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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 "discovery learning" or "constructivist." This is because each child is given a chance to "construct" or discover 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!


Homework: To learn more about the contentions of the traditionalists vs. constructivists:





National Council of Teachers of Mathematics:


By Susan Darst Williams Math 01 2008

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