Math Wars: Traditional Vs. 'Constructivist'
Q. I've
heard a lot about "fuzzy math," but am not sure if that's what we have in our
district. Why are some people up in arms about math education? What's their
beef?
It comes down to a fight between
those who believe that traditional math instruction methods are best, vs. those
who are for more "progressive" methods.
In two states, California and Massachusetts,
this battle has become the most heated, with websites set up, petitions
presented to top policymakers, testimony made before legislators, and so forth.
Employers and mathematicians in high-tech industries and universities have
largely aligned with parents on the side of traditional math. Meanwhile,
educators continue to favor the "progressive" or "constructivist" style that
has been in vogue in teachers' colleges and public K-12 schools for a couple of
decades.
In most public schools right now,
the "progressive" methods are being used because most states adopted the
"progressive" standards promulgated by the National Council of Teachers of
Mathematics in the 1990s. However, even that group now admits that some or most
of the concepts in their philosophy have been counter-productive. So gradually,
state departments of education and local districts are switching back to the classic
methods of delivering the basics in math education. But it's a slow transition.
"Progressive" math methods have been
pejoratively called "fuzzy math." Those who approve of the methods usually
label them as "constructivist." This is because each child is given a chance to
"construct" his or her own math understanding and techniques in a
child-directed path, rather than a teacher-led one. Under constructivist math,
there's a minimum of book learning and relatively few pages of problems to
solve with only a pencil as a tool. Estimates are acceptable; it's the process
of finding an answer that's important, not the answer itself. A constructivist
classroom will feature children even in early grade school using calculators to
find answers instead of working problems out on paper or in their heads. There
also will be groups of children working on problems together, instead of independent
thinking and problem-solving. There will be hands-on projects such as role
plays, art and writing assignments, rather than the familiar pages and pages of
problems that are either right or wrong.
A traditional classroom features
teacher-led instruction, with prescribed methods and skills that have been
decided by adults to be important for math students to master. There will be
memorization of math facts, lots of drill and practice, and direct and
systematic teaching of the algorithms, step by step. Students don't need
calculators until the level of algebra, because their own minds are trained to
calculate instead of relying on a machine. Ironically, the traditional method
is far cheaper because it doesn't require that much teacher training, and just
textbooks, paper, pencil, a chalkboard . . . and lots of erasers, because, in
contrast to constructivist philosophy, with traditional math, there's only one
answer, and all the others are wrong!
To learn more about the contentions
of the traditionalists vs. constructivists:
California: www.mathematicallycorrect.com
Massachusetts: www.wgquirk.com/Massmath.html
National
Council of Teachers of Mathematics: www.nctm.org
By Susan Darst Williams • www.GoBigEd.com • Arithmetic,
Etc. 115 • © 2007
