Whatever Happened To New Math?

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In some Catholic schools, though, “Illinois math” took root early and flourished. Each summer scores of nuns, most of whom had never had more than a high school geometry course, made a trip to Urbana to “get modern.” In all, several thousand of them went over a thirteen-year period; those who couldn’t go could subscribe to one of twenty training films paid for by the U.S. Office of Education. What did these teachers learn? Robert Kanske, a former summer-institute teacher and now the senior program officer for the National Academy of Sciences’ Mathematical Sciences Education Board, remembers that it was supposed to be the Beberman technique. “But in four or six weeks you couldn’t teach Max’s instructional genius. You spent all your time on the math itself.”

While remedial training was undoubtedly useful for the teachers, it denied them initiation in the greater mysteries of discovery learning and nonverbal awareness—Beberman’s twin pillars of pedagogy. Both stemmed from his faith in the mental agility of children to discover an answer. To illustrate, Beberman believed students could “discover” that the order in which numbers were multiplied did not affect the sum, if they could grasp such equations as:

 
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He believed students could “discover” that multiplying parts of an equation together yielded the same result as adding them separately, if they could perform such computations as:

 
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Then, when the same students encountered a sentence like

(73 x 87) + (27 x 87) = (73 + 27) x 87

they could assert that it was true because they’d see it as a logical consequence of their other discoveries. With this knowledge a student who later took algebra and confronted the algebraic expression 3 a + 5 a would know that it was equivalent to 8 a —and also would know that 3 a + 2 b is not 5 ab .

The goal was for teachers to guide younger students toward the concrete discovery of abstract mathematical principles by deduction. This was unlike traditional methods, which usually had the teacher present a rule—“You can’t add unlike quantities”—and a sample problem, solve the problem, and then drive the solution home with a number of practice exercises. This old approach taught students to consider problems as types that, once recognized, could be solved by applying a formula. If the problem didn’t conform, most students were lost.

Creativity and curiosity died in those old-fashioned workbooks, and Beberman knew it. That’s why he often began classes with a note from a mythical student who thought that 5 plus 7 equaled 57 and that 9 goes into 99 twice. Trying to explain why he was wrong opened the door to understanding the decimal system and its morphological link to our ten fingers. From there one could move to the principle of zero and to the number system used by Martians with seven fingers—and to the binary code of computers.

But as Peter Braunfeld, a mathematician and Beberman associate at the University of Illinois, says, “Max could teach math to anybody. He was a wizard.” To make every teacher into a Beberman was impossible, as even UICSM’s own summer institutes were beginning to show. And as the appeal of new math spread to the elementary grades, the sheer numbers of teachers involved—more than 1.2 million in 1965—made the upgrading a nightmare.

Begle and his SMSG colleagues at Stanford (the program had moved there from Yale in 1961) attacked from a different direction. Their dream was to produce teacher-friendly new-math courses from summer writing sessions. Michigan-born, but with a “New Englander’s conscience,” Begle was careful to mix mathematical theorists and public and private school teachers in these sessions.

 
 
One associate said “Max could teach math to anyone. He was a wizard. ” But to make every teacher into a Max Beberman was impossible.

The mass appeal of SMSG texts speaks for itself. Beginning with the New Mathematical Library series, in 1959, the number of SMSG texts sold jumped from 23,000 copies to 1.8 million in just three years. Grant money poured in from the National Science Foundation—more than five million dollars bv the mid-1960s.