Throwback Thursday! Successful implementation: Buying books is just the first step

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!

Successful implementation: Buying books is just the first step

Originally published 12/17/2010

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

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

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

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

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

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

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

(Click to enlarge)

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

Note that the subsequent three lessons are:

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

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

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

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

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


Mantra for 2017: Make math make sense!

The return from winter break brings with it a refreshed outlook on teaching.  Teachers return with an eagerness and enthusiasm for the profession and students return seeming just a little more mature.

Return from winter break also brings with it a sense of urgency.  Maybe you’re not as far along in the curriculum as you had hoped. You realize that the frantic push to cover material before break has left students unable to recall content taught.  You are feeling the pressure of standardized tests looming.

The 2015 TIMSS results were recently published and once again, Eastern Asian countries top the charts.  In fact, the gap between the top 5 scoring countries and the United States was 54 points.  What sets them apart is their commitment to teaching mathematics at a deep conceptual level with a focus on thinking and problem-solving.

All of that can be very sobering.  Take a deep breath and set some goals.

Ask more, tell less

  • How do you know that’s correct?
  • Are you sure?
  • Why does it make sense?
  • I wonder why that works.
  • Can you solve it in another way?
  • Can you build or draw a representation?
  • What do you see in your head?
  • Can you prove your answer is correct?
  • You and your neighbor have different answers, who is correct?

Allow time for understanding

It’s easy this time of year to get caught up in the pressure to cover content, but remind yourself that memorization is not the end goal, understanding is.  Taking the time to focus on the concrete-representation-abstract approach will ultimately lead to deep conceptual understanding.  Your students (and their test scores) will reap the benefits.

Help students make connections

  • How is this like what we just learned?
  • Does this remind you of anything?
  • Can you make a connection between this and what we have already learned?

By setting a few simple goals, you will set yourself and students up for a successful remainder of the year!


Manipulatives Make the Math Concrete

Manipulatives and Models
From a school that introduced Math in Focus materials this fall comes a great image of a fourth grader working with manipulatives to understand both algorithms and bar modeling. The class is learning long division. Number disks are a vital part of developing number sense in Singapore curricula.

Parnassus pennies
Another school is using Primary Mathematics and the class is doing the first lesson in multiplying and dividing by twos (Count by Twos). Students hadn’t used a lot of manipulatives before. This student excitedly exclaimed:

Hey, this is really useful!

Comments from observing teachers provided some interesting insights:

Wow, it sure is loud!

You can use a pre-cut sheet of felt from the craft store, or a laminated mat to help deaden the sound of working with louder manipulatives.

My kids would be bored to tears with this activity.

And she’s right, they would have. Her students were the higher ability group and need fewer concrete examples to understand the concept. (Note, not zero concrete examples, just fewer)

Number Discs
The red, white, orange discs with large numbers and the square set are available at as well as many online stores. The set with the smaller numbers is sold in conjunction with Math in Focus materials from Houghton Mifflin and corresponds to the colors used in the textbooks.

Looking for more on manipulatives? Check out this post: If I had a million dollars, ok $1000…

Quick thought from NCTM conference


Tweet from the National Council of Teachers of Mathematics conference regarding a discussion of number lines.

Archived twitter conversations from last week’s conference can be found by searching #NCTM12 or #NCTM2012.



Bar Model Method challenges

Photo taken in a third grade classroom using Primary Mathematics. The teacher had posted the question on the board and students recorded the question and their solution in a math journal.