The following letters were in response to a pair of Op-Ed articles by Lynne Cheney and Thomas Romberg in the New York Times, August 11, 1997, under the heading: Dialogue: Creative Math, or Just Fuzzy Math?. Lynne Cheney's article carried the title, Once Again, Basic Skills Fall Prey to a Fad.
The New York Times
Sunday August 17, 1997
When Fads Fail
As a parent of a second grader who has completed the first year of a math program associated with the University of Chicago, I found Lynne Cheney's cautionary comments on the latest fad in teaching math striking close to home. My frustrated child quickly became a competent and interested student of math upon a few weeks of "traditional" remedial instruction at the same school. - Lewis Goverman, Brooklyn, Aug 11, 1997
Parents Pick Up Pieces
Lynne Cheney put my own frustrating experience as a parent in perspective. For four years my son, a fourth grader, has been a student at a Chicago public school that uses an experimental "concept math" program developed with the University of Chicago. In the second year I started comparing what he learned with the problems a second grader in Bulgaria solves. I did not want my son, upon returning to our native Bulgaria, to be behind.
By the end of second grade, Bulgarian students are at ease with multiplication and division. That is not the case in my son's school. His program doesn't use textbooks, and homework is given on loose sheets of paper. I was told textbooks and drills "develop inhibitions." It was hinted that I was conservative because I did not accept the latest product of progress by University of Chicago experts.
I now teach my son math in addition to what he learns in school. But that isn't a solution for the millions of working parents who want their children to do well beyond elementary school. Besides, this responsibility should not be shifted to parents. - Mila M Ganeva, Chicago, Aug 12, 1997
Your citations from the MathLand curriculum guide left me wondering if members of the National Council of Teachers of Mathematics have ever met an actual child who gets together "with peers in cooperative learning groups to 'construct' strategies for solving math problems"?
I recommend that we try to learn from successful systems, whether in Singapore of the Czech Republic, but not from the Never Never Land of MathLand. - George Koese, Princeton, NJ, Aug 12, 1997
Don't Deny Math's Rigor
"The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell." Sixteen hundred years later after St Augustine, we're still struggling to teach and learn this lovely subject, with questionable success. Lynne Cheney and Thomas Romberg's Aug 11 Op-Ed articles begin at the same point" We're ailing.
Both sides of the "whole math" debate recognize the need to equip our children with the mental acumen to investigate, pursue, discover and create. It is argued that if we begin with creativity, our children will learn to create. This misses the point.
We have turned from the rigor, precision, tools and language of mathematics, in the hope that our children will understand more, engage more and create more. But we've denied them the very things they need. Math's rigor and its tools will not stifle our children; it will empower them. - Suzanne Sutton Rockville, MD Aug 12, 1992. The writer teaches math in the Montgomery County, MD, schools.
The Building Blocks
Thomas Romberg defines mathematics as a "human activity involving the ability to represent quantitative and spatial relationships in a broad range of situations." The Oxford English Dictionary defines it almost the same way but adds: "It includes as its main divisions geometry, arithmetic and algebra." Mr. Romberg is really saying we should not teach arithmetic in the early grades but all aspects of mathematics throughout the curriculum. But he fails to present evidence that learning the "signs and symbols of mathematics" is superior to learning arithmetic as a foundation for the other divisions of mathematics. Unfortunately, unlike in my field of science, new hypotheses can't be tested in animals before being applied to humans. - Bernard F Erlanger, Whitestone Queens, Aug 11, 1997. The writer is professor emeritus of microbiology, Columbia University
A Question of Choice
At first I thought: How odd that Lynne Cheney and Thomas Romberg would debate an esoteric question of mathematical pedagogy on your Op-Ed page, a venue usually reserved for politics an public policy. But then I thought: "Yes, quite right." Right, because the ills that afflict public education are not technical but political. The technical differences between Ms Cheney and Mr Romberg are of far less interest to me the father of a 4-year-old, than the fact they are making the decisions for my son, not I. Once the like-minded people of the National Education Association, the American Federation of Teachers and the teachers' colleges decide on a particulare method it is impossible to escape it unless one can afford private school or home school.
While the problem may look to them like mathematical pedagogy, the answer looks to me like public school choice. I can be persuaded on whether choice should be implemented by vouchers, charter schools or another method, but choice is the answer. - Edmond David, Brooklyn, Aug 12, 1997
Research Backs Reform
[Note: Fran Curcio helped develop the fuzzy math program, CMP used in District 2. She was also paid to evaluate use of the NSF "teacher enhancement local systemic change" grant that funded TERC and CMP in District 2 schools. - NYC HOLD]
Based on my familiarity with mathematics education research and my own research, I strongly disagree with Lynne Cheney's' comments about the lack of a research base for instructional reforms in mathematics and the lack of achievement by children in classrooms that support the standards of the National Council of Teachers of Mathematics.
Children fortunate enough to have math teachers who allow them to build on their own understanding and experiences have outperformed children who are products of rote drill on mathematical problem-solving takes and on traditional standardized tests.
Thomas Romberg's call for "new teaching for a changing society" is a challenge to improve our teacher preparation, to support professional development and to strengthen communication among school, home, business and government. This takes planning, time, money and cooperation. - Frances Curcio, New York, Aug 14, 1997. The writer is an associate professor of mathematics education at NYU.
Lynne Cheney is right that there are too many fads in mathematics education and that they vacillate from one extreme to the other. But she is wrong to cite silly extremes in one direction to make her point, while not mentioning the overriding reason for modifying the curriculum. Recent technological advances have affected what we teach and how we teach it. We don't teach logarithms to simplify complicated arithmetic computations; the calculator does it faster and more accurately. The computer allows us to demonstrate geometric relationships dynamically and give students a deeper understanding of these properties. The hand-held calculator frees us from tedious computational work so we can focus on problem solving.
The most important modification needed in mathematics teaching is to focus on problem solving, not only as a means to an end but also as an end in itself. - Alfred S Posamentier, New York, Aug 11, 1997 The writer is a professor of mathematics education at City College
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