An Introduction to Singapore Math

original prepared July 6, 2008, last update August 7, 2009

This is an ongoing, evolving site.  Please feel free to comment, suggest changes, provide additional info, etc.  Email feedback to me and I'll add to the file.  Thanks,
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How this page is organized:

  1. What is Singapore Math and its success
  2. Annotated list of articles and reports (in Jason's priority order)
  3. Video links about Singapore Math and demonstration lessons
  4. Suggested reading and additional information links

1.  What's all the fuss?

In the 1980's, students in the U.S. and Singapore were both ranked in the lower half of all countries tested in mathematics.  Beginning in 1993, Singapore ranked number one in the world in mathematics, and it continues to hold the top or second position to this day.  Regrettably, the U.S. continues to rank low.  The question is "Can we incorporate aspects of what Singapore has done to improve our overall math performance?"  The answer is "yes!"

What is Singapore Math?

Singapore Math is the name given to the math curriculum developed in the country of Singapore and now used in many schools and districts across the U.S.  The math content in Singapore Math is the same as the math content that we were taught in school.  The content hasn't changed.  What is most different about Singapore Math is the philosophy about what is to be emphasized and the pedagogy about how the content is taught.  The word "elementary" in "elementary school mathematics" from a Singapore Math perspective means fundamental, foundational.  It does not mean easy or simple.   Singapore Math recognizes that for children, what they learn in elementary school is the basis of all future math learning and thus focuses on problem solving and the base-ten system. 

What makes Singapore Math such a strong curriculum?

What are some of the biggest differences between Singapore Math and the more traditional U.S. approach?

First, it’s important to recognize that there is no single “U.S. approach.” In this country, most curriculum decisions are made at the local or state level. In Singapore, the Ministry of Education determines what will be taught nationwide. That said, certain elements of the Singapore approach are distinctly different from what’s typical in the U.S. Although some of these strategies may be used on their own in U.S. schools, it would be rare to find all of them in an American classroom that is not adopting or supplementing with Singapore Math. Examples include:

"The Singapore Math curriculum is concept-based, with a progression from visual to pictorial to abstract that ends with mastery. It is not “New Math” – it is math the way it should be taught; math the way mathematicians understand it.... It is conceptual, not algorithmic; visual not rote, and it is fun. Fun to teach and fun to learn, since it is based on understanding, not memorization."  (from The Pi Project homepage.)

President Obama's endorsement of math reform

On April 27, 2009,  President Obama gave a speech to the National Academy of Sciences.  He devoted an entire section to the critical nature of math (and science) education, and the idea of rewarding States in the Race to the Top in improvement.  And, in his comparison of math scores between US to foreign countries, the first country he mentioned was Singapore.  The entire speech is linked below, but here are two highly relevant paragraphs:

(near beginning):  "Our schools continue to trail other developed countries and, in some cases, developing countries. Our students are outperformed in math and science by their peers in Singapore, Japan, England, the Netherlands, Hong Kong, and Korea, among others. Another assessment shows American 15-year-olds ranked 25th in math and 21st in science when compared to nations around the world."

(toward end):  "Fifth, since we know that the progress and prosperity of future generations will depend on what we do now to educate the next generation, today I’m announcing a renewed commitment to education in mathematics and science.  This is something I care deeply about. Through this commitment, American students will move from the middle to the top of the pack in science and math over the next decade — for we know that the nation that out-educates us today will out-compete us tomorrow. And I don’t intend to have us out-educated."  (speech begin after cover story)

... district wide success...

My interest in Singapore Math began after reading the article in the LA Times about Ramona Elementary School in downtown Los Angeles (discussed next).  While this is compelling in and of itself, from a district perspective, the report from North Middlesex Regional School District (NMRSD) in Massachusetts is equally compelling.  This district is comparable to Culver City:  four elementary, two middle and one high school.  In 2000-2001 they began introducing Singapore Math, and in 2005-06 achieved 100% implementation at grades 1-6;  75% at grades 7-8.  But, its the quality differences in the mathematics learned as represented by scores on the Massachusetts State High School Exit Exam that we need to think about:
Equally exciting improvement scores were reported for grades 2, 5, and 6 using the Iowa Tests of Basic Skills, but these scores are not easily compared to CCUSD scores.   (Comments on the implementation of Singapore Mathematics program, September 2006).  Also, see Wall Street Journal article on the district's success.

In L.A., Singapore math has added value

Los Angeles Times March 09, 2008

Jason's notes:  Describes LAUSD Ramona Elementary in downtown LA  and overview of Singapore math program.  Ramona introduced Singapore Math textbooks in K - 1 at start  of 2004-2005, and expanded to the rest of the school in 2005-2006.  Quotes Ramona Principal Susan Arcaris:  It’s wonderful.  Seven out of 10 of the students in our school are proficient or better in math, and that’s pretty startling when you consider that this is an inner-city, Title 1 school."

A U.S. Department of Education sponsored study (discussed below) found Singapore math textbooks a major factor in the success.  The textbooks are now on the list of California state-approved elementary school math texts.

Article describes contrast of current texts used in our schools with Singapore math texts:  The content is carefully thought out to reinforce patterns of mathematical thinking that carry through the curriculum. “These are ‘procedures with connections,’ ” Robin Ramos, math resource teacher.  This thoughtfulness is the true hallmark of the Singapore books, advocates say.  Underlying philosophy is concrete to pictorial to abstract, and is carried through all grades.  Another hallmark of the Singapore books is that there is little repetition. Students are expected to attain mastery of a concept and move on. Each concept builds upon the next. As a result, the books cover far fewer topics in a given year than standard American texts.

Article ends emphasizing that training is the key critical successful factor.

Amy Anderson (Howe Elementary principal) and I visited Ramona on October 8, 2008.  My observations confirm what was written in the LA Times article, and in fact the reality was more impressive than the article.  My notes are posted here as Ramona Elementary Visit Notes.

As a comparative note on Ramona's success, on the May 2008 California Standards Test,  58% of Lin Howe students achieved proficient or advanced levels in mathematics, while 71% of Ramona achieved proficient or advanced levels.  Conversely, 14% of the students were below or far below basic at both schools.

other success stories...

Singapore Math is in its infancy in terms of U.S. adoptions with an estimate of about 1500 schools from the book publisher.  So, test scores are hard to come by.  As I find them I  shall list t hem  here:

Singapore Math is a plus for South River students:  South River (a New Jersey school) charted the progress of its pupils who took the statewide achievement test for third-graders in 2005, and those same students took the fourth-grade state test in 2006. The number of students who achieved advanced proficiency in math increased from 18 to 53 out of 173 students.

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2.  Articles and reports about Singapore Math

Jason's notes:  The next two link are to the Singapore Math publishers web site.  They have information on California approval of textbook series (which means CCUSD can use the books knowing the children will cover all required topics to meet California Standards), and to the overall world wide success of Singapore Math, and a list of schools and articles related to the successful introduction of Singapore math across the country. 

Singapore Math approved for CaliforniaNovember 14, 2007 Press Release

Singapore Math global dominance:  This link lists numerous articles on Singapore math.  Many of these are summarized  below.

Miracle Math

A successful program from Singapore tests the limits of school reform in the suburbs

Barry Garelick
Hoover Institutes, Stanford U
Fall 2006

  Jason's notes:  There is an excellent summary of the major differences in approaches between current US adopted textbooks and Singapore math textbooks:

Unlike many American math textbooks, such as Math Thematics, published by Houghton Mifflin, which are thick, multicolored, and multicultural, Singapore’s books are thin and contain only mathematics. There are no graphics (other than occasional cartoons pertaining to the lesson at hand), no spreadsheet problems, and no problems asking students to use a calculator to find the mean number of dogs in a U.S. household. With SM, students are required to show their mathematical work, not explain in essays how they did the problems or how they felt about them. While a single lesson in a U.S. textbook might span two pages and take one class period to go through, a lesson in a Singapore textbook might use five to ten pages and take several days to complete. The Singapore texts contain no narrative explanation of how a procedure or concept works; instead, there are problems and questions accompanied by pictures that provide hints about what is going on. According to the AIR report, the Singapore program “provides rich problem sets that give students many and varied opportunities to apply the concepts they have learned.”

"Another key difference is the number of topics covered by Singapore’s texts for a single grade. The AIR study frequently criticizes American math texts for being an inch deep and a mile wide, covering a great range of topics with little time spent on developing the material, including mastery of math facts. (One of the texts with which the AIR study compares Singapore’s Primary Mathematics series is Everyday Mathematics, a program developed with NSF funding and used widely in Montgomery County.) The MCPS 1st-grade curriculum goals, for instance, contain a number of nonessential topics, such as sorting concrete objects (like Post-its with names of favorite pets on them) into categories, activities that take up instructional time which, critics of the MCPS curriculum argue, could be better spent laying the foundation for algebra in 8th grade.

"Singapore’s texts also present material in a logical sequence throughout the grades and expect mastery of the material before the move to the next level. In contrast, mainstream American math texts and curricula frequently rely on a “spiral” approach, in which topics are revisited and reviewed. The expectation of that approach is that not all students achieve mastery the first time around. One Ohio school teacher familiar with the spiral approach summed up much of the criticism of the method on an Internet math forum, saying, students “can’t remember how to do it when [they] do return—or if they do remember it, it’s now being taught in a different way.”


Barry Garelick
Third Education Review, Essays: Volume 2, Number 8, 2006

Jason's notes:  Summarizes background and major successes of SM.  Has long discussion of the politics of math education in the US and the role of the mathematics establishment in hindering the introduction of Singapore math.  My take:  SM uses a very different philosophy and pedagogical model from what has become the adopted established norm in the US, adopted by National Council of Teachers of Mathematics and all the textbook publishers, so lots of people have to admit they "got it wrong" in order for SM to be introduced.

AIR Study:              (Return to LA Times article)

What the United States Can Learn From Singapore’s World-Class Mathematics System

(and what Singapore can learn from the United States):  An Exploratory Study

U.S. Department of Education
Policy and Program Studies Service (PPSS)
American Institutes for Research®
1000 Thomas Jefferson Street, NW
Washington, DC 20007-3835
January 28, 2005

Jason's notes:  This is an 200 page detail study comparing math instruction in the U.S and Singapore.  This report has test score data and other detailed analysis useful in documenting Singapore Math successes and statements regarding differences with current curriculum approaches.  (Click here to download the study.)  Here is a three paragraphs overview identifying major finding and issues:

"Analysis of these evidential 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.... 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."

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What we can learn from Singapore's math

Wednesday, February 16, 2005

Jason's notes:  This is a series of very interesting and informative posting of teachers and parents in response to the American Institutes' report about the success of Singapore math..  Overall consensus is that Singapore Math outperforms current US based math approaches.

Future of successful math program hazy

Nov. 3, 2003
Eric Kelderman
Staff Writer

Jason's notes:  Very good description of pilot at four Maryland’s Montgomery County Public Schools, what was done and success at the schools.  Indicates that district is considering dropping the program (which in light of the reported information in the article just doesn't make sense).  Next article is sequel.   (Oct 1, 2008 note:  the  Barry Garelick article A TALE OF TWO COUNTRIES AND ONE SCHOOL DISTRICT noted above explains the politics behind the scene.)

District Drops Successful Singapore Math Program

Written By: School Reform News staff
Published In: School Reform News
Publication Date: December 1, 2003
Publisher: The Heartland Institute

Jason's notes:  Critical of district dropping successful program because Singapore Math doesn't align with state testing mandates.  The criticism that state guidelines are "a mile wide and inch deep" while Singapore Math goes deeper and more thorough with fewer topics.

As Math Skills Slip, U.S. Schools Seek Answers From Asia

The Wall Street Journal
Staff Reporter
December 13, 2004; Page A1

Jason's notes:  Article states "Under the Bush administration's No Child Left Behind policy, funding and jobs depend on how each school rates on standardized state exams. Many district officials are reluctant to try something new for fear of slipping up on those exams."  The article describes Singapore math programs around the country, including mention of the private Rosenbaum Foundation of Pennsylvania, which funds Singapore math programs in the U.S. and Israel.

The articles sites teachers won over, but is short on hard statistics on student score improvements across the many schools sited.   Lots of good anecdotally comments.  E.g., the article quotes one of fifth-grade math teacher Bob Hogan students a saying  "I don't know where Singapore is," she said, "but I like the way they do math."

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other material

The Singapore Story: A Nation's Effort to Develop Human Resources

by Swee Fong Ng
November 2001

Jason's notes:  Summarizes how Singapore went from #16 of 26 countries in 1983 in the international math and science studies to #1 consistently since 1996.  Singapore's culture, structure, size, homogeneity, and approach are NOT replicable in the US, let alone Culver City, BUT, there is a lot of positive material that can be transferred.

Being the Best Teacher You Can Be in 2005

Jason's notes:  Another NCTM dialog and Singapore Math barely mentioned (in any of these dialogs), but one IMPORTANT comment from Gaithersburg, Maryland was buried:
Our school was asked to pilot Singapore Math with little background knowledge and training. We planned as teams. We had staff meetings to share the mathematics at each grade level so we could all get a more vertical view. We modeled lessons for each other and discussed best practices. Every teacher and student learned new approaches and strategies for teaching and learning math. In time and with hard, focused work, teachers and students succeeded in implementing the Singapore Math pilot.

Singapore math in LA

Published by Joanne Jacobs March 13th, 2008 in Education.

Jason's notes:  Nicely summarizes critical issues;  critical success factor is teacher training.  Has homeschooling parent dialog, not too useful.

article to be acquired

Parents grade math programs By Nanci G. Hutson
March 4, 2006

Jason's notes: 

Should the United States Emulate Singapore's Education System to Achieve Singapore's Success in the TIMSS?      

Ramakrishnan Menon
February 2000, Volume 5, Issue 6, Page 345
The author lists five possible reasons for Singapore students' success on TIMSS and poses questions to ponder.

Jason's notes: 

Homogeneous Groups Develop Thoughtful Mathematics      

Sylvia A. Bulgar and Lynn D. Tarlow
April 1999, Volume 4, Issue 7, Page 478
The results from the third International Mathematics and Science Study (TIMSS), which tested a half million eighth-grade students in forty one countries, have recently been publicized. Students in the United States ranked below average in mathematics, whereas students in Singapore earned top scores. Examining how students in Singapore study mathematics should provide useful information to mathematics educators on how to improve the performance of students in the United States. Problem solving is emphasized in Singapore, where students are expected to struggle with problems that have real-life implications.

Jason's notes: 

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3.  Video links about Singapore Math and demonstration lessons


Wentzville School District, Missouri:  district wide implementation with statement from superintendent.
Singapore Math Success!  "News flash" type overview of Singapore Math at Benchmark Elementary School.

There are many classroom lessons available for viewing.  These are very instructive if you want a sense of what is actually happening in the classroom.  I'm listing the first of any series, and then use the Utube listing to go to the next in any given series.  Also, these videos are just listed here, not evaluated in terms of their quality.

Second Grade Singapore Math Sprint  Sprints are an approach to drill which makes it into a exciting learning event. 
Mental math lesson
Singapore Math: Grade 3a, Unit 1 (part 1)
Singapore Math in Action - with Char Forsten
Sandy Chen Singapore Math in the Classroom
Helping Parents Explain Math - Word Problems

These next two video are related to Singapore Math adoption issues.  Although they seem related, the first was posted in Jan 2008 while the "response" was posted in February, 2007 (so they really aren't):

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4.  Suggested reading and additional information links

The book Knowing and Teaching Elementary Mathematics by Liping Ma (Lawrence Erlbaum Associates, Publisher, 1999) is the single most influential book I've read professionally in thirty years.  Ma asked a sample of teachers to explain typical students errors found in four elementary school math problems:  a subtraction with regrouping problem, a multidigit multiplication problem, a division by fractions problem, and a geometry problem involving area and perimeter.   Her insights into how teachers and students think were incredible, completely changing how I thought about how and why we teacher as we do, as well as how to work with teachers to help them improve their ability to teach mathematics.

Elementary Mathematics for Teachers by Thomas Parker and Scott Baldridge (Sefton-Ash Publishing, 2004) is a book I wish I had written intead of the one I did write for teachers more than thirty-years earlier (Theory and Applications of Mathematics for Teachers, Wadsworth Publishing, 1975).  Parker and Baldridge explain the math teachers need to know referecing problems in the student's Singapore Math textbooks.  They use the strategies incorporated in Singapore Math in explainig the concepts and provide an outstanding explanation of mental math, a major and critcal component of the Singapore Math program.

Some online resources and consultant info

Jason's disclaimer:   This is just a list of consulting sites I've come across.  I  have not used any of their consulting services and am NOT endorsing them.  I've listed them solely as a convenience in response to a feedback request that I do so.

Worcester State College, Massachusetts, has created a Singapore Math Implementation Web Site to support the wide spread implementation of Singapore Math throughout their state.

The Pi Project   (I attended one their training sessions and it was excellent)
Staff Development for Educators
The Singapore Maths Teacher   

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Please feel free to email me with questions and suggestions.

Jason Frand, PhD.
Math Olympiad Coach and
Los Angeles County-wide Math Olympiad Tournament Chairperson
Linwood Howe Elementary School
Culver City Unified School District
Adjunct Assistant Professor, Retired
Assistant Dean and Director, Retired
UCLA Anderson School of Management
prepared July 6, 2008
updated August 7, 2009