> >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.

--
Terry W. Colvin, Sierra Vista, Arizona (USA)
< fortean1@... >
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