Michael Atherton <[EMAIL PROTECTED]> wrote:
: I work in a university environment dominated
: by constructivists. I have been trying to find authors
: or researchers who are publishing views contrary to
: the NCTM standards...without much luck. Can any
: one tell me who are the national figures with views
: opposed to the constructivist approach to mathematics
: education?
You might be interested in the writings of Martin Gardner, the author and former
math columnist for Scientific American, on this. I quote from him below. For
more, see, e.g.,
http://forum.swarthmore.edu/epigone/amte/hiljixprer/199809090724.
[EMAIL PROTECTED]
" I seldom agree with the conservative political views of Lynne Cheney, but when
she criticized extreme aspects of the new new math on the Op-Ed page of The New
York Times on August 11, 1997,2 I found myself cheering. As Cheney points out, at
the heart of fuzzy-math teaching is the practice of dividing students into small
groups, then letting them discover answers to problems without being taught how to
find them. For example, teachers traditionally introduced the Pythagorean theorem
by drawing a right triangle on the blackboard, adding squares on its sides, and
then explaining, perhaps even proving, that the area of the largest square exactly
equals the combined areas of the two smaller squares.
"According to fuzzy math, this is a terrible way to teach the theorem. Students
must be allowed to discover it for themselves. As Cheney describes it, they cut
from graph paper squares with sides ranging from two to fifteen units. (Such
pieces are known as "manipulatives.") Then they play the following "game." Using
the edges of the squares, they form triangles of various shapes. The "winner" is
the first to discover that if the area of one square exactly equals the combined
areas of the other two squares, the triangle must have a right angle with the
largest square on its hypotenuse. For example, a triangle of sides 3,4,5.
Students who never discover the theorem are said to have "lost" the game. In this
manner, with no help from teacher, the children are supposed to discover that with
right triangles a^2+b^2=c^2.
""Constructivism" is the term for this kind of learning. It may take a group
several days to "construct" the Pythagorean theorem. Even worse, the paper
game may bore a group of students more than hearing a good teacher explain
the theorem on the blackboard.
"One of the harshest critics of fuzzy math is the writer John Leo, whose
article on the subject, "That So-Called Pythagoras," was published last year
in US News and World Report (May 26, 1997). (His title springs from a
reference he found in a book on ethnomathematics to "the so-called
Pythagorean theorem.")..."
--
Michael P. Cohen home phone 202-232-4651
1615 Q Street NW #T-1 office phone 202-219-1917
Washington, DC 20009-6310 office fax 202-219-1736
[EMAIL PROTECTED]
