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.
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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 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."
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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."
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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:
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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.
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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
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