Singapore’s Math Results, How Do They Do It?

Apr 27, 2017 by

by Danaher M. Dempsey, Jr. –

Since the creation of “New Math” in the 1950s and delivery via the SMSG (School Mathematics Study Group) textbooks, the USA’s progressive math education establishments have believed that conceptual understanding is the holy grail of math instruction.  Supposedly, once a child has conceptual understanding, math skills will be easier to acquire. Yet after 60 years of placing the cart before the horse, this plan is still not working well, but will anyone notice?  The fact is that for most children the acquisition of math skills comes effectively via traditional instruction and practice with some memorization  involved. Conceptual understanding comes later.

The Common Core thinkers have it backwards as well.  Many school districts downplay the Content Standards and push the eight Standards for Mathematical Practice. This method has yet to demonstrate that it is an effective and efficient way to learn mathematics.

The eight Standards for Mathematical Practice are:

(1) Make sense of problems and persevere in solving them

(2) Reason abstractly and quantitatively

(3) Construct viable arguments and critique the reasoning of others

(4) Model with mathematics

(5) Use appropriate tools strategically

(6) Attend to precision

(7) Look for and make use of structure

(8) Look for and express regularity in repeated reasoning

Singapore has much different ideas about instruction and how math is learned than the USA’s math gurus.  So who should be trusted and believed?  Singapore’s instructional practices should have been the center of intense interest over the last 20 years.  The third (TIMSS) Trends in International Math and Science Study revealed Singapore’s prominence in 1995 testing.

Mean scores    — Lower Grade  —   Upper Grade   in 1995 testing

Singapore —  552.08  —  624.95

USA   ——–  479.80  —  554.57

Korea  ——   560.90  —  610.70

Japan ——-   537.91  —  596.83

Hong Kong –  523.95  —  586.64

Australia —-  483.82  —  546.69

Netherlands – 492.88  —  576.66

Over the next 20 years the East Asian dominance became even stronger.  In 2015 (TIMSS) Trends in International Math and Science Study, the USA’s results are far worse than Singapore’s results.  It is particularly interesting when the fourth grade cohorts of 2011 are followed to 2015 in grade 8.

Singapore vs USA compared from grade 4 2011 to grade 8 2015

————grade 4 :: grade 8 :: change over 4 years for the cohort

USA  ——-   541 :: 518 :: change -23 lower

Singapore —  606 :: 621 :: change +15 higher

USA Gap : :  -65 :: -103 ::

The drop in score for the USA 4th to 8th cohort has been consistent for the last several TIMSS cycles.  There has been a perception by some that “unlike East Asia the USA leaves no one behind we focus on helping the lower performer achieve”.  Let us check the results.

8th grade TIMSS 2015 math results with percent of students able to achieve at given benchmarks
country – advanced — high — intermediate — low
Korea  ——-43%  — 75%  —  93% —  99%
Singapore54%  —  81%  — 94% —  99%
Japan   —– 34%  —  67%  — 89%  — 98%
USA ——–  10%  —  37%  — 70%  — 91%

I’ve been puzzled by the lackluster performance in math of USA 8th graders on the TIMSS testing for two decades and recently a drop on NAEP 2015. It seems inexplicable to me that the Math Ed gurus at the state and school district level have very little interest in how Singapore consistently scores so far above the USA. Does saying USA ranks in top 10 suffice?

I’ve reached the conclusion that the current USA math education gurus believe so strongly in their current  ideologically-based pedagogical superiority that there is no reason to consider anything else.  It is downright anti-science.  While East Asia leaves us in their mathematical dust the NCTM plods along with a failed ideology.

So how does Singapore do it?

July 29, 2016 at the 13th International Conference of Mathematical Education in Hamburg, Germany,  Berinderjeet Kaur, PhD of Singapore, presented the in depth pertinent information about teaching practices in Singapore.  Dr. Kaur’s Findings: Analysis of the interview transcripts revealed that students deemed a mathematics lesson as a good one when some of the following characteristics were present. The Teacher:

(1) explained clearly the concepts and steps of the procedure

(2) made complex knowledge easily assimilate through  demonstrations, the use of manipulatives, and real life examples.

(3) reviewed past knowledge

(4) introduced new knowledge

(5) used student work/group presentations to give feedback to individuals or the whole class

(6) gave clear instructions related to mathematical activities for in class and after class work.

(7) provided interesting activities for students to work on individually or in small groups

(8) provided sufficient practice tasks for preparations towards examinations


In a lesson there may be more than one instructional objective but the structural patterns of the lesson are done in sequence. Instructional approaches may involve:

D – Whole class demonstration (aimed to develop students’ understanding mathematical skills and concepts)

S – Seatwork

R – whole class review of student work

M – Miscellaneous –  managerial and administrative

Q – Group Quiz

T – Test

[D] [S] [R] were present in all 3 classrooms observed

Singapore bases its instructional program not on “inquiry” or “student-centered design” but on a combination of teacher-centered Traditional Instruction with Direct Instruction and then builds from this to Teaching for Understanding.   Why is the USA not doing the same?

The evidence is all there, if anyone wants to read it and believe it.  But THEY DON’T!

An adherence to ideological beliefs is apparently required of those in the current math leadership positions.  Information is simply IGNORED apparently because it does not compute in their ideologically bound frame of reference. Shockingly this dismissal of facts is representative of the entire US K-8 ed corps, with a few exceptions.  Why are agents like OSPI, school districts, and The Center for Strengthening the Teaching Profession not intelligently applying the relevant data to greatly improve USA’s math practices and performance?  Isn’t a 103 point gap enough to elicit some interest in change?

Is the Educational-Industrial behemoth incapable of change because of entrenched bureaucrats, ideologues, NGOs and profit margins?

Part 1 NCTM Fooled Me Twice, but No More

Danaher Dempsey suffered through the New Math in high school.  He served on the Washington State Board of Education’s Math Advisory Panel, which contributed to the development of the 2008 Washington Math Standards.  He has attempted to teach mathematics efficiently and effectively to students in six western states.

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