>NEW YORK TIMES >April 27, 2000 > >FUZZY ANSWERS / A SPECIAL REPORT > >The New, Flexible Math Meets Parental Rebellion > > >By ANEMONA HARTOCOLLIS > > >Three years ago, one of New York City's most adventurous school districts >set out to tackle a nagging problem: the math phobia that afflicts many >students, and the disparity between the test scores of white >middle-class students and their poorer black and Hispanic counterparts. > >The district, which stretches from the Upper East Side to Chinatown, >embraced a new "constructivist" curriculum without textbooks. This >approach preaches that it is more important for children to construct >their own solutions to mathematical problems than to learn the standard >rules -- from multiplication tables to the value of pi -- handed down >through the centuries. > >Long ranked near the top of the city in mathematics, the district has >held its place, although there is still a disparity in test scores >between the poorest schools and the more affluent ones. But the new >curriculum has enraged many parents who find that their children cannot >multiply easily or understand basic algebra. > >One parent, Anna Huang, said her son, Mack, a fourth grader, "felt a >lack of clarity" when his teacher insisted that he estimate answers, >rather than compute them precisely. Another parent, Anne Cattaneo >Santore, said she was troubled because her son, William, a second grader >at P.S. 124 in Chinatown, spent months counting with coins and solving >equations using "friendly numbers," for instance, converting 71 + 19 >into the easier 70 + 20. > >"Those strategies don't work when you get to larger numbers," Ms. >Santore said, "and they have been doing those strategies all year." > >Ms. Huang and Ms. Santore have joined other parents, mathematicians and >many teachers in a rebellion that has shaken education from New York >City to Plano, Tex., and Lincoln, Mass. As school districts from >affluent enclaves in Greenwich Village to poor minority neighborhoods >like East New York have embraced constructivist math, parents have >formed e-mail networks and turned out in force at school meetings to >protest what they say is "fuzzy math" and the systematic "dumbing down" >of mathematics teaching. > >"Parents are worried," said Elizabeth Carson, an actress, the mother of >a seventh grader and a leader of the protest movement in New York City. >"They're scared that their kids are not going to be competitive. The >math is not in their bones.' > >The new math has at its core a passionate belief shared by tens of >thousands of teachers around the country that they can reach more >children, especially low-achieving minority students, by dropping >standard rules in favor of exercises that allow students to discover the >principles of math on their own. Constructivist programs are being tried >in more than half of New York City's 1,145 schools, Board of Education >officials said. > >Educators who support the new math say that old-fashioned teaching >through memorization and rules produced generations of people who hated >math and never deeply understood it. Indeed, the manifesto of >constructivist mathematicians, the 1989 standards of the National >Council of Teachers of Mathematics, urges teachers not to demand too >much accuracy too early. Math should be "flexible," the standards say, >and "reasonable" answers should be valued over a single right answer. > >The constructivist movement has led to the widespread rejection of >textbooks, in favor of exercises using blocks, beans and other >materials. One popular program, MathLand, suggests that students count a >million grains of birdseed to get a feeling for the size of a million. >Another, Everyday Mathematics, teaches children an ancient Egyptian >method of multiplication. > >It also suggests that fourth graders measure angles with bent straws >instead of protractors. Connected Mathematics, a popular middle-school >program used widely in New York, teaches sixth graders to add fractions >by folding paper strips into segments representing halves or fourths or >thirds, instead of by converting to common denominators. > >Lucy West, the director of mathematics at Manhattan's District 2, where >the new math has been most aggressively adopted, said that old-fashioned >math had been oversold. "There is a misconception that in the good old >days everybody could add and subtract, multiply and divide really easily >and efficiently," she said. > >But professional mathematicians say the activists have set up a false >dichotomy between conceptual understanding and basic skills. Parents >chafing at constructivist math tell stories of their children coming >home confused and dispirited by lessons in which getting the right >answer to problems is devalued in favor of strategies that are often >primitive, cumbersome and indirect. Used by inexperienced teachers who >are weak in math, they say, the curriculum can be murky. > >And tutoring services say that they are seeing an epidemic of children >coming to them for basic math instruction. > >THE MOVEMENT >Good Intentions, Unproven Theories > >How schools got to this point is a saga of good intentions, unproven >theories and a progressive education movement that has has had its most >profound impact in reading and math. In many ways, the math wars echo >the once ferocious disputes about reading between advocates of the >intuitive "whole language" approach, which stresses acquiring skills >through simple reading of books, and the phonics method, which stresses >decoding of letters and words. Until "whole language" became a dirty >word, constructivist math was known as "whole math." One obvious >solution is to mix a bit of both. But while educators have called a >truce in the reading wars, deciding that compromise is best, the math >wars continue to rage. > >The high point for new math advocates came last October, when a panel >set up by the United States Education Department endorsed 10 >constructivist math programs as "exemplary" or "promising." Within a few >weeks, nearly 200 university mathematicians and scholars sent an open >letter to Education Secretary Richard W. Riley warning that the 10 >programs had "serious mathematical shortcomings" and would leave >students ill-prepared for college-level courses. > >R. James Milgram, a mathematics professor at Stanford University, >analyzed three programs and found that they consistently neglected to >teach basic rules of multiplication, division, addition and subtraction. >The programs are typically one or two years behind grade level, he said, >and aimed at what he considered underachieving students. > >On April 12, the National Council of Teachers of Mathematics, the >nation's most influential group of math teachers, made a gesture to the >critics as it revised its 1989 standards for teaching mathematics, the >closest thing this country has to a national curriculum. Though not >abandoning its original constructivist agenda, the council put the >arithmetic back in math, by adding language emphasizing accuracy, >efficiency and basic skills like memorizing the multiplication tables. >The chairwoman of the standards committee declared that the group's new >message was "Get the right answer." > >Still, there is ambivalence in the teaching field. When the national >council of mathematics teachers endorsed more of a balance between >basics and the constructivist approach at the group's annual meeting in >Chicago, the president-elect, Lee V. Stiff, ardently defended >constructivism. "If I only teach it the way I understand, then only >students who understand it the way I do will be successful," he said. > >The evidence to support the educational virtues of new math is >inconclusive at best. Publishers have provided studies in which they >compare the results in pilot schools that adopted the program to other >schools that made no change. > >But those studies have been challenged by critics who say improvements >may be the result of better training of teachers, and the extra >attention given to pilot programs. > >District 2, which has a high percentage of affluent students, has long >ranked near the top of the city school system. Last year, when a new >math test was introduced, scores across the city declined, and District >2 was the only district in the city to remain stable. > >Ms. West, the math coordinator, said that was evidence the program was >working. And other officials noted that the new test was closely aligned >with the District 2 curriculum, and many parents attributed the good >scores to tutoring by professionals and parents. And they noted that the >district had been spending $800,000 a year on training math teachers. > >Even experience in the classroom can be ambiguous. Roberta Schorr, an >education professor at Rutgers, is using a computer simulation of a frog >and a clown walking back and forth across a plane to help teach the >concept of velocity at Central High School in Newark. Ms. Schorr sees >the simulation as an intuitive introduction to calculus that does not >require what she called "formal symbol structure." But during a recent >class, half the students seemed baffled, while Tieyon Hendry and Rahul >Patel, the star students, told a visitor that they had arrived at the >answer to one exercise by using a mathematical formula: y = mx+ b. > >THE OPPOSITION >Unconvinced by Unconventional > >As the new math -- a cousin of the "new math" popular in the 1960's -- >entered the educational mainstream, first in California in 1992 and then >around the country, it sparked waves of opposition. Hostility came first >from conservative parents who opposed any change in education, then from >university math professors who felt it was not rigorous, and finally >from liberal, affluent parents who were worried their children were not >getting enough math to succeed in school and in life. > >In Plano, Tex., parents have sued the school district for refusing to >provide an alternative to Connected Math. In New York, the opposition >first emerged not in a failing school but in one of the city's best, >Public School 234 in TriBeCa. Edgy schoolyard conversations grew into a >parent Math Committee, which gathered members across the district, >sending out surveys and making angry statements at school board >meetings. > >Parents said they were stunned as they talked to their friends and >realized how many had hired tutors. Those who cannot afford tutoring >tell of scouring educational bookstores for workbooks and textbooks to >help them make sense of the new math. > >Ms. Huang said she became alarmed when her son, Mack, a fourth grader at >the Bridges School in Chelsea, came home complaining that he hated math. >The emphasis on estimation, she said, was confusing him. She bought him >workbooks consisting of straightforward calculations and he enjoyed the >sense of mastery. > > > >Constructivist teachers celebrate the unconventional exercises they use >as a way of keeping weaker children engaged, especially those from >groups that have historically lagged in mathematics performance, like >girls and black and Hispanic students. > >But some parents are insulted by them. Ms. Weinberg, a dentist, said she >was appalled when her daughter, Kelly, a sixth grader at East Side >Middle School, came home with assignments to write her math >autobiography and to write about her favorite number. "She was being >graded on grammar and spelling," Ms. Weinberg said. > >Wilfried Schmid, a professor of mathematics at Harvard, became a critic >of constructivist programs after his daughter, Sabina, began using one >of them, TERC Investigations in Number, Data and Space, at her >elementary school in Lincoln, Mass. When she started second grade last >fall, Sabina knew how to carry tens and add two-digit numbers, Mr. >Schmid said. Sabina's teacher, who is well-intentioned but too >inexperienced to deviate from the program, Mr. Schmid said, told the >child that she was not allowed to use this method; she had to >demonstrate her work with blocks or by counting on her fingers. > >"So Sabina is reduced to drawing 39 little men to solve problems like >39-14," her father said. > >He worries that this rudimentary and tedious approach is quashing >Sabina's spirit. "Last year, she would have complained that this is >below her level," Mr. Schmid said, "but she doesn't rebel anymore." > >"I'm a professional mathematician, and I myself very often use >mathematical methods that I understand only imprecisely," he said. "It >is while I use them that I begin to understand. After a while, the use >and the understanding are mutually supporting." > >In their worst nightmares, parents fear that schools are producing a >lost generation of math illiterate children. Bruce Winokur, a math >teacher at Stuyvesant High School, New York City's most selective public >school, says he is seeing more and more students who are gifted in math >but unable to keep up with high school work. They understand concepts, >he said, but have not internalized the rules. > >THE FUTURE >Easing the Rules to Allow the Old > >There are some signs of change. > >Andrew Lachman, a spokesman for District 2 in New York City, said the >district was responding to parent concerns. "We are not purists," he >said. > >California recently adopted new standards with a stronger focus on >computation, and many districts will be putting them into place this >fall. Some teachers, often the most experienced, have instinctively >combined the old and the new. > >The Daniel Boone School, in West Ridge, a tidy working class part of >Chicago brightened by magnolia trees and the babushkas of Russian >grandmothers, has been a laboratory for the development of TIMS Math >Trailblazers, a constructivist program created by the University of >Illinois. Math scores have risen since the program was put into effect. >The principal, Paul Zavitkovsky, credits the program, but does not rule >out increased attention to math, teacher training and collaboration. > >In fifth grade the other day, Mila Kell, a Russian immigrant, taught a >crisp lesson in probability, improvising riffs on the probability that >the sun would rise in the morning and that she would fly to the moon. >The class was enchanted. > >Mrs. Kell said she loved the freedom and creativity of the new math. But >on her desk was a secret weapon: a stack of worksheets -- the antithesis >of constructivist math -- pages of classic problems in long division, >the addition of fractions and reducing the sum of fractions to its >simplest terms. > >------------------------------------------------------------------------ > > > <A HREF="http://www.ctrl.org/">www.ctrl.org</A> DECLARATION & DISCLAIMER ========== CTRL is a discussion & informational exchange list. 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