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,
jason
Link
to my homepage.
How this page is
organized:
- 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
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?
- 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).
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:
- 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.)
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."
http://dotearth.blogs.nytimes.com/2009/04/27/obamas-call-to-create-not-just-consume/
(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:
- 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
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.
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.
back to top
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 global dominance: This link lists numerous articles on Singapore
math. Many of these are summarized below.
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
PREPARED FOR:
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
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.
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.)
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.
The Wall
Street Journal
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
other material
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.
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.
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
THE
NEWS-TIMES [Danbury, CT]
March 4,
2006
Jason's notes:
Ramakrishnan Menon
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
3.
Video
links about Singapore Math and demonstration lessons
Overviews
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
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
back
to top
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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