For all the debate about overhauling math education in the US, there have been few actual gains in student achievement. That's why news of a program in Puerto Rico has drawn attention from those interested in math reform.
In 1992, the island launched an initiative in its public schools, aiming to close a 70-point gap between public school students and their private-school counterparts on standardized tests. Educators expected modest improvement, but got a lot more.
Six years later, children who had attended reform classes every year outscored private-school students by 58 points in math reasoning and 79 points in math achievement on College Entrance Examination Board tests. And though reform focused only on math and science, students inched 10 points above private-school children in verbal reasoning.
The scores left observers wondering what had taken place in Puerto Rico. Educators involved in the project - the Puerto Rican Statewide Systemic Initiative (PR-SSI) - pointed to better teacher training, methods similar to those of Japanese that focus on teamwork and problem solving, and a systematic approach that unified management with teachers. Now, the island is capturing international attention for its success story.
Simple yet far-reaching
At first glance, Puerto Rico might have seemed to some an unlikely site for a major experiment in math reform. About 83 percent of Puerto Rico's 620,000 public school children live in households where the income lags behind the federal poverty level.
But the changes urged upon the schools participating in the initiative - which currently include a quarter of the island's schools and by this summer will reach half - were far-reaching and yet fundamentally rather simple.
Interestingly, much of the thought behind them dovetails neatly with current practices in Japanese math education, although those involved with the program say they did not consciously model Japanese methods.
The program closely links science and math instruction. It simplifies the curriculum in both disciplines and yet keeps it carefully aligned with standards specifying what children should know and be able to do at each grade level. The end result is that teachers present students with fewer concepts over the year, but ensure that those concepts are being more deeply explored.
There's a practical, hands-on approach, with a focus on the visual. A math class could look like an art class, with kids cutting and pasting colored string to measure circumference. Other times, it resembles a gym class, as students hang tags with math symbols around their necks and then line up to form human equations. It's an approach that, at first, can appear flaky. At least, that's how it initially struck some Puerto Rican math teachers.
"Our math teachers tended to think teaching math was about teaching kids to add, subtract, multiply, and divide," says Hector Alvarez, curriculum coordinator for the initiative.
"They didn't think so much about understanding. They thought that if they stopped and did more hands-on things they weren't doing enough real math." But then, he says, "they realized kids were really understanding the concepts."
Group work, with lots of discussion and mutual support among the students, is a regular feature of the teaching method urged by PR-SSI trainers. At the heart of the process is the belief, central also to Japan's approach, that discovery of ideas must be done by the students. While traditional US methods require the teacher to explain a concept and then assign problems illustrating its use, PR-SSI reverses the procedure.
In this method, without offering a lecture beforehand, the teacher simply presents the class with a problem. Arranged in teams, students are asked to seek solutions. The theory is that as they tussle with the question, they'll begin to grasp the concept. Only then does the teacher answer questions that lead to explanation.
For instance, when Linda Ferrer wanted to introduce her fourth-graders at a public school in Humacao to multiplication, she began by presenting them with an exercise in wardrobe creation. She asked students to imagine they had three shirts and four pairs of pants, all different colors. They were told to draw possible combinations and calculate the total number of outfits. Joshua Lopez Varga was soon happily sketching a yellow shirt tucked into green pants. Math is great, he says. "We draw, we do things here that are fun."
It's exactly the kind of exercise that critics of what's being called "the new new math" deride as being soft and insufficiently grounded in practical mathematics.
Not just fun and games
But if the system is working, advocates claim, Joshua wasn't just having fun using his colored magic markers. He was encountering the idea of multiplication head-on in a real-life situation, a learning experience intended to be more powerful than any verbal explanation.
But such a method requires a completely different approach from instructors, and that's why teacher training is at the heart of the Puerto Rican reforms. Not only are PR-SSI teachers trained in the new instructional style, but they are also encouraged to begin viewing themselves as students as well.
PR-SSI begins with a four-week summer workshop to help teachers deepen their own grasp of math concepts, and to adopt the ideal of lifelong, ongoing learning in math. The teachers are also taught to work in groups, often designing lessons and curriculum together. Teachers in different grades work together as well, ensuring better continuity throughout the program.
The success of the initiative has not gone unnoticed by the education establishment. Department of Education Secretary Richard Riley has traveled to Puerto Rico to learn more about it, and US Congressman Jose Serrano (D) has arranged a $1.5-million grant to bring PR-SSI personnel to New York to set up programs in his mostly Hispanic district in the Bronx. Three Bronx middle schools are using the method, with nine more scheduled to join them.
Some educators who have examined the results of PR-SSI suggest the highly centralized nature of Puerto Rico's education system has been a plus in implementing the program. Others point out the size of the student population on the island would equal one of the largest of the US urban school systems - groups that have never found centralization has aided in reform.
The NSF offered SSI grants similar to the one that has been the cornerstone of the Puerto Rican program to 25 on-shore sites as well as Puerto Rico. But few of those programs, which were highly diverse in nature, were deemed successful.
Some ideas on math reform found at the core of the Puerto Rican program hold real promise, says Sandy Scofield, former head of the Nebraska SSI program, especially the focus on meaningful, ongoing development for teachers and teaching kids fewer concepts grounded in deeper understanding.
"If that's effectively linked with teacher preparation and effective assessment, we may start to make some progress," she predicts.
(c) Copyright 2000. The Christian Science Publishing Society