It can’t all be Singapore Math…

This tweet posted by the National Council on Teacher Quality (@NCTQ) caught my eye:


Now, I’ve heard decomposing called “branching” but can’t remember ever seeing this in a Singapore textbook. Where did this problem come from?

It’s nice that NCTQ recognizes Singapore’s Math as “tops in the world.” But it’s discouraging to see methods and terminology that are not a part of the Singapore curriculum attributed to it. Especially in the context of the nasty debate about CCSS. And especially since Singapore’s math curriculum–with its rigor, coherence, and focus–is often cited as a basis for more rigorous standards, including CCSS.

The problem posted is based on the concept of “Number Bonds,” which calls for students to decompose numbers (this is the term used in Singapore and in all major Singapore Math® textbooks distributed in the U.S.). Below, I’ve posted some examples of how this concept is presented in Singapore Math® series available in both the U.S. and Singapore.

This matter points to my BIG concern: As publishers and others adapt Singapore’s Math for the American market, new approaches creep in. These often are not based on the curriculum that helped Singapore’s students go from mediocre to best in the world in a dozen years. I’ve written about this in my comparison of Singapore math textbook series available in the United States.

So my plea to NCTQ: please use examples from an actual Singapore mathematics text when citing the components that make it so successful. And feel free to ask if I can help you find those examples.

Number Bonds problems in Singapore Math® textbooks

Here are some materials covering Number Bonds and “decomposing” numbers from actual Singapore textbooks:

From My Pals are Here, the most-used materials in Singapore:

MPAH 3A Mental Addition

From the U.S. Edition of Primary Mathematics, available in North America since 2003:

PM US 3A Mental Addition

From the Common Core Edition of Primary Mathematics, released in the U.S. market in 2014:

PM CC 3A Mental Addition_0001

And finally, from Math in Focus:




Ugh! One more similar tweet from NCTQ.






Manipulatives Make the Math Concrete

Manipulatives and Models
From a school that introduced Math in Focus materials this fall comes a great image of a fourth grader working with manipulatives to understand both algorithms and bar modeling. The class is learning long division. Number disks are a vital part of developing number sense in Singapore curricula.

Parnassus pennies
Another school is using Primary Mathematics and the class is doing the first lesson in multiplying and dividing by twos (Count by Twos). Students hadn’t used a lot of manipulatives before. This student excitedly exclaimed:

Hey, this is really useful!

Comments from observing teachers provided some interesting insights:

Wow, it sure is loud!

You can use a pre-cut sheet of felt from the craft store, or a laminated mat to help deaden the sound of working with louder manipulatives.

My kids would be bored to tears with this activity.

And she’s right, they would have. Her students were the higher ability group and need fewer concrete examples to understand the concept. (Note, not zero concrete examples, just fewer)

Number Discs
The red, white, orange discs with large numbers and the square set are available at as well as many online stores. The set with the smaller numbers is sold in conjunction with Math in Focus materials from Houghton Mifflin and corresponds to the colors used in the textbooks.

Looking for more on manipulatives? Check out this post: If I had a million dollars, ok $1000…

Singapore Math in Ghana: Working with Teachers at the Association International School

Association International Teachers gives "thumbs up" on Singapore Math

Sometimes, life throws you the most wonderful curve balls. Late in July, I was contacted by Audrey Doryumu, Head of the Association International School in Accra, Ghana. Six weeks later, I was on my way to spend a week working with her teachers as they prepared to teach Singapore Math.

Association International School (AIS) has a student body that is both local and global; many students attend AIS while their parents are posted in Ghana for work, giving it a wonderful diversity of experience. International teachers provide unique perspectives to the school’s students as well.  The school prides itself on working with the Ghanian, British, and American systems of education and plans to offer an International Baccalaureate Diploma Program when it grows to include 11th &12th grades.

Morning Open House for new students was crowded!

Implementing Singapore Math

Association International School  is so excited to be the first school in Ghana to use Singapore’s Primary Mathematics. Head of School Audrey Doryumu considered starting the Primary Mathematics Standards Edition for the students last school year, but wanted to ensure students had the necessary place value skills to truly be successful and on grade level. The teachers spent last school year backfilling some gaps and hitting place value concepts hard, and feel students are ready to go with Primary Mathematics materials this year.

Delivery to Ghana is a challenge, so the books were delivered first to New Jersey, then sent in shipping containers to Accra. The school is still awaiting some workbooks for new students.

 Always more to learn!

After four invigorating  days of training with Singapore Math concepts and materials, we ended our week with a test. That’s right, each teacher took the “A”-book placement test for the grade level they will be teaching.

The 5th – 7th team tackled the 5A placement test and found much to discuss (and debate!) over this question:

Estimate the value of 492,396 x 7.

Should they be thinking 500,000 x 7 or 500,000 x 10?

The fourth grade team discovered that teaching mental math was going to require some practice on their part. I always mention that we, as teachers are “handicapped by our superior knowledge“. We know algebra and we have certain strategies for computation that we are used to using. The mental math strategies taught in Primary Mathematics are different than many teachers have worked with and it is important to practice to become fluent with them, particularly if teachers are used to relying on pen & paper. (Or mobile phones).

Second Grade was surprised to see students were expected to know the equivalence of pounds and grams.

18. Fill in the blanks with lb or oz.
(a) The apple weighs about 6 _____.
(b) The watermelon weighs about 5 _____.
(c) 28 grams weigh about the same as 1 ______ .

We pulled out the 2A text book and found the only reference to this on a textbook page. There was no additional discussion included in the Teacher’s Guide.

Having teachers new to Primary Mathematics take their placement test was a fabulous learning exercise for the teachers and one I’m sure I’ll be using again.

It was such a pleasure to visit AIS and spend time with their committed, professional teachers and staff. Thank you Audrey Doryumu, for inviting me to Ghana and giving me the opportunity to work with Association International School. I look forward to visiting the school next spring to get an update on their Singapore Math  adoption and to see how far the students and teachers have come.

By the way, Association International is always interested in bringing exceptional teachers to Ghana. If you’re looking for a rewarding teaching experience, contact their Human Resources department.

Last year, former U.N. Secretary General Kofi Annan visited the school:




Singapore Math Adoptions – including Corporate Support – Among News from the summer of 2012

More adoptions of Singapore Math are in the news, with notable support from corporate partners in a couple instances…

Ogden district invests in Singapore Math program

Following a very successful pilot of Singapore Math at three of its elementary schools, the Ogden (Utah) school district is adopting the curriculum district-wide. Leanne Rich, the district’s coordinator for curriculum and professional development, said of the success of the Singapore Math pilot program:

We saw immediate, dramatic results…Now what we will have is independent mathematicians for all our students.

Rich also noted that students don’t have to rely solely on the teacher for everything — they learn to think independently.

Jessica Namovicz, a first-grade teacher at James Madison (one of the pilot schools), said the program teaches students how to manipulate numbers and to see numbers in concrete terms:

I can watch them set it up in their heads.

As an aside, it’s nice to see the headline that indicates the District’s implementation of Singapore Math is an “investment!”

DPS considers Singapore math pilot program for Y.E. Smith

Next week, the Durham (North Carolina) Board of Education will consider a proposal experiment with Singapore Method Math at Y.E. Smith Elementary School thanks to funding from the SAS Institute.

Lewis Ferebee, Durham Public Schools (DPS) chief of staff, said that the pilot program aligns with the new Common Core curriculum standards that go into effect this fall, as those standards call for problem-solving skills and depth of understanding in the first year.

Caroline McMullen, director of education initiatives at SAS Institute, said that the prominent software engineering company has a vested interested in making this pilot program work: SAS wants workers skilled in mathematics and statistics:

We’re a global company, but we want to focus on North Carolina.

While acknowledging cultural distinctions between Singapore and Durham, area superintendent for elementary schools Stacey Wilson-Norman, said:

The focus on problem-solving and emphasis on the essential math skills recommended in the National Council of Teachers of Mathematics Curriculum Focal Points aligns with our focus….No one thing yields substantial and continued success. Key transformation strategies have been selected to aid in the progress of Y.E. Smith to support instructional and operational changes. We are very proud of the recent results achieved and see a shift in the culture of learning.

MasterCard Grant Helps Train Wentzville Math Teachers

Since the Wentzville (Missouri) School District implemented the Singapore Math curriculum in 2008 (funded with a grant from MasterCard), improvements in student test scores have continued to outpace the state average. MasterCard provided funding for additional Singapore Math teacher training this summer.

Curriculum Coordinator David Brothers said:

Singapore Math makes sure that students have a deep understanding of mathematical concepts before getting them to the memorization of traditional algorithms and that allows the teachers to dive into the rigor much sooner and at deeper levels than a traditional math curriculum.

And you thought schools took the summer off.


Implementation challenges: It’s not necessarily the curriculum

Sometimes the strategies used in the Singapore Math materials look different. Number bonds, bar models, place value charts, arrays and area models can be unfamiliar to parents. Most schools adopting Primary Mathematics host Parent Nights to walk parents through the new materials, the program and to share why the school decided to switch from their old curriculum.

I’ve done dozens of these parent nights and common concerns run through the questions. After a presentation and Q & A parent session this week, a parent approached me about her son’s home enjoyment that afternoon.

“How am I expected to help my fourth grader?” she asked, “This Singapore Math is so different.”

She opened her son’s 4A workbook and showed me the problems she couldn’t help her son with:

Unfortunately for this parent, there’s nothing “Singaporean” about order of operations.

She couldn’t help her son because she didn’t remember elementary school math. In fact, she had never heard the term “Order of Operations”. I tried, “Please Excuse My Dear Aunt Sally,” something many adults were taught back in the day… Nope, that drew a blank as well.

After I explained what the order of operations is, I offered the parent two pieces of advice.

  1. Include a note with her son’s home enjoyment, something along the lines of “We struggled with these problems.” The teacher needs to know this. Home enjoyment is practice for your student and provides feedback for their teacher. The teacher needs to know if the lesson taught that day at school could be completed individually by the student that night at home. If not, there was a breakdown somewhere.

This parent note tells the teacher a couple of things:

  • The student was able to complete the first two parts of the assignment that included problems with two operations, but couldn’t work the final exercise where the problems had three operations.
  • Something was lost between the teacher’s lesson and this student. Was he in the bathroom? Did the teacher’s lesson and guided practice not include three operations? Are there attention issues? Did the student just not “get it” and not ask questions? Many things could have created this disconnect. Was it a single student, or are there more that struggled?
  • This parent may not be able to help her son with 4th-grade math.
  1. Pick up a copy of a book on elementary mathematics. One of my favorites is Arithmetic For Parents: A Book for Grownups about Children’s Mathematics.  In the foreword, the author includes insights from his time in an elementary classroom:

Elementary mathematics isn’t simple at all. It has depth and beauty.

The book is written for parents that want to be an active participant in their child’s studies, as well as the “reader who wishes to return to his childhood mathematics, from a different angle.”

Good math teaching is just good math teaching. While there are some differences in the strategies used in the Singapore books, teaching math so students understand the concepts as well as master the algorithm or rule is the goal.

Do you help your child with their home enjoyment? What happens when you are fuzzy on the concepts your child is learning?