To anyone who last set foot in a math classroom a decade or more ago, a visit to Marilyn Mayer’s eighth-grade algebra course would reveal little that is familiar.
Desks are arranged so students face each other instead of the chalkboard. The walls, window blinds and the hallway outside her room at Long Beach’s Bancroft Middle School are plastered with artwork reflecting students’ use of mathematical concepts.
The room often reverberates with the chatter of students working together to solve problems, and Mayer constantly exhorts her budding mathematicians to “use your calculators if you need to” and “tell us why you did that.”
Math experts say those are the kinds of things that should be--and will be--happening in classrooms across America as part of the biggest transformation of math teaching in three decades. In this widely heralded new approach--which also has its critics--work sheets and drills at the chalkboard are out. So is an emphasis on complicated paper-and-pencil computations, such as long division.
Students still learn how to multiply and divide, but they also work in groups to solve problems that touch on their daily lives and talk and write about the solutions.
“It’s not enough to get the right answer anymore,” said Mary M. Lindquist, president of the National Council of Teachers of Mathematics. “We have to be able to look at all the possibilities in solving a problem, to understand the process and to communicate it. . . . That is what is going on out in the workplace today.”
The council helped launch the math revolution in 1989 by spelling out high standards for students in an increasingly complex, technology-oriented, rapidly changing world. The goal is to move students beyond computational skills--especially those that can be done more efficiently with calculators or computers--and prepare them to tackle problems in new situations.
“We want students to make sense of mathematics, to be able to see the uses of it and be confident in their ability to do mathematics,” Lindquist said.
More than 40 states have signed onto the effort to transform how math is taught. California is at the forefront after adopting in 1992 a widely acclaimed curriculum guide for math teachers from kindergarten through high school. It embodies the new approach, introducing youngsters to more advanced concepts at an earlier age and training them to understand the logic behind basic math principles.
Still, the first test results from the California Learning Assessment System, also part of the math reform movement, found that the new thinking on math has yet to take hold in classrooms. Designed to measure how well students understand math concepts, the tests discovered that a third or more of the students showed little or no understanding of math basics.
Math educators say they do not expect to see a lot of improvement soon. Many expect that it will take several more years for the new methods to reach every classroom and to yield results. They estimate that no more than 10% to 15% of today’s students are receiving significant exposure to the new math curriculum.
There are several reasons for the delay, including a dearth of textbooks and other teaching materials geared to the current thinking on math education. A new generation of textbooks is just now coming off the presses, but the books are not expected to be in California classrooms before fall, 1995.
Other obstacles are the budget pinches most California districts have been feeling since the recession began four years ago, leaving them little money to buy materials or help teachers learn the new methods.
“These are quite major changes,” said Nicholas Branca, executive director of the California Mathematics Project, a state program that taps public colleges and universities to help schools make the transition.
“We’re asking teachers to do things in completely different ways, using techniques and tools they didn’t have when they were students. We are making progress, but it’s slow,” Branca added.
Finally, there is a small but vocal group of critics, including some math teachers, who believe that the new approach keeps students from learning important computational skills. Their message appeals to parents leery of the changes, especially those who struggled under the short-lived “new math” trend in the 1960s.
“Go into some of the classrooms and watch the open-ended activities, and you’ll find a lot of nothing under way,” said Cal State L.A. math professor Wayne Bishop, a frequent critic of the new approach.
Bishop prefers some of the methods espoused by John Saxon, a retired Air Force officer who has written a series of textbooks that do not pass muster with many state boards but have attracted a following among those who favor more familiar, traditional ways.
Saxon calls for teachers to present methods and concepts in small pieces, spending about 10 minutes a day on a lecture, then having students practice in repetitive class and homework assignments until the techniques become second nature to them. Students who fail to grasp the lesson cannot move on until they get it.
Saxon’s critics include virtually all the mainstream math education leadership and many of the growing numbers of classroom teachers who are sold on the new approach. They say his system produces students who do well in computational skills and may get good scores on traditional standardized tests but they would be hard-pressed to do higher-level mathematical thinking and problem solving.
Mayer, the Long Beach middle school teacher, tries to find ways to relate mathematical concepts to her students’ everyday experiences.
She recently began a lesson in her seventh-grade pre-algebra classes with a discussion on playing video games and how the outcomes are improved as a player’s reaction time gets faster with practice. Students then paired off for some exercises in reaction time. First, students sat face to face and tested their reflexes by slapping each other’s palms. Then, one set of students repeatedly dropped rulers, and their partners grabbed them as fast as they could, keeping score by writing down the centimeter marks closest to their thumbs when they caught the rulers.
The students plotted the results in graphs and answered questions about the exercise: Does a higher score represent a faster reaction time? Why? Did the score change over 10 trials? How? Would it be likely to change in 100 trials? Would the results have been different if a heavier ruler had been used?
“I try to find something concrete for them to do” in teaching every concept, Mayer said, voicing one of the basic tenets of the system. “If they make it (or) hold it, they can understand it.”
This is a far cry from the “new math” that held sway for a brief period during the 1960s. In trying to teach students math theories without connecting them to youngsters’ daily lives, the “new math” movement sputtered because it worked only for the brightest students and left teachers frustrated.
“It was an effort to try to provide students with a fundamental understanding of mathematical systems, but what happened was that it had virtually no support from anyone other than the people who were promoting it at the time,” said Lindquist of the math teachers council.
Today’s reformers, armed with a better understanding of how children learn, are making a concerted effort to ground the lessons in children’s experiences and to build consensus on the standards and methods not only among teachers but also with parents and business leaders, Lindquist said.
Robert J. Kansky, associate executive director of the Mathematical Sciences Education Board, said the search for a new way of teaching math began in the late 1980s because business and industry leaders complained that students were not learning what they needed to know on the job.
“They were saying: ‘Look, it isn’t a matter of doing a better job of teaching what people used to need. We expect our workers to tackle problems they have never seen before, find alternative solutions, to work together and to communicate their ideas to others.’ ”
Putting the new math approach into practice has moved slowly in part because school districts do not have the money to retrain teachers and buy new textbooks. Some use federal or state grants to train teachers, while others seek help from private organizations.
Encouraged by an enthusiastic assistant principal, a handful of math teachers at Roosevelt High School in Boyle Heights began re-crafting their teaching methods in 1989 with a grant from the Los Angeles Educational Partnership, a private, business-funded organization working for school reforms.
“LAEP served as the spark,” said Robert C. Ochoa, head of the Roosevelt math department.
Ochoa said three-fourths of Roosevelt’s students, nearly all of whom are Latino, now take more than the one math course required for high school graduation and he has noticed greater enthusiasm in his students.
“They’re doing more writing, working more with technology and losing that ‘I can’t do math’ attitude,” Ochoa said.
But he added that measurable progress has been slow, in part because only about half the department’s 21 teachers have embraced the new system. And none is given time during the school day to plan together, which he said hampers the program’s success.
Reformers say the new approach to math is most crucial in the earliest years of schooling because youngsters need to be familiar with basic mathematical concepts to succeed later on.
Kindergartners in Ann Carlyle’s class at Ellwood School in Goleta spend about an hour a day on math activities, usually working with one or more partners. Students work with tubs containing beads, blocks and other familiar objects that help teach numbers, patterns, geometry, sorting and classifying. The math teaching tools also include games to hone skills in number recognition, “books” to make by arranging nursery tale pictures in sequence, a make-believe store and a miniature town the children constructed with boxes.
At the end of the activity period, when the children have put away their materials and gathered on the rug near the front of the classroom, they tell what they have done.
“Who has news?” Carlyle asked, ready to write down their answers on a large sheet of poster paper.
Derrin showed off the object he made using interlocking plastic tiles. “It has three rectangles and two triangles, and there is a cube inside,” he informed his classmates.
Debbie held up a large hexagon that she had fashioned from pattern blocks “all by myself,” while Joshua told about the number game he and Nicky had been playing: “I won three times and he won one time.”
Such activities lay the groundwork for children’s understanding, enjoyment and self-confidence in math, said Carlyle, who has been a leader in creating and disseminating the new approach in California. She was honored by the White House with the 1993 Presidential Award for Excellence in elementary school math teaching and spends summers leading workshops for other teachers.
Carlyle said her switch 12 years ago to kindergarten after years of teaching sixth-graders brought home an important point.
“With children this young, you can’t use grades as a motivator,” Carlyle said. “What you are doing has to make sense to the children, and it has to be engaging.
“If they’re not interested, they just turn and walk away.”