## Making math masters: A brief overview of Singapore Math®

My students love math class. In fact, many will tell you math is their favorite subject. Why? They’ll tell you it’s because Singapore math is fun. I’d say it’s because once they understand how math works, they become confident in their abilities. So what exactly is Singapore math?

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

Primary Mathematics is based on a 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 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:

1)  Ginny has 40 cherry and grape gumballs in all. She has 24 cherry gumballs. How many grape gumballs does she have?

2)  Ginny has 24 gumballs. She has 3 times as many gumballs as Paul does. How many gumballs does Paul have?

3) 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?

4)  The ratio of the number of boys to girls in a class is 2:3. After 6 boys join the class, the ratio becomes 5:6. How many boys were in the class at first?

This is a sixth-grade problem from a unit on changing ratios. Can you see the answer? Note that the number of girls doesn’t change.

1 unit = 6 boys

4 units = 24 boys

### Mastering Math Makes Math Fun!

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.

1) Ginny has 16 grape gumballs

2) Paul has 8 gumballs

3) There are 14 boys in the class

4) There were 24 boys in the class at first

Bar Models generated from ThinkingBlocks.com

## 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.

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## One School’s Challenges with Singapore Math

D.C.’s Bruce-Monroe school faces challenges as it tries Singapore math method
The Washington Post 6/6/2011

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.

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## Successful implementation: Buying books is just the first step

Schools considering Singapore Math programs in their schools frequently ask me what the biggest challenges are when adopting  the curriculum. Let me give you an example from a third grade classroom I visited recently.

The math period started with a mad math minute type of activity of either addition or subtraction, depending where the students were working.  For the lessons on multiplication and division by 8’s and 9’s, the teacher chose to list the tables from 2 x 8 through 9 x 8 on the whiteboard and have the students copy them down, like this:

Next, the teacher had the students make flash cards and quiz each other.  Finally, in a class of 27, they played around the world. The game where two students compete against each other to see who can get the answer to the problem on the flash card faster.

The lesson in the textbook does include some multiplication charts. The textbook was open on the teacher’s desk and she did refer to it at least once during the lesson:

Primary Mathematics 3A Textbook, U.S. Edition:

Notice how the textbook draws out a student’s prior knowledge to show the patterns behind the computation?

The 3A Teacher’s Guide includes a more comprehensive lesson based on a deeper understanding of the number 8 and it’s multiples. I couldn’t find it in the room.

##### (Click to enlarge)

Can you see the difference in the depth of a student’s understanding  after the Primary Mathematics lesson?

Note that the subsequent three lessons are:

• Multiplying a 2 or 3 digit number by 8.
• Dividing a 2 or 3 digit number by 8.
• Word problems that require multiplying and dividing by 8.

The sequence of lessons follows the same pattern for the number 9.

When I asked the teacher about the lesson, she essentially said, “well, I didn’t think to look at the teacher’s guide. I’ve always taught this way.” She’s new to the school and only had about 2 hours of training.

Back to the original question. One of the biggest challenges for schools adopting the Singapore Math curriculum is the need for adequate training. If teachers don’t understand what makes Singapore different or if they lack content knowledge,  they’ll continue to teach the way they always have. Effective training will give teachers an understanding of Singapore Math’s philosophy and approach and leave them with confidence in their ability to teach it.

Buying the curriculum is the first step. Successful schools invest in content-based training.

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