By Paul Moreno
October 2000

The city of Boston is launching a plan to improve students' math ability by shifting from basic computation to "analytical" work.

But this will not help the students, Harvard mathematician Wilfried Schmid, a leader in the effort to restore traditional methods in math teaching, tells Massachusetts News.

"Students who are exposed to this plan the way it is supposed to be taught will not learn 'the basics,' not by a long shot," said Schmid.

Boston certainly needs help. Almost three-quarters of its students failed the math section of the 1999 state exam.

Schmid points out that Boston is going to use a curriculum called Investigations for the elementary grades.

Investigations is the latest version of the "progressive" or "new new math" fad from the American educational establishment.

It was developed by a nonprofit educational think tank in Cambridge and funded by a $7 million grant from the National Science Foundation. It is most popular in affluent suburban school districts.

Critics have pointed out that fashionable, progressive theories like this are particularly harmful in poor, urban districts where students are most in need of basic skills.  Wealthier districts can afford to play games - although Lexington parents were recently among the leaders in the revolt against "new math."

The authors of Investigations are loyal to the 1989 National Council of Teachers of Math guidelines, which have become notorious as the foundation of the "new new math" movement.

Progressive Gimmicks
Investigations is full of progressive gimmicks. Old-fashioned math classes had students work alone; Investigations recommends "group work." This is the essential element in the progressive, "student-centered" classroom, where the teacher is supposed to be a "facilitator" while students "construct" their own lessons and teach each other.

Instead of attempting to get the right answer, students should "consider their own reasoning and the reasoning of others."

Instead of writing numbers and formulas, students communicate about math orally, or with pictures and models.

This progressive curriculum does not teach standard mathematical formulas because "they interfere with a child's growing number sense and fluency with the number system."

Investigations is also fashionably multicultural. As the start of a third grade math lesson, it tells teachers to mimic holding a newborn baby and to write its birthday on the blackboard. "Sing 'Happy Birthday' and encourage students to sing along with you. Ask for volunteers to sing the song in their native languages. Students might also make a poster with the words to "Happy Birthday" in all the languages spoken in the class."

Schmid calls the math substance of Investigations "very shallow." It discourages memorization and keeps students dependent on crutches - fingers, blocks, clock faces, and calculators.  It insults the intelligence of brighter students and is two years behind the fifth-grade curriculum of Singapore.

Advocates of the new program say that it helps to "demystify" math by avoiding abstraction.  But Robert Herriot, a software engineer and former computer science professor in California, says that this is the greatest weakness of Investigations. Students who cannot think abstractly by middle school will not be able to advance.

"Even in fifth grade, students of Investigations are still comparing 11/25 with 1/2 by folding paper."

He does not claim that Investigations is completely without value. "If the authors could moderate their philosophy and improve their mathematics, Investigations could become an excellent supplement. Abstractions are frequently easy to learn when directly taught, but very hard to learn by discovery."

Other Schools Are Similar
The middle and high school programs are similar, "constructivist" programs. A spokesman for the Boston schools says that the middle schools will be using a program called "Connected Mathematics" and that the high school program will be "Math Connections."

These programs help students "develop their own algorithms," he noted.

The Christian Science Monitor reported that parents in Texas petitioned against "Connected Math" when they found that it gave sixth-graders assignments like this:

"Choose a whole number between 10 and 100 that you especially like.  In your journal, record your number, explain why you chose that number, list three or four mathematical things about your number, list three or four connections you can make between your number and the world."

Parents in New York also rebelled against this program when they found out that it asked sixth-graders to add fractions by folding paper strips into segments representing halves or fourths or thirds, instead of by converting to common denominators," says The New York Times.