What are They Shooting At?
Making sense of the
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
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
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?