Last week I presented with Lauri Susi at the National Council of Teachers of Mathematics (NCTM) 2012 Annual Conference in Philadelphia.  Here was our session description:

470 – Technology + Singapore Strategies = Number Sense
Lead Speaker: Cassandra Turner
Co-Speaker: Lauri Susi

Visual reasoning is a powerful tool for making sense of mathematics. Learn successful visual strategies and instructional methods from Singapore that allow students to develop a deeper understanding of number concepts using hands-on manipulatives and software. Walk away with strategies for guiding students’ learning that you can use tomorrow.

We displayed the above image of lions on the screen while discussing the Concrete-Pictorial-Abstract progression of understanding. A teacher raised her hand and said something along the lines of:

I don’t like that picture. There are male lions and female lions, they aren’t the same. I can’t add them together and students get confused in upper grades when they think that these can be added.

Which is such a great comment. Why? Because this illustrates one of those interesting points that isn’t always in a student textbook and as the teacher you have to be aware of it : labels matter. Yet it isn’t so obvious at a kindergarten level.

2 male lions and 3 female lions make 5 lions altogether.

Well, they’re all lions and we’re looking at a part-whole understanding of addition. Here’s another image from the kindergarten book:

2 boys and 3 girls make 5 children.

2 daisies and 2 tulips make 4 flowers.

So how does this apply to later, more advanced concepts? Consider:

• 2 ones and 3 ones make 5 ones.
• 2 tens and 3 tens make 5 tens.
• 2 tens and 3 ones make 23 ones.
• 2 dimes and 3 pennies make 5 coins and they also make 23 cents.
• 2/5 and 3/5 make 5/5
• 2/5 and 3/4 make…hmmm, we need some common terminology here.

Thanks kindergarten and first grade teachers for laying this foundation!

Wait, math from Singapore? Isn’t that some little island in Asia?

Primary Mathematics is based on program of study introduced by the Ministry of Education in Singapore in 1981, a time when Singapore’s students were middling in math. Fifteen years after the adoption of its new Primary Mathematics Syllabus, Singapore students led the world in global Math achievement tests (Singapore topped international rankings first in 1995, and again in 1999, 2003 and 2007).

The Singapore math success story—from mediocre to world-class in a generation—is no secret. The curriculum provides students with a solid foundation in mathematics by focusing on visual understanding, connections, number sense, mastery, and word problems.

Concepts in Singapore math are taught in a concrete – pictorial – abstract sequence

Hands-on manipulatives or real life objects are used to demonstrate the concept, then students use and create pictorial representations. This interim visual step is typically missing from many curricula used in the U.S. It provides a transition from the words to an abstract algorithm. The goal is always to use the concrete and visual components  to get to a standard algorithm.

To gain number sense, students are taught to make connections between topics. While first graders will still work on “fact families”, Singapore math also uses a pictorial representation called a “Number Bond” to help students see the connections between addition and subtraction.

Fact Families:                  Number Bonds:

Understanding numbers and operations is critical to mathematics. Singapore materials focus on place value to provide a deep knowledge of numbers. As students work with and manipulate numbers, they work towards fluency by learning and using mental math strategies.

For example:

“If I know that 7 and 3 make 10, I could solve the problem of 47 + 8 by breaking the number 8 apart into 3 and 5. Adding the 3 to 47 gives me 50, then I can easily add on 5.”

These mental math skills show flexible thinking and provide a “check” students use when the algorithm is learned. I was in a first grade classroom last week where the teacher was talking about addition and subtraction strategies with her students. They were working with numbers like 9 + 5 and the teacher had asked the students how they got their answers:

“I counted on from 9”
“I took 5 apart to 1 and 4 and made a ten first”
“I used automaticity!”

To get to mastery, students work on focused concepts and skills. U.S. curricula are typically criticized for being “A mile wide and an inch deep”. Topics continually spiral and “It’s ok if kids don’t have their multiplication facts memorized this year, we’ll reteach them again next year.”

And next year and next year…

Not so with schools using Singapore math. In first grade, students will learn and master multiplication of twos and threes within 40. In second grade, they’ll master multiplication and division by 2,3,4,5 and 10. Each year builds on the prior foundation and extends student understanding. By the end of third grade students will have mastered all of their multiplication tables as well as multiplying and dividing by a single digit. Yep, they will even become proficient with  the dreaded “long division algorithm”.

Understanding problem solving

Another component of mastery is the ability to take what you already know and apply it in a new context. Remember being tortured in school with story problems? The heart of the Singapore curriculum is an emphasis on problem solving — and that means word problems. They are incorporated throughout the materials to provide context to each topic as it’s taught. The key to solving these begins with a bar model, or pictorial representation of the word problem. For instance:

John has 34 baseball cards and football cards in all. He has 18 baseball cards. How many football cards does he have?

John has 18 baseball cards. He has 3 times as many baseball cards as Paul does. How many baseball cards does Paul have?

2/5 of the students in a class are boys and the rest are girls. There are 35 students in the class. How many boys are in the class?

Singapore math is a great foundation for elementary math success. Working with teachers in their classrooms, I see the impact the materials have on students every day. Singapore math can help make every child in every classroom a competent and confident mathematics student.

If you’ve been wondering what the difficulties are when implementing Singapore math, look no further. This school in D.C. has them all; school closures, lack of enough professional development, mobile student and teacher population, and it’s a dual-language school. Standardized test scores dropped significantly after the change to Singapore math.

The story  evoked responses from many in education. Joane Jacobs mused:

The fact that it ( Singapore Math) requires elementary teachers to understand math well has to be a serious obstacle.

In a letter to the editor dated June 14, 2011, Dr. Alan Ginsburg suggested that the problem at Bruce-Monroe may be bigger than just the Singapore math adoption. He pointed out that the school’s reading scores

declined by 15 percentage points in a single year, and Hispanic students’ scores declined by 21 percentage points.

Bill Jackson, in another great Daily Riff article (Going Beyond Singapore Math: Resisting Quick Fixes), ennumerates the complex issues behind plunking a program like Singapore math into the American classroom.

While most educators familiar with Singapore math agree that it is not the oft-quoted “silver bullet”, Jackson reminds us that:

if we keep throwing out promising ideas just because they don’t immediately improve scores on tests whose quality is questionable at best we’re doomed to repeating the haphazard and fragmented reform efforts that got us here in the first place.

He closes with a word to schools that are currently using Singapore math:

I would like to say that you are definitely moving in the right direction. There will be challenges along the way but they are the same ones you would face with any math program and they can be overcome if you understand the bigger issues behind effective math teaching and learning.

Faced with so many challenges, it’s impressive that Bruce Monroe’s  instructional coach, Nuhad Jamal remains upbeat about the school’s Singapore math adoption.

Melrose Elementary School Mathematics/Science/Technology Magnet has seen impressive results with their new Singapore Math program, Primary Mathematics. Math Coach Lacy Endo-Peery announced:

We had a 32% increase in students who were advanced or proficient in Math last year. Our students went from 43% to 75 % in one year!

The school has put together an informative 8 minute video about their experiences with Singapore Math. Its always helpful to hear  teachers sharing the reasons why Singapore math works with their students, the importance of sustained training, and why the school selected Singapore math.

Click here to view the embedded video.

Singapore math materials tend to be light on practice for mastering math facts. To compensate for that, many schools supplement using the activity in the video referred to as a math sprint. These were designed by Professor Yoram Sagher (also in the video) and are used widely in U.S. schools. While sprints are designed to help students become fluent with computation, they are not a part of the Singapore math curriculum. (Sprint books for teachers are available at SingaporeMath.com.)

Reynolds School District in Fairview, Oregon is expecting student achievement to rise with their adoption of the Math in Focus version of  Singapore math materials. Before the adoption, the 12 elementary schools in the district were using different curricula, which was an issue for students that changed schools within the district.In the video, both teachers and students report  how much they like that visual component of the materials.

Click here to view the embedded video.

In September 2007, NBC’s Today Show  launched an ambitious 13-year project to follow a school class from kindergarten through their high school graduation. Students in the Today Show’s “Class of 2020″ segment are now in 3rd grade. From an episode that aired on May 2, 2011, we learn that the class of 2020 is learning Singapore Math.

This story does a very nice job of presenting some of the key features of Singapore Math and the ways American teachers are effectively implementing it. Mrs. Kaprelian explains the curriculum’s emphasis on place values, mental math and mental flexibility with math, all leading to a firm grasp of bar modeling. Note how Mrs. Kaprelian highlights the important role of manipulatives (in this case, cubes) in the concrete -> pictorial -> abstract progression. That groundwork leads seamlessly to the use of the bar model method to solve highly complex problems.

I Wish I Had Singapore Math

The role of parents also is addressed. Mrs. Kaprelian offers lessons to parents to introduce Singapore Math and tell them how it differs from other elementary math curricula. Initially, parents may be puzzled by Singapore Math, but typically there’s an “Ah Ha” moment when they get it and say, “I wish I had (Singapore Math).” (This is very common, I see the same reaction whenever I host Parent Nights at schools implementing Singapore Math.)

Involved parents, with knowledge of Singapore Math, on the same page with their child’s teacher…no wonder math is Eileen’s favorite subject.

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Thanks to a $1.2 million grant, six North Carolina schools will participate in the Singapore Math Pilot, a partnership with the Department of Public Instruction and State Board of Education. The selected schools were among 19 targeted by the initiative. The Singapore Math Pilot will provide approximately $240,000 over six years for teacher training and the purchase of Singapore Math workbooks and manuals.

The schools participating in the Singapore Math Pilot are:

* Murphey Traditional Academy, Greensboro
* Elizabethtown Primary School, Elizabethtown
* East Arcadia School, Riegelwood
* Eastfield Global Magnet School, Marion
* Gallberry Farm Elementary School, Hope Mills
* North Wilkesboro Elementary School, North Wilkesboro

The Singapore Math Pilot is the result of an effort launched by North Carolina foundations, policymakers, educators and business leaders in 2008, when a delegation visited Singapore. I’ll share more about this project in coming weeks.

Here’s Milgram on Everyday Math:

There is a pretty good program hidden inside EM.  But no more than 1 in 500 teachers are capable of locating and delivering it.  However, that one teacher would almost certainly be able to do better on her own.

Both Milgram and Wurman are pretty warm and fuzzy on Singapore Math, though.  From the interview with Milgram (full interview):

JM: There are no major deficiencies in the Singapore program, just a few points where it could be better than it is.  On the other hand, the recommended lessons in EM are mostly useless.

ZW: Proficiency is hard to define. I would use the preparation for an authentic Algebra 1 course (Nat’l Advisory Math Panel definition) instead.

TERC = 2,

EDM = 4,

Saxon = 7 or 8,

Singapore (Primary Math) = 10

Fourth-graders, from left, Chloe Bernal, Kristofer Kimes and Emma Leamy are ready to answer a question in their math class at Santa Catalina School. The school uses a method of teaching called Singapore Math. (REG REGALADO/Herald Correspondent)

From The Herald, Monterey County:

NEW MATH = HIGH SCORES: Singapore system working at Santa Catalina
By John Sammon

It seems a small thing, concentrating on basics, making sure students master concepts before moving on, but proponents of Singapore Math say the system is dramatically improving math scores at Santa Catalina School.

“We had a good math program before, but we wanted a great math program,” said Christy Pollacci, division head at the private K-12 independent Catholic school in Monterey.

Singapore Math specialist and sixth grade teacher Bill Davidson on the Singapore Math sequence:

Davidson said a lack of emphasis on teaching basic skills in the lower grades is partly to blame for poor test results at schools nationwide. For example, students are expected to grasp algebra and geometry without having mastered fractions and ratios.

“What makes Singapore Math special is the sequence in which the skills are taught,” Davidson said. “Addition and subtraction aren’t taught as separate subjects, but simultaneously, instead of being compartmentalized.”

Maybe it is time to try a new way of teaching math. Like Singapore math, for example. While Singapore math now is being taught as part of a pilot program in nine Lexington schools, don’t be surprised if it soon is taught in schools across the state. That’s because the early results from the schools using Singapore math have been positive.

Full article: Singapore math: Expect more schools in state to copy method used in Asia.

More on Singapore Math in Kentucky: Fayette County to expand Singapore Math program.

Utah’s budget situation played a role in the fate of S.B. 179. However, before adjourning, the Legislature did include a Singapore Math incentive program as an item worthy of further study prior to the 2012 Session.

Under H.J. R. 24, the Master Study Resolution, the Legislature gives the Legislative Management Committee items of study for consideration prior to the 2012 Annual General Session. Items may be assigned to the appropriate interim committee, which is to study and make recommendations for legislative action in the 2012 Session.

H.J.R. 24 includes the following math study items:

• Math Instruction – to study a proposal to provide a pilot program for incentives for Singapore math instruction.
• Algebra and Geometry Pilot Program – to study whether to provide a pilot program for honors algebra and geometry.
• Secondary Math Requirements – to study high school math requirements versus college readiness.

H.J.R. 24 passed both the House and Senate without opposition.