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What is Singapore Math?

A few years back I attended the SDE National Conference on Singapore Math Strategies, and it was four days of non-stop learning! It was my second time attending the conference, and it was even better than the first time. While there were many great sessions and presenters, the highlight for me was definitely getting to learn from Yeap Ban Har. Dr. Yeap is an internationally known educator, author, and speaker. His presentation style made you feel like you were in his classroom–he was informative, engaging, and entertaining.

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One of the first comments he made is that in Singapore they don’t call it Singapore Math. It’s just math. He went on to explain the history of how the math curriculum we know as Singapore Math came to be. In the 1980’s, Singapore was at the bottom of the educational heap. Their scores on international assessments were among the lowest and their country’s GNP was dismal. The government decided that something needed to be done, and they turned to research for the answers. They decided to focus on numeracy, rather than literacy because research shows that mathematics skills are more directly correlated to the economic success of a country than literacy.

With the focus set on improving mathematics instruction, they studied the research about how students learn in general and, specifically, how they learn math. From the research, they developed a national curriculum and philosophy of teaching math that was implemented in the early 90’s. Just over twenty years later, Singapore consistently ranks very high on international assessments and their GNP continues to rise. Quite the success story.

While many people associate Singapore math with bar model drawing, Dr. Yeap said that was actually a small part of their curriculum. Here’s a graphic showing the framework.

One of the fundamental pieces of the Singapore philosophy is the concrete, pictorial, abstract (CPA) sequence of instruction based on the work of Jerome Bruner in the 1960’s. In the United States, we more often refer to it as CRA, with the R standing for representational, but it’s essentially the same thing. Anchor tasks (think of these as their mini-lessons) feature concrete learning experiences and typically conclude with students documenting their mathematical thinking in their math journal–the representational and sometimes abstract piece. So, for example, after doing an anchor task activity using ten-frames to explore different ways to add 8 + 6, the journal entry might look something like this:

It’s also interesting how they use the student textbook. He told us that although all the lessons he showed us came from the student textbook, the textbook stays closed during instruction. This allows the students to construct their own learning, rather than being constrained by the textbook method.

Another piece of research that helped shaped math instruction in Singapore is Zoltan Dienes’ Six-Stage Theory of Learning Mathematics. Basically, Dienes states that Free Play, without formal vocabulary or rules, must be the first stage of all learning. He describes it as a “trial and error” activity.  Think, for example, about the ten-frame anchor task I mentioned previously. Students might be asked to build 8 and 6 on two different ten-frames and then be asked, “I wonder how we could add 8 and 6?”  This would be followed by a share-out of different solutions. At the conclusion of the anchor task, students would be asked to record three solutions that make sense to them in their math journals. I love how Yeap described an easy way to differentiate: “Boys and girls, we have just discussed and shown many different ways to add 8 and 6.  Please record three ways that make the most sense to you in your math journal. If you are really fast, record five ways. If you are really, really fast, make up another way.”

Yeap also referred to Vygostsky’s theories on social learning and the zone of proximal development. Yeap summed up the social learning theory as students doing individual thinking, then small group work, and finally whole group sharing. Vygostsky’s zone of proximal development theory states that we learn best when asked to do tasks that are just beyond our comfort zone.

I hope you see that Singapore Math is really a philosophy for mathematics instruction–it’s as much about how to teach as it is what to teach. After reading this, you may even realize that YOU are a Singapore Math teacher.

If you’re interested in reading more about number bonds, which are a fundamental part of early numeracy in Singapore, check out this blog post.

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  1. I love this blog. I am going from Full Day Kindergarten to teaching Grade 2 this fall. I want to carry on the excitement and risk taking that was developed in Kindergarten doing similar activities using the thinking and sharing approach. Please pass on more information and names of resources, if possible.

    1. It is a wonderful way to teach! I often blog about my favorite resources, and I tag the posts with the keywords Book Review. Here’s a link to all posts tagged with that keyword: Book Review

    1. Thanks, Tara! I think it’s a shame that many people have such a narrow view of Singapore math. It is an amazing philosophy for teaching math!

  2. Thank you for sharing! I leave today for Chicago to attend the Math in Focus conference and Dr. Yeap will be speaking. I can’t wait to hear more. This fall will be my 4th year teaching with Singapore math in Kindergarten and I can’t imagine teaching any other way. I love your insights.

    1. How exciting, Debbie! He was amazing! I’m so happy to hear that your Kinder babies are benefiting from the Singapore strategies.

  3. Thank you Donna for posting such a great introduction about Singapore Math’s history. I really enjoyed reading your article!

  4. Thanks for sharing with us! We also used Singapore math books before but we found the content was much more challenging than regular US math. The workbook was dry and sometimes confusing. We quit after three months and returned to US math. I know a solid foundation is crucial for future study. So I kept looking for an enrichment home learning site for more than two months. Fortunately my son’s teacher recommended Beestar to us. It provides many subject programs and best of all, the math program is free.
    I subscribed to it for my son. He was very slow at beginning but he promised me to complete Beestar’s weekly practice on time. I could easily follow his practice report online. After just two months, I found I didn’t need to remind him any more because he started liking it. Beestar questions are very clear and interesting, leading students to comprehend every math concept step by step. The practice doesn’t take much time but my son has gained interest and confidence in math. I will let him enroll Beestar’s GT math program very soon.

  5. I am currently reading Step-by-Step Model Drawing by Forsten and I can’t wait to use what I have learned next school year!

    1. Awesome! Be sure you practice on your own using the samples in the book, Caroline! It really is a learned skill.

  6. Hi,i would like to ask you:what to choose US or Standard edition.i am in Canada,i am not a teacher and i would like to reinforce the math my child is going to have in school.And another question:do you think that these books contain the real singapore method?Thanks

    1. I can’t really speak to which books to use. I incorporate the philosophy of the Singapore method in my instructional strategies.

    1. Not really. Eureka is a math program in the United States. Singapore Math is the math curriculum in Singapore, which now serves as the inspiration for some math programs in the US.

  7. I have taught in this style for ages but am now in a school that prescribes to ‘Singapore maths’ designed for the British curriculum. In my opinion the British curriculum’s pace is way to fast for children to learn in this was effectively. In Singapore children don’t start grade one till their 7 and the curriculum outcomes are developmentally appropriate (basically working with numbers to 20 and starting to learn number to 100). The same children learning in the British curriculum are required to do multiplication, division and fractions. It’s absurd.

    The philosophy is amazing and I am 100% on board but taking it and trying to jam it into the British curriculum to sell the program ‘Singapore maths’ is just wrong.

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