What are They Shooting At?

Making sense of the math wars

By Gary S. Stager

Published in the October 2001 issue of Curriculum Administrator

If we are indeed in the midst of a math war, I'd like to know when our terribly math-phobic nation developed such a passionate interest in mathematics education? Why are the casualties predominantly women and children? Who gave special interest groups the right to fly into urban schools and attack excellent teachers teaching mathematics in a manner they believe benefits their students. Why are we so obsessed with turning kids into poor imitations of $5 calculators?

The best I can tell, this battle is between Concerned Citizens for the Preservation of Long Division and an unidentified band of progressive education bogeymen. While I share the frustration of customers charged $74 for Cheezwhiz and a Slim Jim by a zombie-like supermarket cashier, I don't think it's fair to blame the current state of numeracy on methods designed to engage children in the understanding of mathematics. Marilyn Burns is right when she points out that the problems we encounter in everyday life require mental math abilities yet the classroom remedy seems to be impose lots of similar problems to be solved with pencil and paper.

Folks from organizations like Mathematically Correct are terribly agitated by the suggestion that we should teach children "fuzzy" concepts like estimation when in fact a cashier capable of estimating the sum of the two items could have averted the Cheezwhiz incident. The great Satan to the Taliban of math education is the notion that a problem might not have one solution.

Nobel Physicist, Arno Penzias once wrote, "An Inexact Number is Almost Always Good Enough." Apparently, that's only untrue in school. No wonder there are so few Nobel Laureates in fifth grade!

Constructivism is a favorite target of the math fundamentalists. Constructivism is simply the belief that knowledge is not transmitted, but constructed by the individual based on context, motivation, negotiation, experience and interaction with others in a community of practice. What is controversial about kids constructing meaning through varied, rich and collaborative activities? Sure there are classrooms full of kids mindlessly pushing manipulatives around a table, but that does not indict constructivism. It merely suggests that math teachers need help understanding how children learn mathematics. The idea could be good even if the implementation still needs improvement.

If teachers have not learned to teach in a constructivist style, how can we blame constructivism for wrecking our schools? Most teachers never received the memo telling them to embrace constructivism, let alone changed their practice. In other words, math education has remained relatively untouched for the better part of a century.

A few years ago I met a group of impressive Bulgarian mathematics educators. Bulgaria had just been freed from the shackles of communism and its educational leadership viewed high-quality, child-centered, problem-based, dare I say constructivist mathematics education as a vehicle for restoring democracy to their nation. During the totalitarian regime of the communists the people were told that every problem had precisely one solution and that the government had that solution. Wise Bulgarian educators realized that educating a generation of children to think like mathematicians would help reverse their reliance on political demagogues.

Dr. Constance Kamii proves in her exhaustive research that children taught to memorize the trick (algorithm) for solving a particular kind of problem will be less proficient in that skill and have much less understanding of the underlying concept. Dr. James Stigler of UCLA has carefully analyzed thousands of hours of video taken in TIMMs classrooms around the world and discusses how America's obsession with repetitive decontextualized problems solved on pieces of paper puts us at a disadvantage when compared with other nations.

I recently heard someone express concern that Marilyn Burns might be considered a kooky constructivist because she encourages kids to reinforce their mathematical understanding through the act of writing and dialogue. What objection could there possibly be to kids reinforcing their knowledge through the development of written and oral communication skills? Why do the Chicken Littles feel that allowing children to experience the joy, wonder and power of mathematics through meaningful activities is at odds with their goals? If rigor and results is what they desire, then they should respect a variety of methodologies. Otherwise they are just a pack of censors.

The 1990 National Council of Teachers of Mathematics Standards said that 50% of mathematics has been invented since World War II. Try finding any of that reflected in math textbooks! There is perhaps no discipline with a larger gap between the actual discipline and the teaching of that discipline than school math and mathematics. New forms of mathematics such as fractals, chaos, cellular automata and number theory are more playful than factoring quadratic equations. Surely the social science's dependence on number and the availability of computing technology opens the door for some outdated content and methodology to be discarded.

Talk is cheap. There are more kids taking more advanced (titled) school math classes at a younger age than at any time in our history, yet we have little evidence that anyone is becoming mathematically proficient. Hasn't insanity been defined as doing the same thing in the same way over and over again but expecting a different result? Would you really wish the kind of math education you experienced on your worst enemy, let alone your child?