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,jason

Link to my homepage.

- What is Singapore Math and its success
- Annotated
list of articles and reports (in Jason's priority order)

- Video links about Singapore Math and demonstration lessons
- Suggested reading and additional information links

- Singapore Math emphasizes the development of strong number sense, excellent mental-math skills, and a deep understanding of place value.
- The curriculum is based on a progression from concrete experience—using manipulatives—to a pictorial stage and finally to the abstract level or algorithm. This sequence gives students a solid understanding of basic mathematical concepts and relationships before they start working at the abstract level.
- Singapore Math includes a strong emphasis on model drawing, a visual approach to solving word problems that helps students organize information and solve problems in a step-by-step manner.
- Concepts are taught to mastery, then later revisited but not re-taught. It is said the U.S. curriculum is a mile wide and an inch deep, whereas Singapore’s math curriculum is said to be just the opposite.
- The Singapore approach focuses on developing students who are
problem solvers (from Staff
Development for Educators).

- Model drawing and an emphasis on the concept of part-whole that precedes the teaching of model drawing
- Mental Math: Techniques encourage understanding of mathematical properties and promote numerical fluency
- Daily activities to build on teacher-directed lessons
- “Look and talks” to build understanding of mathematical language
- Number bonds, ten frames, and place value charts
- The connection of pictures, words, and numbers
- Absence of Clutter and Distraction: Presentation is clean and
clear and uses simple, concise explanations (from Staff
Development for Educators).

"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.)

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."

http://dotearth.blogs.nytimes.com/2009/04/27/obamas-call-to-create-not-just-consume/ (speech begin after cover story)

- 1999 NMHS: 54% of 10th graders passed state math exit exam, only 7% achieved advance level.
- 2006 NMHS: 98% passed and 57% achieved advanced level
- 2007 CCHS: 85% passed and 1% achieved advanced level

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.

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.

back to top

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.

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.”

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.

U.S. Department of Education

Policy and Program Studies Service (PPSS)

PREPARED BY:

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."

back to top

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.

Nov. 3, 2003

Eric Kelderman

Staff Writer

Published In:

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.

By CRIS PRYSTAY

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."

back to top

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.

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.

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

THE NEWS-TIMES [Danbury, CT]

March 4, 2006

Jason's notes:

February 2000, Volume 5, Issue 6, Page 345

Abstract:

The author lists five possible reasons for Singapore students' success on TIMSS and poses questions to ponder.

Jason's notes:

Sylvia A. Bulgar and Lynn D. Tarlow

April 1999, Volume 4, Issue 7, Page 478

Abstract:

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:

back to top

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):

- Connected Math or Singapore Math Video letter to Seattle Board of Ed challenges math adoption practice using language intense textbooks rather than Singapore math which has a minimal language requirement.
- School
Board response to suggestion to dump Everyday Math
School board trustee response to
suggestion that the district should investigate alternatives
to Everyday Mathematics (which has been used in the district
for seven years without showing any benefit ...) This
trustee makes several points, the most important from my
perspective is that every math curricula has pros and
cons; Singapore Math and like any other other program is
not a panacea. As the trustee said, if we spent the time
on math that they do in Singapore, we'd probably get the same
results. But we don't. The question the trustee
doesn't address is "how can we get the most from the time we
do spend." That is where Singapore math has been
effective, and his response really doesn't address this.

back to top

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.

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

Staff Development for Educators

The Singapore Maths Teacher

back to top

Return to Enrichment Directory Return to Jason Frand's Homepage

Please feel free to email me with questions and
suggestions.

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