NCSM Session: Singapore Teacher Training

In late April, two mathematics conferences were held in San Diego: The NCSM (National Council of Supervisors of Mathematics) and the NCTM (National Council of Teachers of Mathematics). This is the fourth in a series of posts from those conferences.

NCSM Session:

  • Integrating Curriculum, Assessment, and Teacher Professional Development: Singapore and the United States by Ban Har Yeap, Khoon Yoong Wong, Jeremy Roschelle and a colleague.

The final Singapore Math-related sessions at NCSM was the result of a joint research project between the National Institute of Education (NIE)  in Singapore and the Stanford Research Institute International Center for Technology in Learning in Menlo Park, California (SRI).

Dr. Wong spoke first about the teacher training provided in Singapore. The National Institute of Education is the sole teacher preparation facility in Singapore. This allows for standardized pre-service program. He shared the Pre-service Mathematics Teacher Education Framework that guides teacher training in Singapore:

(click to enlarge)

Teachers in Singapore take one of a couple of routes:

  1. Diploma in Education (Dip Ed): 2 years, full-time, Primary.
  2. Bachelor Degree: BA (Ed) or BSc (Ed): 4 years, full-time, Primary or Secondary.
  3. Postgraduate Diploma in Education (PGDE): 1 year, full-time, Primary or Secondary.

Most interestingly, Dr. Wong added the number of courses out of the total courses that each pre-service track requires:
SK = Subject Knowledge (math for school teaching)
CK = Curriculum Studies (math pedagogy)

  1. Diploma: SK =  6 /69    CK = 8 /69
  2. Degree: SK = 4/126    CK = 10/126
  3. PGDE (primary) SK = 4/44    CK =  8/44

Further reading on teacher preparation: Breaking the Cycle: An international comparison of U.S. mathematics teacher preparation.

Dr. Yeap then spoke about professional development for teachers in Singapore. Many people believe that Singaporean primary teachers are specialists, which they pointed out was simply not factual. From his presentation:

Regardless of where it is initiated, most professional development in Singapore has been workshop-style. One of the big challenges of this type of professional development is that there is no follow-up with the teachers on the material presented. Teachers attend the workshop, then go back to their classroom. (Sound familiar?) Singapore is now working on developing a professional learning culture through more reflective teacher practices. Newer avenues for professional development include Lesson Study, Action Research and Professional Learning Communities.

A major difference between United States and Singapore is the allotment of 100 hours of professional development each year for teachers. This statistic is commonly cited as something that could never be achieved in the United States. In actuality, 100 hours amounts to two and a half weeks of time. Additionally, in Singapore, these 100 hours can be spent on activities that enhance the teacher as a person. Calligraphy, school-based team meetings and pottery-making are among activities that might count for these 100 hours. When questioned, Dr. Yeap also qualified that teachers in Singapore might worry if one teacher was putting in more hours than they were. High expectations among the population dictate that the 100 hours is usually a minimum.

You can view Dr. Yeap’s entire presentation on his website, along with other presentations he has done around the world. Best quote from the session comes from him:

Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence.

The researchers from SRI spoke next on the findings from their research project. In the NCSM Conference book, Integrating Curriculum, Assessment, and Teacher Professional Development: Singapore and the United States promised to go beyond the “popular but oversimplified views of Singapore’s successes.” The researchers at SRI repeated that merely adopting Singapore’s textbooks will not be enough to guarantee success here in the United States. It is a wide-spread, but mistaken belief, that a school can simply buy Singapore’s textbooks and duplicate their success in mathematics.

Specifically, they found that it wouldn’t be too challenging to duplicate parts of the Singapore Mathematics Syllabus in the United States, including:

  • Creating standards that align to a common assessment.
  • A guiding document like Singapore’s pentagon. Dr. Roschelle proposed that the U.S. could use Adding it up: Helping children learn mathematics. At over 450 pages, it doesn’t have quite the allure of the Singaporean document.
  • Visual models. Singapore uses a concrete-pictorial-abstract methodology incorporating the model method and the U.S. has the Geometer’s Sketchpad.

Dr. Roshelle listed several items that would be somewhat harder to bring to the United States:

  • A high level of professionalism among teachers.
  • Systemic rotations through positions (at NIE, Ministry of Education and classrooms).
  • Allowing teacher input at all levels of education.
  • Systemic leadership.
  • A culture of high expectations.

I’m starting with that culture of high expectations. Every school, every student.

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NCSM Sessions: Singapore Math

In late April, two mathematics conferences were held in San Diego: The NCSM (National Council of Supervisors of Mathematics) and the NCTM (National Council of Teachers of Mathematics).  This is the third in a series of posts from those conferences.

NCSM Sessions

  • Singapore Math for the U.S. Classroom – Patsy Kanter, Andy Clark
  • Lessons from Singapore: The Professional Development Required to Implement a World-Class Curriculum  – Andy Clark
  • Developing a Singapore Math Curriculum: From Theory to Practice – Dr. Ho-Kheong Fong

These three sessions were all presented by authors of the Math in Focus (MIF) program published by Great Source, a division of Houghton Mifflin Harcourt. You can read about the product in my post about the NCTM exhibit hall.

The first session, Singapore Math for the U.S. Classroom covered the Math in Focus materials. This was a commercial showcase session…

provided by NCSM elite sponsor partners to share information about their products. – NCSM Conference Handbook

And the session went according to those parameters.  According to Kanter, the company took My Pals are Here, the program used by 86% of primary schools in Singapore and asked, “How do we bring engaging together with the standards?” Math in Focus is the result of that question.

Clark’s session, Lessons from Singapore: The Professional Development Required to Implement a World-Class covered challenges faced by schools that adopted Math in Focus this past school year, including schools in:

  • Old Bridge, NJ
  • Lexington, KY
  • other small districts in KY
  • Duluth, MN
  • New York City

From these adoptions, Clark listed four main challenges facing teachers and school adopting the MIF materials

  1. Teacher math knowledge
  2. Lack of embedded professional development
  3. Lack of a sense of the math trajectory
  4. The U.S. tends to have skill- based standards rather than organizing ideas

These needs should all be addressed when considering adopting a Singapore Math program. While Clark was using examples from Math in Focus, the truth is that the schools adopting the  Primary Mathematics series face similar challenges. Clark listed specific content knowledge deficits many teachers had when starting with Math in Focus and how the program helps teach the teachers the content.The topics that were most difficult included:

  • Teaching algorithms with understanding – Many teachers have mainly a procedural knowledge of mathematics.
  • Mental Math – Teachers lack strong mental math skills.
  • Modeling word problems – Teachers are not used to representing a word problem.
  • Fractions-  Teachers struggle to teach both concepts and operations of fractions.

Clark was challenged to get all of his material into the hour provided, but did provide this slide from the handouts that suggested some ways to meet the content knowledge challenges teachers have had:

Finally, in the session Developing a Singapore Math Curriculum: From Theory to Practice, Dr. Fong provided an overview of the philosophy and pedagogy that underlies the Math in Focus program. He showed several problems and demonstrated various philosophies applied. Here’s one to try!

Put the following numbers into the diagram so that each line of three numbers is equal:

1.2, 2.4, 3.6, 4.8, 6, 7.2

This problem applies overarching ideas from the Singapore Mathematics curriculum, specifically visualization and making connections.

Can you “see” the number bonds? How can you simplify the problem?

Other posts in this series

Math Conference Mania: Part 2

Last week, two mathematics conferences were held in San Diego: The NCSM (National Council of Supervisors of Mathematics) and the NCTM (National Council of Teachers of Mathematics).  This is the second in a series of posts from those conferences.

The vendor exhibit hall at the National Conference of Teachers of Mathematics reminds me of a state fair Merchandisers Building. Many of the large corporations have presenters with headsets a la Brittney Spears and offer a reward for sitting through a presentation. With 175 vendors, many of whom have presentations running continuously, the hall floor can be crowded and hard to navigate, but well worth taking the time to visit.  There were people waiting for the exhibit hall to open each morning and many talked about needing an additional suitcase or paying luggage fees to get their samples and freebies home. (And some just bought extra luggage right there on site from the vendor, Tutto.)

I spent quite a bit of time at the Houghton Mifflin Harcourt exhibition booth perusing the available Math in Focus books. According to the series authors, Math in Focus started with the same math covered in My Pals are Here, which is currently used by 86% of the primary schools in Singapore, and then made some additions.

Here’s a full list of the program components on the Math in Focus.

Additions to My Pals are Here content include:

  • Aligning to NCTM Focal Points
  • Addition of a Kindergarten Level
  • Chapter Opener and Chapter Reviews to each textbook
  • Adapted language and units of measure for US market
  • Added worked examples to Student Workbook

Additional materials for the U.S. market include:

  • American Teacher’s Guide
  • Assessment books
  • Differentiation materials: Reteach and Enrichment student books
  • Technology materials:
    • CD-ROM of Virtual Manipulatives and Teacher resources.
    • Online versions of the Student Books and Workbooks, the Teacher’s Edition
    • Online assessment generator
  • Complete manipulative kits

In addition to Math in Focus,  the NCTM Exhibit Hall featured several Singapore Math-related displays. Both of the following booths had a sample and flyers for a new book on bar modeling, which will be available later this month:

Bar Modeling: A Problem Solving Tool by Yeap Ban Har

Bar Modeling: A Problem Solving Tool by Yeap Ban Har

  • had samples of both the Primary Mathematics U.S. and Standards Editions as well as the secondary materials and Singapore science they offer. Copies of the new Challenging Word Problems series, aligned to both Primary Mathematics versions will be available soon.
  • Marshall Cavendish Online demo-ed their online version of Primary Mathematics. Register now for trial access. Full access should be available in the fall. I’ll post a full review when I’m done working through all of the lessons currently available.

Two companies that provide Professional Development on Singapore Math curriculum also had exhibit booths:

  • SMARTTraining, LLC, had samples of their materials for sale, including a  Sprint Library series, and place value disks that match the colors of the materials used in the Primary Mathematics books. (Full disclosure, I was a co-founder of this company, though I’m no longer affiliated with them, I continue to offer Singapore Math training and related-services.)
  • Staff Development for Educators also provides training and hosts a Singapore Math Strategies Conference in Las Vegas, Nevada in July.

Of course, most vendors were unrelated to Singapore Math. Of these, one in particular got my attention. T-ime Education is introducing a new curriculum to the United States based on the Korean Mathematics model, Numino which is:

a classroom-based and computer-based curriculum developed by T-ime Education to develop elementary students’ critical thinking and problem solving abilities and builds upon their skills to acquire mathematical competence.

Coming up, session reviews…

Other posts in this series

Math Conference Mania: Part 1

Last week, two mathematics conferences were held in San Diego: The NCSM (National Council of Supervisors of Mathematics) and the NCTM (National Council of Teachers of Mathematics. The first focuses on mathematics teacher-leaders and includes supervisors, coaches, and just about anyone who works at a department head level or is involved in a Professional Learning Community. The NCTM national conference is a whopper! Over 10,000 people attended this year and while those numbers are down from prior years, there were plenty of interesting sessions to attend and informative people to meet.

Singapore Math was well represented at both conferences, which prompted this tongue-in-cheek tweet from a @ddmeyer, a high school math teacher:

“Hey you guys! Has anybody heard anything about this “Singapore Math”?! #nctm10”

From the session descriptions alone, I counted:

NCSM: Six Singapore Math sessions for 1500 attendees

  • Singapore Math for the U.S. Classroom *
  • Lessons from Singapore: The Professional Development Required to Implement a World-Class Curriculum *
  • Intriguing Lessons About How Math is Taught and Assessed in High Performing Asian Countries
  • Developing a Singapore Math Curriculum: From Theory to Practice *
  • Using Singapore Math Model Drawing to Help Special Education Students and Struggling Learners Become More Capable and Willing Problem Solvers
  • Integrating Curriculum, Assessment, and Teacher Professional Development: Singapore and the United States *

NCTM: Twelve Singapore Math sessions for about 10,000 attendees

  • Linking Concepts, Context, and Problem Solving through Singapore Math Model Drawing
  • A Glimpse of Singapore Math in the Primary Grades
  • The Cutting Edge of Singapore Math: Problem Solving, Creative Thinking and Inquiry Thinking
  • The Singapore Math for Helping Children Solve Challenging Mathematical Problems
  • Singapore Math: Contextual Word Problem Solving Leads to Concept Mastery
  • Math with Meaning – Success the Singapore Way: Foundations of Number Sense
  • Does Singapore Mathematics Enhance Students’ Learning in the United States *
  • Making Connections: Problems from Singapore Classrooms
  • Lessons from Singapore: Using Visual Models to Teach Algebra and Number Sense
  • Using “Strip Diagrams” to Solve Algebra Word Problems
  • Intervention Strategies: The Singapore Way
  • Let’s Make Triangles With Sticks! Geometry in Asian Textbooks

Sessions with an asterisk (*) are ones that I attended and reviews of those are forthcoming. With over 750 total sessions, scheduling at NCTM was a challenge. There were three different venues and many of the Singapore Math-related sessions at NCTM ran concurrently or overlapped. Anyone truly interested in learning about Singapore Math could have attended six entire sessions or parts of all of them.

Of the six sessions at the NCSM, half were by Houghton Mifflin Harcourt’s Math in Focus series authors Patsy Kanter, Andy Clark and Dr. Fong Ho Kheong. They were the only sponsors at the NCSM conference sponsor area that displayed materials related to the Singapore Math Curriculum. (Also published by Houghton Mifflin Harcourt divisions and on display in the booth: Saxon Math, Think Math, McDougal Littell, Destination Math, Go Math)

This was my second NCTM conference (takeways from 2009 here) and my first visit to the NCSM. I can see that I will need to reserve the full week in the future to attend both. In addition to the Singapore Math-related sessions, I attended sessions on formative assessment, writing effective homework, coaching, asking good questions and fractions. My mind was expanded by renowned professors such as Deborah Loewenberg-Ball and Hung-Hsi Wu (session reviewed at Kitchen Table Math II).

Start saving now for next year’s annual conferences in Indianapolis, April 11 – 16, 2011!

Other posts in this series

April is Math Awareness Month

Sponsored by the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics, the theme for April’s Math Awareness Month (MAM) is Mathematics and Sports.  From the press release:

Sports offers a cornucopia of instances involving data, strategies and chance, each of which is perfectly suited to mathematical analysis. Beyond the obvious uses of mathematics for things such as rating baseball players and football quarterbacks, mathematics is used to design the dimple patterns on golf balls and the composition of racing tires; it is used for scheduling tournaments and for ranking teams; and it is used to determine tactics and to predict the ultimate limits in sports records.

Organizations and teachers from around the country have posted some ideas for the classroom and events at their schools on the MAM site. Even better, head to Subadra’s Math Awareness Month post on her blog: Library of Books, Links & More. Be sure to have a snack first, you might be there a while. There are over 50 great links to articles, activities, and books on mathematics and sport!

Pi Day 2010

Are you ready?

Ice cube tray available at Amazon.

Pi Clock  at

Clock in Terms of Pi

The San Francisco Exploratorium

is celebrating their 22nd annual Pi Day:

Come create Pi puns, participate in Pi-related antics—and have a slice of pie

Activities, music, and stories at

The site owners have sorted through hundreds of ideas and chosen their 50 ideas best  for celebrating Pi Day. (Be sure to check out the Pi Day Carols, too!)

Upcoming Singapore Math Workshops

(Image courtesy of Indexed.)

I’ll be presenting “How to Use Strategies from Singapore Math to Strengthen your Math Instruction” at four workshops this winter. You can read more about these 1 day seminars and register by clicking on the city.

February 10 – Harrisburg, PA – Rescheduled for March 9th

February 11 – Atlanta, GA – Rescheduled for March 10th

March 29 – Rochester, NY

March 30 – Buffalo, NY

Whether you’re new to Singapore Math or just interested in learning more about some of the strategies, you’re sure to leave with a new understanding of the curriculum. (And a handy-dandy handbook!)

i-Excel: Heuristic and Model Approach

From a discussion on the Well-Trained Mind Forums is a question about some the supplemental material available for the Primary Mathematics curriculum:

On the ( site there are some supplemental books I don’t recognize, but I can’t tell what they’re for–if they’re new-new or replacing-CWP-new

Math Works?
Math Express?
Brain Maths?

I wrote here about the MathExpress: Speed Maths Strategies.

i-Excel Heuristic and Model Approach (Update 2/2013 – Series going out of print and will be replaced with: Process Skills in Problem Solving)
Author: Li Fanglan
Published by Fan-Learning
Levels 1-6 available in the U.S. from

The i-Excel: Heuristic and Model Approach is a completely different type of workbook than the MathExpress series.  i-Excel books focus on problem solving. Can you deduce the meaning of “heuristics” based on the following description from the introduction?

At primary levels, Model Approach has been proven to be the most versatile and effective method to help pupils solve many difficult problems.Heuristic Approach, on the other hand, helps them handle the higher level problem solving by unconventional means.

Heuristic Approach

The first part of each book includes eight different Heuristic Approaches and then focuses on different Model Approaches based on topics taught at each level. Heuristic Approaches in Level 2 include the following:

  1. Guess and Check
  2. Act it Out
  3. Draw a Diagram I
  4. Make a List
  5. Look for a Pattern I
  6. Draw a Diagram II
  7. Draw a Diagram III
  8. Look for a Pattern II

Upper level Heuristic Approaches include: Simplify the Problem, Work Backwards, Make a Supposition, Solve Part of the Problem, Use Before-After Concept and Restate the Problem in Another Way. Each Heuristic Approach has a worked example, four or five practice problems and one more challenging problem to solve. (Some levels put these challenging problems into a separate unit.)
Here’s the challenge problem from Level 2 – Draw a Diagram II:

A pizza was cut into halves.
Jolene took one half and ate 2/3 of it.
a) What fraction of the pizza did she eat?
b) What fraction of the pizza was left?

Completed guided examples are included in the Answer Key at the end of this section. Make a note, however,  not all questions have worked solutions.

Model Approach

The second portion of the books works with the Model Approach as it applies to mathematical topics.

    • Levels 1-3 focus on applying the Model Approach with the four operations. They also have yellow, pink and blue rectangular stickers in the back of the book for students to use with the model drawing problems. These are important for students who are learning or struggling with drawing proportional bar models.
    • Level 4 has two parts consisting of 28 units on the Model Approach: Whole Numbers and Fractions. There is also a Part IV: Non-Routine Problems – Challenge Yourself 4.
    • Level 5 has sections on Whole Numbers, Fractions, Ratio, Decimals, and Percentage. Part VII includes 3 assessments.
    • Level 6 parts include ratio and Proportion, Percentage and Speed. The final section is entitled “Examination Practice”. Some of these problems are double starred for extra challenge.

Here’s an example of a ** problem from that unit:

Grace had a total of 120 red and blue pens in the ratio of 3:5. After she gave away an equal number of each type of pens, the number of red and blue pens left was in the ratio 3:8. How many pens did she give away altogether?

Good news if you’re scratching your head right now. All problems in Level 6 have detailed solutions worked in the answer key.

In the classroom

Most who have used Primary Mathematics would agree; the focus is on the bar model as the main problem solving strategy. The i-Excel series brings explicit instruction in additional problem solving strategies into the classroom. This is one of my favorite supplemental books to use with students. The challenge and variation makes it a favorite of students as well. I have incorporated the heuristics into a self-directed activity and have used the challenge problems for a “Problem of the Week”.

The Level 3 book includes a unit entitled “Act it Out” that became a great independent activity/group center. The example given is to use 10 coins to form the figure below. Moving only one coin at a time, what is the least number of moves to turn the shape upside down?

After working this example as a whole group activity, I could now have chips (coins) and new problems available in the classroom: as part of centers, as a substitute lesson plan, or for students to use as a quiet desk activity.

Have you used the i-Excel or Brain Maths series? Share your experiences in the comments below. I’d love to know how the books have worked in a classroom or in your home.

MathExpress: Speed Maths Strategies

From a discussion on the Well-Trained Mind Forums comes a question about some the supplemental material available for the Primary Mathematics curriculum:

On the ( site there are some supplemental books I don’t recognize, but I can’t tell what they’re for–if they’re new-new or replacing-CWP-new

Math Works?
Math Express?
Brain Maths?

First, these aren’t replacing CWP (Challenging Word Problems series), but they are fun books that are great supplements for homeschooling families or classrooms.

MathExpress: Speed Maths Strategies
Author: Li Fanglan
Published by Fan-Learning
Levels 1-6 available in the U.S. from

I recommend MathExpress if you are interested in becoming faster and more fluent with mental mathematics. Book levels 1 – 3 focus on basic mental math strategies with the four operations. Beyond that level, if you’re using them with students, some of these approaches can start making math look like a series of algorithms to memorize or tricks. It’s important that students understand the reason why these “short-cuts” (as they are referred to in the books), make mathematical sense.

An example from Level 1- Express Strategy 13:

Can you get the answer in 10 seconds?
26 + 49 = ?
58 + 37  = ?

There is a visual & written solution for each problem on the next two pages. Here’s the first written solution:

1 and 49 make 50.
Rewrite 26 as 25 + 1.
Add 1 to 49 to get 50 before adding 25.

An example from Level 2 – Express Strategy 9:

Can you get the answer in 10 seconds?
342 – 190 = ?
237 – 172 = ?

Again,  there is a visual and written solution page for each problem. Here’s the first:

190 is 10 less than 200. Subtract 200 from 342 before adding 10.

After an explanation of the strategy, there is a page of practice, a page with two word problems and a Speed & Accuracy Test.

There are six volumes in the series:

Levels 1 and 2 include addition and subtraction.
Level 3 adds in multiplication and division.
Level 4 includes all four operations and decimals.
Level 5 has fractions and decimals.
Level 6 has strategies to check answers, percentages & advanced problem solving. Here are two 10-second problems from Level 6 and the first solution:

125 x 25 x 32
1/2 x 50 x 28 x 11

4 and 8 are factors of 32.
24 x 4 = 100 and 125 x 8 = 1000.
Multiply 25 by 4 and 125 x 8 before multiplying the two products.

Before working the solution to the second problem, the book provides this word problem:

A rectangular tank measuring 50 cm by 28 cm by 11 cm is half filled with water. Find the volume of water in the tank.

I highly recommend the upper level books for adults looking to improve their mental math abilities. I should also mention that the books have two diagnostic assessments at the back of the book, along with an Answer Key and Detailed Solutions. (You’ll find the solution to the 6th grade level problem above on 69.)

In the classroom

My students have so much fun working on these strategies. In a classroom, I’ve used these books with students AFTER concepts have been mastered to help students become faster with their mental computation. As an example, in a 3rd grade classroom, I would focus on the strategies in the Level 2 book for the first half of the year, then, depending on the students’ understanding of multiplication and division, I’d introduce some of the strategies from Level 3. These can conclude in wonderful mathematical conversations. Here’s an Express Strategy from Level 3 that should lead to an interesting discussion:

Can you get the answer in 10 seconds?
26 x 5 = ?
148 x 5 = ?

And the strategy:

2 fives = 10
Multiply 26 by 10 instead, then half the product.
26 x 5 = 26 x 10 ÷ 2

= 260 ÷ 2
= 130

I’ve used the i-Excel and Brain Maths series. I’ll post reviews on those also. If you’ve used these materials, please share how in the comments below. I’d love to know how they worked in a classroom or in your home.

Problem Solving and Literature


Denise at Let’s Play Math has written up a some fourth grade level multi-step word problems (and provided bar model solutions) based on C. S. Lewis’  The Lion, the Witch and the Wardrobe. She concludes:

…as word problems become more complex, the bar diagrams offer significant help for students who struggle with the question, “What do I do?” Diagrams make visible the abstract relationships between numbers, enabling the student to decide which arithmetical operation makes sense in the context of the problem.

This is the fourth installment of her series on Pre-Algebra Problem Solving. Other posts  use Mr. Popper’s Penguins and Poor Richard to illustrate problem solving using bar models in earlier grades.