Introduction
Singaporean students ranked first in the world in mathematics on the Trends in International Mathematics and Science Study (TIMSS)-2003; U.S. students ranked 16th out of 46 participating nations at grade 8 (Mullis, et al., 2004). Scores for U.S. students were among the lowest of all industrialized countries. Because it is unreasonable to assume that Singaporean students have mathematical abilities inherently superior to those of U.S. students, 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.

This exploratory study compares key features of the Singapore and U.S. mathematics systems in the primary grades, when students need to build a strong mathematics foundation. It identifies major differences between the mathematics frameworks, textbooks, assessments, and teachers in Singapore and the United States. It also presents initial results from four pilot sites that introduced the Singapore mathematics textbook in place of their regular textbooks.

Analysis of these evidentiary streams finds Singaporean students more successful in mathematics than their U.S. counterparts because Singapore has a world-class mathematics system with quality components aligned to produce students who learn mathematics to mastery. These components include Singapore’s highly logical national mathematics framework, mathematically rich problem-based textbooks, challenging mathematics assessments, and highly qualified mathematics teachers whose pedagogy centers on teaching to mastery. Singapore also provides its mathematically slower students with an alternative framework and special assistance from an expert teacher.

The U.S. mathematics system does not have similar features. It lacks a centrally identified core of mathematical content that provides a focus for the rest of the system. Its traditional textbooks emphasize definitions and formulas, not mathematical understanding; its assessments are not especially challenging; and too many U.S. teachers lack sound mathematics preparation. At-risk students often receive special assistance from a teacher’s aide who lacks a college degree. As a result, the United States produces students who have learned only to mechanically apply mathematical procedures to solve routine problems and who are, therefore, not mathematically competitive with students in most other industrialized countries.

The experiences of several of the U.S pilot sites that introduced the Singapore mathematics textbooks without the other aspects of the Singaporean system also illustrate the challenges teachers face when only one piece of the Singapore system is replicated. Some pilot sites coped successfully with these challenges and significantly improved their students’ mathematics achievement, but others had great difficulty.

Professional training improved the odds of success, as did serving a stable population of students who were reasonably able with mathematics. These mixed results further reinforce the comparative findings that the U.S. will have to consider making comprehensive reforms to its school mathematics system if we are to replicate the Singaporean successes.

The U.S. mathematics system has some features that are an improvement on Singapore’s system, notably an emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics. However, if U.S. students are to become successful in these areas, they must begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.