved by establishing that a ratiornbetween the known amount and fractionrnequals the ratio between the unknownrnamount (x) and fraction and then solvingrnfor X. This method. Beavers pointedrnout, always works, no matter what thernamounts and fractions involved. Parker’srnsolution, which diagrammed the problemrnas nine little circles which the studentrnthen divides up physically into arnjumble of half-circles and quarter-circlesrnultimately adding up to x, “works, graphically,rnfor one carefully chosen problem”rnonly. Parker refused to discuss Beavers’rnobservation, suggesting he get inputrnfrom schoolchildren if he were “curious.”rn”The problem with the ratio method,rnand standard methods in general, is notrnthat they don’t work,” commentsrnBeavers. “Indeed, they have immensernmathematical power. The problem isrnthat too few people, including many elementaryrnteachers who explain them tornour children, understand the simplernmathematical manipulations behind thernmethods.” He is too kind. If fools havernbeen sent to teach math to our children,rnthey have been sent knowingly and withrnmalice.rnTraditionalist Marianne M. Jenningsrnlaments in her critique of the new algebrarncurriculum [Wall Street journal, Decemberrn17, 1996) that current textbooksrn”have all but eliminated numbers…. Byrntaking the math out of math, educatorsrnhave stripped the discipline of its beauty.”rnWhile it may be true that most of usrn”innumerate” masses will never revel inrnthe sheer joy of number theory or bask inrnthe reflected glory of Format’s elusive FinalrnTheorem, that beauty is the heart ofrnthe mathematical enterprise. Never tornglimpse it is to live in a kind of twilight;rnto be taught not to look for it is a crimernOCTOBER 1997/47rnrnrn