To the Editor:
In his spirited attack on what he characterizes as anti-reform forces in math education (“Mathematics and the Pure in Heart,” Feb. 28, 2007), T.C. O’Brien speculates that the British mathematician Alfred North Whitehead must have foreseen Parrot Math when he said, 90 years ago, “In training a child to activity of thought, above all things we must beware of what I will call ‘inert ideas’—that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations.”
With regard to Whitehead’s opinion on carrying out rote procedures, however, there is no need to speculate, for he states quite clearly in his Introduction to Mathematics:
“It is a profoundly erroneous truism, repeated by all copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.”
Only by conflating Whitehead’s statements can one arrive at a holistic perspective, one that has been achieved by every working mathematician. Some mathematics educators focus only on the message of Whitehead’s first statement, but persistently and dangerously ignore the relevant warning of the second: Skills must be mastered to the point of automaticity in order to free the mind for the task at hand.
If young students don’t completely understand the whys and wherefores of what they are doing, they can gain that knowledge when they are older and better able to think abstractly. In contrast, students who don’t master the formal algebraic skills that should be acquired in grades K-12 are virtually impossible to remediate. It is the failure of reform curricula to demand that children learn to work automatically—as Whitehead advocates, without thinking about what they are doing— that threatens the mission of university math and science departments.
Stanley Ocken
Professor
Department of Mathematics
City University of New York
City College
New York, N.Y.
