In a report, the New York Times compared this problem to that of the “color-changing dress that blew out the neural circuits of the internet.” The story’s headline: “A Math Problem from Singapore Goes Viral.” Wow. The world’s response to the “Cheryl’s Birthday question” has inundated my “Singapore Math” Twitter feed. The problem:

Some initial reports suggested that this “Singapore Math” problem was appropriate for primary grade students. The Guardian initially asked: “Are you smarter than a Singaporean ten-year old?” Fortunately, the true source emerged rather quickly. This problem was part of a Math Olympiad challenge that organizers thought could be answered by only 40% of the most gifted high school students. This prompted the Guardian to instead ask: “Are you smarter than a Singaporean 14-year old?”

As we now know, this is not really a problem asked in any classroom using a Singapore Math curriculum. In fact, it isn’t really a math problem; instead, it is a logic problem. And a really challenging one at that.

Many of those who commented said something to the effect that, “it made my brain hurt.” Others chose to rant about Cheryl; this was the approach of the New Yorker in its Daily Cartoon for April 16. [Need help with the problem? See “How to Figure Out Cheryl’s Birthday” by New York Times science writer Kenneth Chang.]

In the midst of all the noise, there were a few responses that offered some clarity.

In a video clip, the Globe and Mail said that the problem, “tapped a nerve…our math phobia.” John Mighton, founder of Jump Math says that this is a universal problem.

I KNOW that math anxiety is a reality, and one that I address in almost every encounter with teachers and parents.

But most insightful of all may be the assessment of Libby Nelson of Vox.com. Early in her piece, she says:

But the problem isn’t nonsense: it’s actually a test of logical reasoning skills. And questions like these help explain how Singapore’s students have come to rank as some of the best problem-solvers in the world — by being taught math differently, and well.

A 2005 study from the American Institutes for Research praised Singapore’s method of teaching math, saying it was much better than the American method. On reason was that word problems and real-world examples were used not just to show students that math is important outside the classroom, but to illustrate how math works.

This brings to mind my favorite quote about Singapore’s approach to teaching math from Dr. Yeap Ban Har:

We’re not teaching math, we’re teaching thinking through the medium of math.

Nelson discusses how Singapore’s students acquire problem-solving skills and become so good at math before asking whether Singapore’s methods can work in the U.S.

After working with more than 100 schools using Singapore’s Math curriculum, I know the answer to Nelson’s last question is an unqualified “YES.”

The Singapore and Asian Schools Math Olympiads (SASMO), creators of the Cheryl’s Birthday problem, have posted a new challenge. It also features Cheryl, this time with new pal Tom. Can you figure this one out?

The problem and solution are on SASMO’s Facebook page.

New bar modeling tool! **Conceptua Math** has a beta version of their bar model tool available to review. Check it out at **http://www.bit.ly/barmodeltool.**

They welcome your feedback.

Greg Tang has a fun fact automaticity practice app – and it’s a game! And there are iPad apps! Visit **Greg Tang Math for Kakooma.** Greg claims the record for the addition puzzle is 8 seconds, set by a student.

Rodel Foundation in Arizona has released a fabulous new book that schools will want in their library: * Math Power: Simple Solutions for Mastering Math. * This handbook is full of visuals and is written in English and Spanish. Here’s a page chock full of great definitions and pictorial models:

Handouts from my sessions:

**NCSM: **#232 Strip Models Tape Diagrams Bar Models Oh My!

**NCTM: **#126 Strip Models Tape Diagrams Bar Models Oh My!

These new pages should help.

Every year, I respond to hundreds of inquiries from teachers, administrators and parents seeking more information about the Singapore Math curriculum.

Some want to learn more about Math from Singapore and why it is so successful. Others are looking for specific resources to use in the classroom or for home enjoyment. Others still are seeking to a higher level of knowledge so they can be more effective math coaches or trainers.

I’ve added three new pages to Singapore Math Source to steer you to the best available books for a variety of needs:

**Singapore Math® Editions – at a Glance: **Which series should I buy? See all your options.

**Best Books to Support Singapore Math in the Classroom: **Supplemental books for use with students.

**Best Books for Grown-Ups Wanting to Learn Singapore Math: **Title says it all, doesn’t it?

-Image via Indexed

The NCTM (National Council of Teachers of Mathematics) Annual Meeting & Exposition program is now online and it’s time for my annual review of Singapore Mathematics sessions.

Due to Common Core and the progressions documents, I’ve included sessions on Tape Diagrams and Strip Models as well as those on traditional Singapore Math® strategies**.** The number of overall choices is one more than the number offered last year.

Bad news? Most of the sessions overlap. Below are my thoughts on which session to choose, if you have a conflict.

**#5 A Model Approach to Teaching and Solving Word Problems
**Lead Speaker: Greg Tang

Visual models are the key to making word problems easier to solve at every grade level. We’ll explore a strategic progression from discrete, to part-whole, to tape diagrams, and then to double number lines that develops the algebraic skills needed for higher math.

**#12 Empowering Students to Deconstruct Word Problems
**Lead Speaker: MaryJo Wieland

Co-Speaker: Lisa Watts-Lawton

Solving word problems is not about underlining key words. Just as writers use organizers, mathematicians need specific models to deconstruct the meaning inherent in addition and subtraction word problem types.

**#36.1 Teaching Number Sense with Math Buddies, the Singapore Online Resource**

Exhibitor Workshop: Marshall Cavendish Education

Research shows that number sense is built on mastery of place value as well as number facts. We’ll discuss place value as a fundamental element of Singapore Math® as well as number bonds and part-whole thinking. We’ll make use of Math Buddies, a K-5 digital resource, to take students through the concrete-pictorial-abstract approach to number sense.

**Recommendations:**

*Not familiar with Ms. Wieland, so can’t comment. Math Buddies is a great digital resource for Singapore Math, and it will also be modeled at their booth. I’ll be in Greg Tang’s session, he’s always engaging!*

**#126 Strip Models, Tape Diagrams, and Bar Models, Oh My!
**Lead Speaker: Cassy Turner –

Co-Speaker: Lauri Susi

These visual components sit at the intersection of Common Core, Singapore Math, and now technology! Learn why this visual model for word problems is so powerful, try some problems from the simple to the complex, and investigate web-based programs and iPad apps that will help anyone incorporate this effective strategy into their classrooms.

**#144.4 Using Technology to Transform Singapore Math® in your Classroom!**

Exhibitor Workshop: Marshall Cavendish Education

Join us to learn about Math in Focus® Digi+™. This teaching and learning tool will transform your class: facilitating class instruction, activities, intervention and differentiation solutions, and deepening the school-to-home connections with practice problems, immediate feedback, and parental support in a fun, interactive environment.

**Recommendations:**

*Well, my session, of course!*

**#254.3 Meaningful Math Models and the Common Core
**Exhibitor Workshop: Houghton Mifflin Harcourt

Come learn about math drawings and other math models that can be used in the classroom to show the mathematical aspects of a situation. Students make math drawings on their MathBoards, where parts of a drawing can be used while a student is explaining their solution method.

**#312 Models to Solve Word Problems: Visualization to See Mathematical Relationships**

Lead Speaker: Andy Clark

Students struggle with word problems whether in elementary grades with a variety of whole number and fraction operations or the middle grades with ratio, proportion, and algebraic problems. This session will demonstrate the power of visual models to help students see mathematical relationships and solve even complex problems and applications

**#321 Singapore’s Model Drawing Approach with a “Units” Sentence**

Lead Speaker: Michael Winders

The Singapore model drawing approach can be used to solve a variety of word problems, but its true power lies in the way the process provides a bridge to algebraic thinking and techniques. I will show how a “units” sentence can be used to solve problems with diagrams, and how this idea transitions to purely algebraic solutions

**#346 Representations with Tape Diagrams? What’s That?**

Lead Speaker: Deborah Rutherford Lane

Tape diagrams help children to represent complex problems found in CCSSM testing. Bar models, in particular, work for all learners to make sense of complex word problems. This session will focus on how to lead children from beginning stages of whole number operations through fraction operation modeling from second up through sixth grades.

**Recommendations:**

*-> I’ll be checking out Michael Winders’ session on units.*

*-> Head to see Andy Clark, one of the authors of the Math in Focus series for a fast paced overview of Models*

**#470 Concrete-Pictorial-Abstract: Singapore’s Approach to Math Instruction**

Lead Speaker: Richard Bisk

Singapore’s students have excelled in international studies of math performance. The concrete-pictorial-abstract approach supports both conceptual understanding and procedural fluency. Abstraction gives math its power, but must be based on understanding. We’ll consider examples from place value, operations, problem solving, and even calculus.

**#494.3 Filling Knowledge Gaps with Critical Singapore Math® Approach (Gr. 3-5)**

Exhibitor Workshop: Singapore Math, Inc.

During Singapore Math® implementation, gaps in student knowledge can be a challenge. Upper elementary students frequently lack the foundation provided by the 1-3rd grade Singapore Math® Curriculum. In this session, you’ll learn the classroom-tested critical lessons and concepts students must master before jumping into their grade-level content.

**Recommendations:**

*-> I’ll be presenting the Singapore Math, Inc. session for them, but I’d love to see Richy Bisk’s examples from Calculus.*

**#549.6 Developing Strong K-2 Number Sense with Singapore Math® Primary Mathematics**

Exhibitor Workshop: Singapore Math, Inc.

Through the use of manipulatives and activities, this interactive workshop gives teachers practical understanding of concrete-pictorial-abstract (CPA) approach. Lean strategies for building strong number sense foundation, composing/decomposing numbers within 10 and regrouping within 20, and formative/summative assessments.

**#664 Ratio Tables and Tape Diagrams #notjustforRP**

Lead Speaker: Melissa Waggoner

Co-Speaker: Lindsay Kelley

Students learn how to use ratio tables and tape diagrams in the Ratios and Proportional Relationships domain of CCSSM. Then what? In this interactive session, we will explore how these tools can be used to build procedural fluency from conceptual understanding in other content domains, including the Number System and Expressions and Equations.

**Recommendations:**

*I’m intrigued.*

For some time, I’ve wanted to share stories of schools that have successfully implemented a Singapore Math curriculum.

To present the first such case study, I asked my colleague Beth Curran to summarize the adoption process at St. Anne’s-Belfield School, an independent Pre-K to 12 school in Charlottesville, Virginia.

Please contact me if your school has a story to contribute.

*by Beth Curran*

*Preschool – 6th Grade Math Department Chair, St. Anne’s-Belfield School*

*Singapore Math Teacher and Trainer*

It all began with a strategic plan. In 2011, St. Anne’s-Belfield School released its 2011-2016 Strategic Plan. The first of six goals focused on teaching and learning in the 21st century. Key elements to this goal included teaching with depth rather than breadth, teaching critical thinking and problem-solving skills, improving the quality of our computation, and ensuring that our pedagogy reflects researched based best practices. The Action Plan that followed gave direct mention to Singapore Math as a curriculum to explore.

While teachers felt strongly that the students were leaving our Lower School (grades Kindergarten through four) very well prepared for Middle School (grades five through eight), we had to ask a tough question; could we be doing better?

As the Lower School Math Coordinator at the time, I was charged with taking a critical look at the Lower School’s current math curriculum and learning all I could about Singapore Math. The more I learned, the more I was convinced that Singapore Math would be a great match for us. It was almost as if the Strategic Plan was written with Singapore Math in mind. The curriculum teaches concepts to mastery, focusing on depth rather than breadth. Critical thinking and problem-solving are embedded within the curriculum, not taught as a stand-alone unit. Concepts are introduced, practiced, and applied immediately to solve problems. Computation and numeracy are also a major focus. Check, check, and check!

Not all of the homeroom teachers were as enthusiastic as I was. It was a daunting task convincing them that learning a new math curriculum, on the tails of learning a new writing curriculum, was a good thing. St. Anne’s-Belfield’s Head of School, being the visionary that he is, saw an opportunity to not only implement a new math curriculum, but to change the way math instruction is delivered at the Lower School level. If we were going to ask our teachers to become Singapore Math specialists, why not hire and train dedicated math teachers? And that’s just what he did. Four math teachers were hired to deliver math instruction and these dedicated math specialists would co-teach math with the homeroom teacher taking on a supporting role. This had an added benefit of cutting our student to teacher ratio in half during math class.

With the faculty in place and the Primary Mathematics materials ordered, we set out to train our dedicated math teachers in Kindergarten through sixth grade. We contracted with Cassy Turner, Singapore Math Specialist and Trainer to work with our math teachers for an intensive one-week boot camp. We learned the ins and outs of mental math and the bar model. We asked questions, practiced, collaborated, practiced, designed an implementation schedule, and practiced. Cassy’s enthusiasm and extensive knowledge left us feeling confident to tackle the upcoming year. We knew professional development was crucial to a successful implementation and with that in mind we continued our relationship with Cassy throughout the year. She made three more trips to the school, observing and teaching lessons and providing her guidance to keep us on track.

Fast forward to today. We are now a year and a half into our implementation. Our students are stronger problem-solvers than ever before. Their computational skills have shown marked improvement. Their overall sense of number and place value has increased. Our students are confident and persevere through challenging problems.

We have done a lot of things really well. We understood and placed value on professional development. This is not a curriculum that can be picked up and taught from the Teacher’s Guides. Most teachers did not learn math the way that a Singapore Math curriculum is taught. Training is key. If not trained, teachers will revert to teaching math the way they learned it. Having a successful plan for ongoing professional development is critical to a successful implementation.

We put value on mathematics instruction at the Lower School level. We saw the need for math specialists and took a huge financial risk to improve our instruction.

We implemented the curriculum in Kindergarten through sixth grade. We felt so strongly about the benefits of the curriculum that we knew that even one or two years of exposure would be better than none. This has been one of the most challenging hurdles of our implementation. We worked with Cassy to anticipate and develop a plan for “back-teaching” missing skills. In grades three through six, this plan guided us through our first year and fortunately, Kindergarteners through second grade students benefited from needing very minimal “back-teaching.” Developing a relationship with a knowledgeable Singapore Math consultant is crucial.

If there was an area for improvement, it was parent communication and education. We hosted a parent night early into the school year to give parents an overview of the curriculum and a brief introduction to some of the components that are unique to Singapore Math. That wasn’t enough. Parents didn’t learn math the way their children were now learning it. The focus of Singapore Math is to develop conceptual understanding before learning the mathematical steps or procedures. Parents need to understand and support the school in teaching math this way. Parent education is not an option; it is a requirement of a successful implementation. In our second year, we designed a plan for parent chats spread throughout the year with topics including fact practice, mental math strategies, and bar modeling as a tool for problem-solving. Your professional development provider or consultant can assist you in designing a parent education program that meets the needs of your school.

Our journey continues and our students are stronger math students as a result. The first year was clearly the most challenging. Our commitment to professional development, perseverance, and acceptance of this unfamiliar approach to teaching math has guided us and we are confident that each passing year will continue to confirm the benefits of teaching a Singapore Math curriculum.

The beauty of pi, in part, is that it puts infinity within reach.

As a full-time trainer and instructional coach, I know the importance of professional development and continuing education. Since embarking on this career path seven years ago, I’ve attended annual meetings of both the National Council of Teachers of Mathematics and NCSM (formerly the National Council of Supervisors of Mathematics). Attending NCTM, NCSM and other regional, national and international math conferences and educational events fulfills my personal ongoing learning goals.

In 2012, I was thrilled to have a proposal to present at NCTM accepted! (Here are two posts on that presentation: tools and thoughts).

For 2015, I submitted similar proposals to both NCTM and NCTM…and *BOTH* were accepted. *Woot!* And good news, my co presenter will be Lauri Susi of Conceptua Math.

Here’s the description:

Lead Speaker: Cassandra Turner

Co-Speaker: Lauri Susi

These visual components sit at the intersection of Common Core, Singapore Math®, and now technology! Learn why this visual model for word problems is so powerful, try some problems from the simple to the complex, and investigate web-based programs and iPad apps that will help anyone incorporate this effective strategy into their classrooms.

The NCSM Presentation is on Tuesday, April 14, 2015, 10:00 AM – 11:00 AM.

The NCTM Presentation is on Thursday, April 16, 2015, from 11:00 AM – 12:00 PM (details here).

This year, Singapore Math Inc. asked me to present an NCTM workshop to address some practical considerations schools face when implementing the curriculum.

One of the biggest challenges during a Singapore Math® implementation can be the gaps in student knowledge. Upper elementary students frequently lack the foundation provided by the 1st-3rd grade Singapore curriculum. In this direct from the classroom session, you’ll learn the critical lessons and concepts students must master before jumping into their grade-level content.

This NCTM Workshop is on Friday, April 16, 2015, from 12:30 – 1:30 PM

When the complete conference schedules for both NCTM and NCSM are available, I’ll publish an overview of Singapore Math® presentations along with recommendations for session at each conference as I have done every year since 2010.

If you are headed to Boston in April, please consider attending one of these sessions. I’d love to connect with you!

2015 NCSM Annual Conference – April 13-15, 2015

SHINING THE LIGHT ON LEARNING:

A Vision for Mathematics Leaders

2015 NCTM Annual Meeting & Exposition – April 15-18, 2015

Effective Teaching to Ensure Mathematical Success for All

Boston, Massachusetts

Boston Convention & Exhibition Center

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.

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:

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

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

And finally, from **Math in Focus**:

UPDATE:

Ugh! One more similar tweet from NCTQ.

A fourth grader at a school I worked with this year included this on a Christmas card for her teacher.

As I enter my eight year as a Singapore Math® trainer, consultant and coach, I continue to be amazed by the wonderful opportunities that continue to come my way.

I say this every year, but it continues to be true:* I am so grateful to be able to champion elementary math education and GET PAID to spend time in classrooms with teachers and students.* I extend my heartfelt thanks to everyone who has played a part in making the year so special.

2014 has been my busiest year ever. I’ve spent more than 30 weeks traveling across North American (and Germany for a week) to work with schools and present seminars. I’ve been to Denver International Airport so much that Google recognizes it as my office. Don’t get me wrong: I love to travel, especially when the end result is helping teachers hone their skills to make students more competent and confident math learners.

This year, more than half of the schools I visited were repeat and long-term clients where my role often was that of an instructional coach. I still love to present introductory workshops and lead implementation trainings (the Ah Ha! moments are truly priceless), but it’s been especially rewarding to spend time with teachers working at a deeper level. At these schools, I’ve also hosted lots of parent education events, including hands-on bootcamps, to help ensure that Singaporean methods are reinforced at home. Best of all schools are achieving remarkable results (more on that to come).

There are many highlights from 2014, including:

- Working with 28 school clients in 9 states and Germany, where I had the opportunity to work with teachers at the International School of Hamburg!
- Acceptance of proposals to present at the 2015 Annual Conferences at Annual Conferences of both the National Council of Teachers of Mathematics (NCTM, for the second time!) and NCSM (for the first time). Lauri Susi of Conceptua Math is my co-presenter;
- Presenting Singapore Math Workshops for the Bureau of Education of Research (for the sixth consecutive year!);
- Presenting at the Tennessee Conference on Singapore Math Strategies hosted by SDE.
- Meeting my personal “continuing education” goals by attending:
- Annual conferences of NCTM and NCSM (for the 6th consecutive year);
- The National Charter Schools Conference (for the first time);
- SDE’s National Conference on Singapore Math Strategies (for the second consecutive year); and

- Earning A-list Preferred status on Southwest Airlines (didn’t I say I love to travel!).

2

Continents visited (I’ve now conducted trainings on four continents; c’mon South America and Asia…I’d love to visit there, too)

9

States visited to work with school clients

19

States visited to conduct Singapore Math seminars or trainings

20+

Singapore Math presentations conducted for parents

25

Seminars presented for BER

97+

Days working directly with teachers

Hundreds

of inquiries from teachers, administrators and parents with questions about Singapore Math curriculum responded to

103,448 and counting

Miles flown

My sincere thanks to all the administrators, teachers and support staff I worked with in 2014. ( You know who you are!) I so appreciate your dedication to students and your trust and confidence in me! A hearty thank you as well to my other long-time partners and supporters:

- Singapore Math Inc.
- Bureau of Education of Research (BER)
- EAI Education
- Staff Development for Educators (SDE)

Now in its seventh year, SingaporeMathSource.com continues to be an authoritative resource for those seeking information about the curriculum. This year, I completed a long-planned, thorough comparison of the two leading Singapore Math® curricula available in the US: Primary Mathematics and Math in Focus. (Quite a few of my school clients are using Math in Focus). I also updated my popular page on Singapore math iPad apps.

2014 has been personally gratifying as:

- We celebrated our youngest son’s high school graduation. It’s hard to believe we have two students at Colorado State University. It’s not hard to believe one is a math major!
- I once again reached my goal of reading 50 books in the year. As of this date, I am at 89!
- I continue to serve on the Board of the Middle School Math Institute, a non-profit dedicated to helping students succeed at algebra.
- I continue to serve on the District Accountability Committee for the Poudre School District.

2015 promises to be just as busy and exciting. I’m really looking forward to:

- Continuing to work with many schools that have retained me on a long-term basis;
- Visiting teachers, administrators and parents at schools that hire me for the first time (believe it or not, my
**fall 2015 schedule**is starting to fill up); - Presenting at the 2015 Annual Conferences of NCTM and NCSM in Boston (and hopefully other events);
- Presenting BER workshops for a seventh consecutive year;
- Sharing news about the successes some of the schools I work with are achieving — please let me know if you want to be a part of this series; and
- Other opportunities that are, as yet, unknown. I can’t wait to see what is ahead!

Once again, my sincerest thanks to my clients, colleagues and partners for making 2014 such a wonderful year. If I may be of service at any time, don’t hesitate to get in touch with me.

As passionate as ever about Singapore Mathematics!

-Cassy