+ Singapore Math: Intensive Teacher Trainings

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Intensive Five-day Summer Institutes in teaching “Singapore Math” are scheduled in Orlando (June 23-27), San Francisco (July 14-18), and Boston (July 28-August 1). 

These three will focus on the fundamentals, and are geared to teachers of grades 1-6 who have little or no experience in Singapore Math, “especially those who intend to supplement a non-Singapore Math program or adopt a Singapore Math program.”

A fourth Institute titled “Advanced” will be held in Boston from August 4-8.  The advanced seminar will be directed at grade 1-6 educators with in-depth training experience in teaching Singapore Math who are either supplementing their current program or adopting the Singapore Math curriculum.

Call toll free 1-800-462-1478 or www.SDE.com/revolutionary.

Conference registration is $1395.  It includes a tool kit containing $500 worth of customizable materials: Singapore Math for US Handout Book; an 8-step Model Drawing Book;  the Teaching Elementary Mathematics book; a voucher to redeem one “sample set” from the Primary Mathematics book series (includes one copy of both A & B versions of a Teacher’s guide, student textbook and student workbook — your choice of grade level).

Trainees receive 26.5 total contact hours plus 2 additional hours upon completion of the on-demand electronic follow-up training.  For futher information about graduate credit through Antioch University Seattle and Chapman University College, visit www.SDE.com/revolutionary and follow the “credit” link.


When the US Department of Education commissioned a study in 2005 to find out why Singapore, a country with a population half the size of New York City, ALWAYS scores No. 1 in a widely accepted comparison of global math skills, it concluded, “Singapore’s textbooks build deep understanding of mathematical concepts through multi-step problems and concrete illustrations that demonstrate how abstract mathematical concepts are used to solve problems from different perspectives.”

By contrast, the study said, “traditional US textbooks rarely get beyond definitions and formulas, developing only students’ mechanical ability to apply mathematical concepts.”

Many eminent mathematicians agree.  In fact, according to an LA Times article on March 9 2008, it is hard to find a mathematician who likes the standard American texts, or dislikes Singapore’s.

An article by Barry Garelick from Stanford’s Hoover Institution shows a US textbook side by side with the Singapore Math book.  “Singapore Math’s textbook is thin, and contains only mathematics — no games.  Students are given brief explanations, then confronted with problems which become more complex as the unit progresses.”

By contrast, the US text, “typical of many math textbooks in the US is thick, multicolored, and full of games, puzzles and activities to help teachers pass the time” but which rarely challenge students.

Singapore’s text contains 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 US 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.

According to the Hopkins article, “While a single lesson in a US 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 (American Institutes for Research, a government group) 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: the number of topics covered 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.

The Singapore 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,” writes Garelick in the Hoover article, “mainstream American math texts and curricula frequently rely on a ‘spiral’ approach, in which topics are revisited and reviewed.  The expectation is that not all students achieve mastery the first time around.”

An Ohio schoolteacher summed up the “spiral” approach on an Internet math forum by writing that 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.”

But the most important feature of Singapore’s texts, according to Garelick, is an ingenious problem-solving strategy built into the curriculum.  Word problems are for most students the most difficult part of any mathematics course.

Singapore’s texts help solve the problem.  A key step in problem-solving is model-drawing.

Typically, in US texts, students are taught to use a method called “Guess and Check” — trying combinations of numbers until the right numbers are found that satify the conditions of the problem (a method that many mathematicians consider inefficient). 

The Singapore bar-modelling technique not only provides a powerful method for solving problems, but also serves as a link to algebra.  Symbolic representation of problems, the mainstay of algebra, emerges as a logical extension of the bar-modeling technique.

On Your Mark — Get Set — Think!

The LA Times article describes the classroom of Arpie Liparian, a first grade teacher.  She stands in front of her class with a stopwatch.  The only sound is of pencils scratching paper, as the students race through the daily “sprint,” a 60-second drill that is a key part of the Singpore system.  The idea, once commonplace in math classrooms, is to practice problems until they become second nature.

Critics call this “drill and kill,” but one math coach calls it “drill and thrill.”  Liparian’s students don’t all finish all the problems in 60 seconds; only one girl gets all the answers right.  But they are all bubbling with excitement, and Liparian praises every effort.  “Give yourselve a hand, boys and girls,” she says when all the drills have been corrected.  “You did a wonderful job.”

That math coach, Robin Ramos, says that what isn’t obvious to the casual observer is that this drill is carefully thought out to reinforce patterns of mathematical thinking that carry through the curriculum.

“These are ‘procedures with connections,’ ”  Ramos says, arranged to convey sometimes subtle points.  This thoughfulness — some say brilliance — is the true hallmark of the Singapore books, according to advocates.

Yoram Sagher, a math professor at the University of Illinois, says that after 10 years of studying the Singapore curriculum, he still has “very pleasant surprises and realizations” while reading the books.  He is constantly amazed, he says, by the “gentle, clever ways that the mathematics is brought to the intuition of the students.”

It is true that the Singapore texts are not as teacher friendly as most American texts.  “They don’t come with teahers’ editions, or two-page foldouts with comments, or step-by-step instructions about how to give the lessons.  And in our math-phobic society, many teachers lack a strong math foundation to begin with.

Key to implementing the Singapore Math curriculum —  and achieving the spectacular results seen in a few select schools — will be intensive training of teachers.

sources: Barry Garelick’s Hoover Institution journal article  on “Miracle Math”from fall 2006; also Mitchell Landsberg’s article in the LA times on 3/9/08 (www.latimes.com ); and SDE flyers promoting the Singapore Math Intensive Institutes.  


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