### Following Singapore’s Lead

#### Posted by John Baez

Some interesting news from the *Los Angeles Times.*

In 2005, just 45% of the fifth-graders at Ramona Elementary School in Hollywood scored at grade level on a standardized state test. In 2006, that figure rose to 76%. Why? They started using the same math curriculum that Singapore does.

Ramona isn’t a rich, fancy school. Nine out of ten students at the school are eligible for free or reduced-price lunches. Most are children of immigrants — most from Central America, some from Armenia. Almost six in ten speak English as a second language. But, they’re doing a lot better in math than kids at other nearby schools!

Singapore math classes are more exciting. From the *LA Times*:

“On your mark … get set … THINK!”

First-grade teacher Arpie Liparian stands in front of her class with a stopwatch. The only sound is of pencils scratching paper as the students race through the daily “sprint,” a 60-second drill that is a key part of the Singapore system. The problems at this age are simple: 2+3, 3+4, 8+2. The idea, once commonplace in math classrooms, is to practice them until they become second nature.

Critics call this “drill and kill,” but Ramona’s math coach, Robin Ramos, calls it “drill and thrill.” The children act as though it’s a game. Not everyone finishes all 30 problems in 60 seconds, and only one girl gets all the answers right, but the students are bubbling with excitement.

And, Singapore math books are just *better*:

The books, with the no-nonsense title “Primary Mathematics,” are published for the U.S. market by a small company in 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.

And, as dedicated readers of this blog surely know, set theory is *simpler* than the syntactic laws governing arithmetic operations on numerals:

• • • + • = • • • •

is easier to understand than

$3 + 1 = 4$

California has taken a promising step forwards by letting Singapore math textbooks be used in grade school:

The Singapore curriculum is not strikingly different from that used in many countries known for their math prowess, especially in Asia and Eastern Europe, math educators say. According to James Milgram, a math professor at Stanford who is one of the authors of California’s math standards, the Singapore system has its roots in math curricula developed in the former Soviet Union, whose success in math and science sent shivers through American policymakers during the Cold War.

The Soviets, Milgram said, brought together mathematicians and developmental psychologists to devise the best way to teach math to children. They did “exactly what I would have done had I been given free rein to design the math standards in California. They cut the thing down to its core.”

[…]

“American textbooks are handicapped by many things,” said Hung-Hsi Wu, who has taught math at UC Berkeley for 42 years, “the most important of which is to regard mathematics as a collection of factoids to be memorized.”

One might think that school districts would be lining up to get their hands on the Singapore texts, but no one expects many to take the plunge this fall.

“Maybe in seven or eight years, but not yet,” said Wu. For now, he said he’d be surprised if the Singapore books claim 10% of the market.

In part, that may reflect the inherent conservatism of the education establishment, especially in large districts such as Los Angeles Unified, whose math curriculum specialists said in December, a month after the Singapore texts were adopted by the state, that they hadn’t even heard of them – or of the successful experiment taking place in one of their own schools.

But there is also an understandable reluctance to rush into a new curriculum before teachers are trained to use it. Complicating that, experts said, is that most American elementary school teachers – reflecting a generally math-phobic society – lack a strong foundation in the subject to begin with.

The Singapore curriculum “requires a considerable amount of math background on the part of the teachers who are teaching it,” said Milgram, “and in the elementary grades, most of our teachers aren’t capable of teaching it… . It isn’t that they can’t learn it; it’s just that they’ve never seen it.”

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 Roger 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.”

It’s sort of depressing that the math teachers need to be taught math. On March 21st, my wife and I are flying to Singapore. Not because of this article… I’m giving a talk to the math and physics departments at NUS, and she’s talking at the philosophy department. We’ve been there before; it’s a fascinating place, but I feel I’ve only scratched the surface. It’s got its good points; it’s definitely got its bad points… but they seem to know how to teach math.

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