Ramona's students are mostly immigrants, with most of them from Central America; 6 of 10 speak English as a second language.
The books, with the no-nonsense title "Primary Mathematics," are published for the U.S. market by a small company inSo why aren't these books more widely used? The L.A. Times article linked above says that the main resistance comes from teachers. The curriculum is not easy to use without special teacher training:
Oregon, Marshall Cavendish International. They are slim volumes, weighing a fraction of a conventional American text. They have a spare, stripped-down look, and a given page contains no material that isn't directly related to the lesson at hand.
Standing in an empty classroom one recent morning, Ramos flipped through two sets of texts: the Singapore books and those of a conventional math series published by Harcourt. She began with the first lesson in the first chapter of first grade.
In Harcourt Math, there was a picture of eight trees. There were two circles in the sky. The instructions told the students: "There are 2 birds in all." There were no birds on the page.
The instructions directed the students to draw little yellow disks in the circles to represent the birds.
Ramos gave a look of exasperation. Without a visual representation of birds, she said, the math is confusing and overly abstract for a 5- or 6-year-old. "The math doesn't jump out of the page here," she said.
The Singapore first-grade text, by contrast, could hardly have been clearer. It began with a blank rectangle and the number and word for "zero." Below that was a rectangle with a single robot in it, and the number and word for "one." Then a rectangle with two dolls, and the number and word for "two," and so on.
"This page is very pictorial, but it refers to something very concrete," Ramos said. "Something they can understand."
Next to the pictures were dots. Beginning with the number six (represented by six pineapples), the dots were arranged in two rows, so that six was presented as one row of five dots and a second row with one dot.
Day one, first grade: the beginnings of set theory.
"This concept, right at the beginning, is the foundation for very important mathematics," Ramos said. As it progresses, the Singapore math builds on this, often in ways that are invisible to the children.
Word problems in the early grades are always solved the same way: Draw a picture representing the problem and its solution. Then express it with numbers, and finally write it in words. "The whole concept," Ramos says, "is concrete to pictorial to abstract."
Many eminent mathematicians agree. In fact, it is difficult to find a mathematician who likes the standard American texts or dislikes Singapore's.
"The Singapore texts don't make a huge deal about the concepts, but they present them in the correct and economical form," said Roger Howe, a professor of mathematics at
Yale University. "It provides the basis for a very orderly and systematic conceptual understanding of arithmetic and mathematics."
Adding to the difficulty is that the Singapore texts are not as teacher-friendly as most American texts. "They don't come with teachers editions, or two-page fold-outs with comments, or step-by-step instructions about how to give the lessons," said Yale's Howe. "Most U.S. elementary teachers don't currently have that kind of understanding, so successful use of the Singapore books would require substantial professional development."This seems to be further evidence for the recent McKinsey study comparing education internationally that concluded that the best results are obtained by hiring the best teachers, providing them with training and support to get the best out of them, and then intervening to provide students who fall behind with support.
Although some U.S. schools have had spectacular results using Singapore texts, others have fared less well. A study found that success in
Montgomery County, Md., schools using the Singapore books was directly related to teacher training. At schools where teachers weren't trained as well, student achievement declined.