Learning from the East: The benefits of persistence

Elementary Math class in Singapore by Cassandra Turner, Singapore Math Teacher, Trainer, CoachWorking with schools, teachers and parents over the last five years, I’m often asked whether cultural differences can explain why Singapore’s students have led the world in international math standings for 15 years while US students rank no better than mid-pack.

When I visited Singapore in 2007, I learned how the country decided to focus on building strong Singaporean citizens beginning with their earliest education.  The country’s mathematics curriculum (Primary Mathematics) was developed in the early 1980s with this goal in mind. At that time, Singapore’s students were mediocre at math. Within a few years after the launch of the second edition of Primary Mathematics, Singapore’s students topped the international TIMSS study.

To me, it’s quite easy to attribute much of Singapore’s Math success to changes in how it approached education, including, most importantly, the new curriculum. Could Singapore’s culture have changed dramatically between 1984 (when Singapore’s students were ranked 16th of 26 in the Second International Science Study) and 1995 (when they ranked first in the TIMSS study)?

Today, much attention is paid to “Tiger Mothers,” who, in the words of the Economist,

“load their cubs down with extra homework and tuition to make them excel at school.”

This trend seems more recent; it’s also one which, remarkably, Singapore’s current Prime Minister wants to curtail (http://www.economist.com/node/21563354).

A more subtle consideration concerns expectations; how do parents and teachers ask students to engage in schoolwork?

I had a driveway moment this fall when NPR ran a story (http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning) titled, “Struggle For Smarts? How Eastern And Western Cultures Tackle Learning.” The piece focuses on the importance of persistence to a student’s learning. Reporter Alix Spiegel cites several examples, then gets to the heart of the issue:

“For the most part in American culture, intellectual struggle in schoolchildren is seen as an indicator of weakness, while in Eastern cultures it is not only tolerated but is often used to measure emotional strength.”

Reporter Spiegel then chooses to NOT to choose between East and West. In this silence, though, I believe there is a teachable moment for those of us in the West.

In training sessions with teachers, it is not uncommon to encounter resistance when I advise (insist) that teachers give students the opportunity to really work on math problems. This can be a difficult skill for teachers to learn.

And if teachers are inclined to want to move their class along before giving students a chance to truly work the math, parents can worse. They are unaccustomed to and uncomfortable at seeing their children struggle, unable to finish their home enjoyment (aka homework). Parents sometimes can be too quick to either give their kids a pass (well, you have tried, haven’t you?) or demand an explanation of the teacher (why can’t my child do the homework?).

Here’s where I find that it’s critical to have laid the groundwork and properly set expectations. Teachers need patience (whew, do teachers ever need patience!). They must let their students work through problems, even if they end up struggling and having to start over. And parents need to appreciate that homework (honestly completed or struggled with) can be the best feedback loop for teachers.

Pointing at cultural differences to rationalize a lack of math proficiency in many of our students serves no one. Instead, I think there’s a lot to be gained by asking that western students work a bit more to earn some of the praise they frequently receive.

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Thoughts from NCTM session on Singapore Math + Technology

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!

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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?

gumballs (1)

 

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

paul_and_ginny

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?

students

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?

Students 2

 

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.

 

Answers to Word Problems

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

 

 

 

 

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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Singapore Math School Videos

Two videos were recently published by schools that adopted Singapore math programs last school year.

Melrose Elementary School Mathematics/Science/Technology Magnet has seen impressive results with its 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. It’s 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.

[vimeo]http://vimeo.com/25362323[/vimeo]

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 the visual component of the materials.

[vimeo]http://vimeo.com/25147891[/vimeo]
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