US vs Singapore in Math

American Institutes for Research (AIR) has released a study (funded by the US Department of Education) comparing Math Instruction in Singapore and the US. The full report is available here. Singapore is a world leader in quality of math education. Its textbooks have been the focus of much interest among conservative educators and home schoolers in the US. American versions of the Singapore math books are now available.

AIR headlines, "U.S. Trails, But Both Nations Could Learn from Each Other."

The main conclusions are

 Singapore’s textbooks and assessment examinations are more demanding
 Their teachers are more skilled mathematically
 U.S. approaches often put more emphasis on certain important 21st century math skills.

In the 2003 Trends in International Mathematics and Science Study, Singapore came in first, while the US was 16th out of 46 participating countries. Well, we've been hearing news like this since at least 1983, haven't we? Remember "A Nation at Risk?" (But for a critique of that report, see here.)

“It is unreasonable to assume that Singaporean students have mathematical abilities inherently superior to those of U.S. students; rather, there must be something about the system that Singapore has developed to teach mathematics that is better than the system we use in the United States,” says Steven Leinwand, the lead AIR author.

Maybe it should be explained why such an assumption is unreasonable, but I'll accept that we need not entertain the "inherent superiority" theory. And I'll agree that the school system, including textbooks, standards, and teacher preparation is the primary place to look. However, there is a third factor, namely cultural values and support, that might be influential. The full report discusses this briefly too.

“And in the process, we came across some things Singapore might think about addressing. For example, the U.S. frameworks more often include high-order thinking skills critical to competing in the 21st century, though they are not obviously taught well enough here.”

I don't think we need to export our non-working theories about what is important in mathematics education to a country that's doing so well. This arrogance is out of place. I believe that the attempt to teach high-order thinking skills in place of critical basic skills is a large part of the problem. But then, I'm making an arrogant assertion as well.

The study also includes initial results from four pilot programs that used the Singapore mathematics textbook in place of their regular textbooks. The pilot programs involved students in Baltimore, Md., Montgomery County, Md., North Middlesex, Mass., and Paterson, N.J. The study found two pilot sites produced sizeable improvements in student outcomes, but overall the study observed mixed results because “the pilot sites, to varying degrees, encountered problems with teachers who lacked the educational preparation needed.” Student mobility also limited prior exposure to the Singapore mathematics curriculum, a serious problem in a curriculum that teaches to mastery and does not repeat content.

Translated, that means 1) our teachers don't know enough math to effectively use a real, results-oriented math curriculum, 2) the real problem is that we don't insist on mastery at each level so we can never count on a student being at grade level, and 3) in spite of hese shortcomings, the Singapore curriculum got "mixed results" with half of the pilot sites showing "sizeable improvements." I think what we are really seeing here is that (the Singapore curriculum)+(qualified teachers)+(insistence on mastery)=(impressive results in mathematics education).

A few other noteworthy points:

 Singapore offers an alternative mathematics framework for lower-performing students that covers all the mathematics topics in the regular framework, but at a slower pace and with greater repetition, and with support from expert teachers.
 Textbooks: Singapore’s textbooks build deep understanding of mathematical concepts while traditional U.S. textbooks rarely get beyond definitions and formulas.
 Teaching: Singaporean elementary school teachers are required to demonstrate mathematics skills superior to those of their U.S. counterparts before they begin paid college training to become a teacher.

And then we have:

 U.S. Strengths: Although the U.S. mathematics program is weaker than Singapore’s in most respects, the U.S. system is stronger than Singapore’s in some areas. The U.S. frameworks give greater emphasis than Singapore’s to developing important 21st century mathematical skills such as representation, reasoning, making connections, and communication. The frameworks and textbooks also place greater emphasis on applied mathematics, including statistics and probability.

For reasons I would like to explore further at another time, I do not accept these "Strengths" as legitimate. While there is nothing particularly wrong with anything on the list, I believe we are seeing an inordinate emphasis on these things, which is driving more necessary activities and emphases from the curriculum. If I am correct about that, then Singapore's supposed deficiency actually contributes to its strength.