Education: Math Is Fun

At the University of Illinois last week, a big man in a rumpled brown suit strode up to a blackboard and wrote: ‘ times zero equals zero.” Then he asked ten junior-high-school students to make the sentence “true” by filling in the blank. As 40 schoolteachers from as far away as Florida and Alaska looked on, the students excitedly gave Mathematician Max Beber-man their answer: the sentence is already true because anything times zero equals zero. What the teachers saw were ninth-graders discovering a math principle entirely by themselves. This approach is so important to Beberman that he may not even tell new students the name of his subject. It is algebra, taught in a way that U.S. mathematicians consider the freshest reform in nearly a century.

Known as the University of Illinois Committee on School Mathematics, Be-berman’s nine-year-old project is an effort to give new life to the most irksome subject in U.S. high schools. Supported by $600,000 in grants from the Carnegie Corp., Beberman’s system was taught this year to 8,000 students in 95 secondary schools across the country. Next year it will reach 120 schools. The only problem is a shortage of teachers versed in the method. At 34, Beberman has a full life’s work cut out for him training them.

Child’s Language. As Beberman sees it, conventional high-school math “turns out rigid little computers with a limited range of programs.” Often detesting the subject, teachers view it as such a painful manipulation of inscrutable symbols that they miss the underlying concepts. They either teach it mechanically or try to liven it up with “interesting” problems, e.g., computing interest. Such teaching is completely alien to the child’s mind, says Beberman. “Children are not miniature adults. They have a thirst for the abstract and the world of fancy.” They may even grasp math relationships faster than reading and writing. As famed Swiss Educator Jean Piaget put it after introducing complex topological math to six-year-olds: “They knew it anyway. It is the language and thought of the child.” All of this still escapes most math teachers. When they introduce equations, they hammer home superficial techniques.

With a stern hand, the teacher writes x+5 = 9 on the blackboard. If a youngster pipes up that the “unknown” is 4. he is shushed. The teacher must first demonstrate the rigmarole of subtracting 5 from both sides of the equation to get 4. Says Beberman: “The student had a notion of what a variable really is — and probably for the last time.” Numbers v. Numerals. In his own elementary algebra course, Beberman first focuses on the semantic difference between a number and a numeral. One is a permanent concept, the other a mere name for it. A number has many aliases. Just as the same man may be called President. General, Ike or Eisenhower, so the word seven symbolizes an idea that can be equally well expressed as 3+4, 49/7 , 100-93, 2X3.5 or 1+O=7.

Beberman’s business is pinpointing the numbers behind numerals.

What distinguishes his method is the emphasis on discovery. To find out algebra’s basic laws for themselves, Beberman’s students solve similar problems until the concept involved becomes clear. On the second day, they work at such disarming exercises as stating whether it is true that __ +984 = 984+793. The point is to discover that adding numerals in varying orders does not affect the sum. Later they watch a movie projector running backward and forward, extract the rules of positive and negative multiplication. Then they see two unpunctuated signs : “Slow Children at Play” and “Save Rags and Waste Paper,” a good case for algebraic brackets and parentheses. It takes time, concedes Beberman. “But we feel that every child needs to experience the delight of a researcher when he stumbles on a new principle.”

Billy Smith’s Law. To spur interest, a law’s proper name is not revealed until long after students have grown skilled at using it. Meanwhile, they make up their own names. A class may find itself with a Billy Smith Law, or using the symbol a, which one student invented for “approximately equal to.” Teachers are expected to lead students as far as they will explore.

How well does it work? In the past five years, Beberman’s students at the university’s laboratory school have won first prize four times in Illinois in the Mathematics Association of America’s national math contest, won second prize the fifth time. “Teaching is not lecturing or telling things,” says he. “Teaching is devising a sequence of questions which enables kids to become aware of generalizations by themselves.”