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

My session entitled Strip Models, Tape Diagrams, Bar Models, Oh My! has been accepted for both 2015 national conferences of the National Council of Supervisors of Mathematics (NCSM) and the National Council of Teachers of Mathematics (NCTM). Lauri Susi of Conceptua Math is my co-presenter on these!

Now you can vote for the session to be held at the National Charter Schools Conference (NCSC) as well. **We’ll reach a whole new crowd of Charter School administrators, teachers and founders!**

Strip Models, Tape Diagrams, Bar Models, Oh My!

These visual components sit at the intersection of Common Core, the Singapore Math® approach, and now technology! Learn why visual models for word problems are 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.

Participants will learn how to create visual models for word problems and then integrate model drawing into their instruction. Questioning techniques for guiding student understanding of problem solving will be modeled for participants. Attendees will learn how the use of visual models for word problems can help students build a deeper understanding of mathematical concepts. Attendees will see and try online modeling tools used to develop and assess students’ deep understanding of word problems.

**Vote by December 19th to get this session on the schedule!**

The Head of School at Trafalgar Castle School in Whitby, Ontario explains why his school adopted Math from Singapore and how it differs from other curricula:

We introduced Singapore Math to our school three years ago after researching a number of programs and determining that this method had the best achievement results internationally.

Singapore Math deliberately slows down the teaching of math, taking more time to ensure students grasp each concept before moving on. For example, students might spend two weeks on multiplying fractions, instead of spending a day or two and then coming back to it later.

Students use visuals aids such as bars and blocks before they start writing equations with “x” and “y,” so they achieve a deeper grasp of the actions they perform. This visualization is not deployed nearly as much in Canadian classrooms. In most settings, you would see a concrete-abstract strategy whereby multiplication would use physical objects then shift to the abstraction of lining up numbers in a multiplication equation. Singapore Math introduces a middle step between the concrete and abstract called the pictorial approach. The students draw a diagram of the concepts going on. This extends to diagraming word problems on paper rather than the often frustrating scenario of trying to picture a problem in their heads.

One happy result of all this is that when students reach algebra, they’ve already met the core concepts pictorially; indeed in most cases students in grade 6 are able to understand algebraic concepts that normally wouldn’t be grasped until mid-way through grade 8.

North Cross School is the first school in the Roanoke Valley (Virginia) to fully implement the Singapore Math® curriculum.

[Editor’s Note: Over the past several years, I’ve had the honor of helping St. Anne’s-Belfield School with its Singapore Math adoption. I’m delighted that Beth Curran was able to take her experiences and successfully train teachers at North Cross School. Congratulations, Beth!]Beth Curran is the Mathematics Department Chair in the lower school at St. Anne’s-Belfield in Charlottesville and led the training at North Cross School. When asked about their conversion to Singapore Math she said “during our first year of implementation our students were saying ‘I understand math now.’ One of our second grade teachers commented, ‘At this point in the year (first trimester), I have never had students with such a solid understanding of place value.’ Upon conclusion of our first year, our math team felt that our students’ problem solving skills made huge leaps. We also noticed that students were persevering through difficult problems that in the past (or even the beginning of the year) they would have given up on. We didn’t teach perseverance, necessarily, but concluded that because students were learning and practicing skills to mastery that it equipped them with the tools to tackle challenging problems. They always had a place to start.”

North Cross Lower School Director, Deborah Jessee, believes that “a strong education in lower school builds a foundation of lifelong learning. It lays the pathways, creates excitement, and energizes students for the future. Singapore Math is a great way to enhance our lower school academic program and teach children not to be intimidated by new concepts and that it’s okay to explore other ways of learning. They learn to not be intimidated by a complex problem. When a student understands how to break down a problem and can figure out how to solve it, that academic skill translates well to other subjects and helps them prepare for ACT and SAT testing down the road.

Learning Singapore Math in Henderson County (Kentucky) first took hard work by teachers; previous math approach “made cooks…this makes chefs.”

At the heart of the Singaporean approach to math is problem solving. This math curriculum doesn’t focus as much on memorizing procedures, but understanding numbers and how they interact, officials said.It’s the how and the why, [third-grade teacher Evelyn] Cummings said.Educators said this isn’t how mathematics has been taught in the United States.

“Before I would teach my students a process, instead of problem solving. Now, we’re teaching these kids to be problem-solvers,” Cummings said.

In a contribution to the Washington Post, Dominic Basulto says that Maryam Mirzakhani could do for mathematics what astronaut Sally Ride did for space travel: give young girls a role model for someone they’d like to be when they grow up. The 37-year-old Iranian-born Mirzakhani, a professor of mathematics at Stanford, has been awarded the 2014 Fields Medal–the most prestigious honor in mathematics.

Here is a New York Times article on Mirzakhani’s award.

Stanford University research funded by the National Institutes of Health explains how the brain reorganizes itself as kids learn math.

Healthy children start making that switch between counting to what’s called fact retrieval when they’re 8 years old to 9 years old, when they’re still working on fundamental addition and subtraction. How well kids make that shift to memory-based problem-solving is known to predict their ultimate math achievement.

“Experience really does matter,” said Dr. Kathy Mann Koepke of the National Institutes of Health, which funded the research.

* I’ll share more about what these stellar students achieved in mathematics in coming weeks!*

*What would you are say the biggest 10 things to consider when using/implementing a Singapore Math curriculum?*

Here’s my response. Did I miss anything?

1. **This isn’t the math most of us were raised on**. It looks different and teachers cannot rely on their knowledge of themselves as elementary students. As such, the Teacher’s Guide is your math bible. You don’t have to read the lessons out loud as you teach, but you need to follow the sequence and pedagogy.

**2. And that pedagogy includes Concrete, Pictorial AND Abstract**. Teachers are usually darned good at the abstract, but above grade 2, not so hot with the concrete and pictorial. Yes, I know your students can solve the 3rd grade word problems without the pictorial bar model, but if you don’t teach the bar model with content they know, you certainly can’t do it with content they don’t know.

**3. Placement tests assess content knowledge. **Keep in mind that a score below 80% on the Singaporemath.com Placement tests **does no**t mean a student is not bright or capable – it does mean that they haven’t been taught the content **yet**. The Primary Mathematics materials are generally one year ahead of current U.S. materials and even bright students can’t just skip a year of content and expect to be successful.

**4. When teaching Concretely, the SmartBoard is not enough.** Students must actually use the manipulatives. Yes they can work with partners, but students must use them, not just the teacher. Buy or make place value disks for whole numbers and decimals if you want your students to understand the content.

**5. The equations are written horizontally to de-emphasize the process** (that algorithm you’re so good at!) and focus on Number Sense. These mental math strategies are challenging for teachers as they were usually taught procedures only. Expect to practice the strategies yourself. Embrace the mental math!

**6. Textbooks are not a curriculum.** The teacher is the most important component of the curriculum. If you don’t understand the math in a lesson, how will the students? Read the Teacher’s Guide and prepare lessons. (See #1 – and below)

**7. Get your own copy of the workbooks and work every problem** as you expect the students to work them. It’s true that the Teacher’s Guides have the answers. You need the solutions to know if a student’s thought process is on target. In Singapore, 50% of elementary teachers have a 2 year degree – they aren’t math specialists either! The textbooks are designed to help teach teachers the math they need to know. (Same with any placement test you give: you work the problems first.)

**8. Follow the maxim: Go slow to go fast.** All teachers do not have to be on the exact same lesson at the exact same time. Sometimes you need to slow down and ensure that your students are understanding the content. In grades 2-4 it seems as though it takes f o r e v e r to get through the “A” books. Then applying the skills mastered in the “B” books is a breeze. (In Kindergarten and Grade 1, the “B” book will slow students down. In Grade 5, the books seem more evenly paced) Knowing what your students know and can do means you must be constantly informally assessing your students.

**9. Rethink your Home Enjoyment**. One big difference between the Singaporean and U.S. cultures is on the emphasis of mastering basic facts. Parents in Singapore believe it’s their job to do this. In the U.S.? Well it’s the school’s. Just as we expect students to read very night to improve their reading fluency, so too should they practice math facts every night to improve fact fluency.

**10. This isn’t your parents math either!** (See #1) Many schools hold a Singapore Math night to introduce the new curriculum to the parents. Share with parents how the curriculum differs from what they’ve seen before, samples of the materials, some strategies, a couple of word problems and you’ll fend off weeks of questions and email.

Listed below are some **recent additions. **I paid for and personally played with all of these in order to offer my candid assessment of each.

You can find these and more Singapore Math-related apps on the Singapore Math® iPad Apps page, which is among the most frequently visited on this site.

*Note: I didn’t include the online version of Discovering Mathematics textbooks as they are designed to support the books only.*

**Archimedes Roost – $**2.99

Kindergarten app based on Singapore Number Bonds and Montessori using parts and wholes and Montessori bead chain and strip board manipulatives. Includes addition and subtraction within 20. Fully narrated for non-readers.

*Opinion? Great graphics and engaging activities. Good number bond and missing addend problems. This is worth $2.99.*

** **** Maths Facts** – $0.99

Four choices: Number Bonds and Fact Families practice to Ten, Addition & Subtraction to Ten. No ability to differentiate or make it more difficult. Addition & Subtraction is find the sum or difference only, no missing addends.

*Opinion? Simple and minimal levels. Very basic, froze a couple of times, but only 99¢.*

** Let’s Count **- Free

For ages 3-6, this is a very basic app with four options. Order quantities of jelly beans from least to greatest, count and label bars to ten, Count beans to ten, match numbers.

*Opinion? Well, it’s free and doesn’t take up much memory.*

Practice Math with Robin and Dob – $2.99

Master addition and subtraction with math whizzes Robin and Dob. 10 levels of each, addition & subtraction, no customizing. The dog pops up when you’ve taken too long and offers help in the form of an abacus, tens and ones place value chart with apples or the problem stacked instead of horizontal. Adorable!

*Opinion? While the game is simple and has minimal levels, the basic practice is solid (and adorable!). This is worth $2.99.*

** Place Value Cards ****Cards** – $0.99 each

A number is given and you must show it two different ways, for example if 3 tens and 6 ones is given, you could also make 36 with 2 tens and 16 ones.

- Level 1: Tens and Ones
- Level 2: Hundreds, Tens, and One
- Level 3: Thousands, Hundreds, Tens and Ones
- Level 4: Hundreds, Tens, Ones, and Tenths
- Level 5: Tens, Ones, Tenths, and Hundredths

** Number Bond Cards** – $0.99 each

- Level 1: Ten Frames and
- Level 2: Number Bonds with missing whole
- Level 3: Number Bonds with missing part

*Opinion? Both of these apps are very simple and have minimal levels. If your child needs this targeted practice you could spend the 99¢.*

** Crackers and Goo – **$2.99

Crackers and Goo uses patterns to teach children to identify patterns and see parts of wholes. Flying crackers need to be dragged down to complete the problems. Starts very basic and finishes with rounding then multiplying 898, 899, 900. Yikes! Mental math strategies are explained.

16 levels with 5 mini-levels on each

- Grades K-1: game levels 1-4
- Grades 2-3: game levels 5 – 7
- Grades 4-5: game levels 8 – 11
- Grades 5 and up: game levels 12 – 16

*Opinion? Great, if repetitive, practice. Turn the volume down on the annoying music. I can’t see kids playing this for long, but it is more of a “game” than typical flash cards. I dig this app, but not sure about young students.*

** Visual Word Problems ** – $4.99

Designed to help 1st and 2nd grade school children to visualize, understand and solve basic addition & subtraction word problems, this is a guided, easy to use app for early learners. I really like how prompted the steps are to maneuver through the program and that the default option is to have the app read the problems aloud. The animated word problems that use actual pictures of cows, oranges and apples are fabulous. They are laid out as a definite precursor to the bar modeling that begins in grade 3.

*Opinion? Worth the $4.99, but this is not a game. If you would like your child working some basic addition & subtraction word problems, here’s your app.*

** Xyla and Yabu ** – $0.99

Help Xyla and Yabu trade gems back and forth by learning to add and subtract with number bonds. Use the relative sizes of number bond bars representing parts and wholes to develop number sense while solving word problems. Understand and become automatic at using tens, doubles, and other recurring patterns with numbers.

Each number bond is presented in the context of a word problem. After mastering sums up to 20 (14 activities), kids explore similar patterns with sums up to 100 (13 activities), for 10 levels in all. There is no option to have the app read the problems aloud. In numbers to 20, there is a picture and a bar hint, in numbers to 100, just some bar hints. After the beginning levels, three possible answers are given.

*Opinion? Best 99¢ you can spend on a word problem app for grades 1-2 working with parts and wholes to 100. Of course, Thinking Blocks is still free.*

** Math Master Bingo **- Free to download, 99*¢* in-app purchase for unlimited play.

Practice your four operations with Bingo. Choose the operands rang and the operation. (% is used for ÷). Answer questions until you get five in a row.Every 5 problems, it asks you to upgrade. Has two buttons on homescreen to send you to Facebook, only one for Twitter

*Opinion? Constantly asks to post to Facebook, I’d pass.*

** Jingle’s Puzzle** – $1.99

For grades 3-6, the website claims this app is designed Singapore primary school’s mathematics model methods. Good luck with that. This is a problem-solving, logic game. Sums are listed on teh left and top of an array and some of the squares are filled in. Students find the pattern and complete the grid.

*Opinion? I think the words of the single reviewer say it best: “VERY confusing…Not for young child…There is NO app support. I want a refund.”*

** Math Olympiad **- Free for first 6 problems, then $15.99 per level to unlock.

Designed for 8-12 year olds, this app has official competition questions from the Asia Pacific Mathematical Olympiad for Primary Schools. And the 6 problems that are included are exactly the types of problems seen on the U.S. version of the Math Olympiads for Elementary & Middle Schools.

*Opinion? This might be a great purchase for Math Olympiad teams looking for new problems. The levels are less expensive than the books in the MOEMS store.*

** Hey Math from Singapore **- Subscriptions from $0.99

Videos and practice with multiple levels from Singapore’s #1 online learning site. Hey Math! is an official Partner of the Academy of Singapore Teachers. They also make Factorama – which my 17 year old son loves to challenge me on.

*Opinion? This is a very good iPad version of the online site. The videos are very directed and the practice is like an online worksheet. *

** Smartest Singapore **- Free

Online learning game for Singapore primary school children. Students play in 60 second speed challenges in languages, mathematics and general knowledge. There is no way I could see to customise this app to focus on mathematics. You need to choose a Singapore primary school in order to register and there is no option for “other” or “homeschool”. If you’d like to study up on topics, there is an option. Choose from activities, animals, food, Geography, Plants, the MRT (subway in Singapore, Singapore history & famous people or a language. you never know when the Chinese word for bricklayer may come in handy.

*Opinion? Pass. Unless you want your child deciding if a picture is of Chimgan Mountain in Uzbekistan or Global Geoparak in Hong Kong. Game portion works about 50% of the time.*

**Math Mastery! **- Free

Secondary and Middle school topics. Supports Ace-Learning.com, who also declares itself the “leading online Mathematics E-Learning system in Singapore”. Must be a registered user of Ace Learning to use.

*Opinion? No need to download unless you already subscribe to Ace Learning.*

** Math Exam Revision Kit **- Free

Also by ACE-Learning Systems and so must be registered to get the full app. Secondary and Middle school topics including notes, questions with guided solutions and more practice questions.

*Opinion? No need to download unless you already subscribe to Ace Learning.*

** Matholia iMath tools & Essential Practice** – Free to download, paid subscription to access

For grades 1-6, Matholia is an another online mathematics learning portal providing pupils, teachers and parents with dedicated content based on the latest primary maths syllabus from the Singapore Ministry of Education – or you could get the U.S. version. Try the program free for 7 days with a code, then you must subscribe to continue. Ther are practice learn and games option available on the desktop version as well as Singapore math tools and virtual manipulatives for differentiated interaction.

*Opinion? No need to download unless you already subscribe to Matholia.*

** Mathematical Quickies & Trickies** -$9.99

Designed for students in grades 6 and up, this is an ipad version of a book of math and math puzzlers. From the Amazon description:

contains more than 300 non-routine problems to enhance students’ problem-solving skills…Mathematical Quickies & TrickiesMathematical Quickies & Trickieswould appeal primarily to students and teachers looking for some fertile trick and tricky questions; mathletes preparing for local and regional contests and competitions; problem solvers longing to be challenged by questions whose obvious solutions are never the correct ones for what offhand appears to be true is false.

** More Mathematical Quickies & Trickies **- $9.99

*Opinion? Cheaper than the books. *

** 2048 SG Army ** – Free

Version of 2048 in which you match tiles to earn your way through the Singapore Armed Forces

*Opinion? Probably not for your typical child. I made it through the ranks to Staff Sargent through sheer luck. Stick with the regular numbers version.*

Here are the just-released Fall 2014 dates for my BER seminars *“How to Use the Best Strategies from Singapore Mathematics to Strengthen your Math Instruction*” and *“Boost Students’ Math Problem Solving Skills Using Singapore Model Drawing” *

“*Boost Students’ Math Problem Solving Skills Using Singapore Model Drawing”* (BER)

- Nov. 3 – Burlington, VT
- Nov. 4 – Manchester, NH
- Nov. 5 – Boston, MA
- Nov. 6 – Long Island, NY
- Nov. 7 – Houston, TX

A whole day of problem solving with Singapore Bar Modeling PLUS that handbook for your own home enjoyment! (- with the answers and fully worked solutions!)

——————————————————————————————————————————–

*“How to Use the Best Strategies From Singapore Mathematics to Strengthen Your Math Instruction”* (BER) – ~~I’ll update this post when the registrations are available.~~ UPDATED 8/16/2014

- Nov. 17 – Peoria, IL
- Nov. 18 – Chicago, IL
- Nov. 19 – Dallas, TX
- Nov. 20 – San Jose, CA
- Nov. 21 – Pasadena, CA

*2015 dates – I’ll update this post with links when the registrations are available. *

This overview of Singapore Math® strategies will put your students on the road to success with number sense, computation and problem solving. (Plus you a get a handy-dandy handbook!)