Why We Often Look to East Asian Math for Math Support

There is a part of Singapore Math everyone skips.

Every few years an education system looks at international test results, notices that East Asian countries are running away with mathematics, and decides to import the method.

The gap is real. In the 2012 PISA rankings, Shanghai scored 613, Singapore 573 and Hong Kong 561. England scored 494 and placed 26th, with 22 percent of its fifteen-year-olds at the lowest level of mathematical proficiency. The United States did not do better.

So the textbooks get bought and the training days get booked. And then, more often than not, nothing much happens.

It is worth understanding why, because the parts that do transfer are genuinely excellent and available to any teacher, tutor or parent for free.

What actually gets imported

Three practices travel under the banner of Singapore or Shanghai math, and all three are worth having.

Concrete, pictorial, abstract. Students meet an idea through physical materials first. Then they represent it visually, in a structured diagram rather than a decorative picture. Only then do they move to symbols.

The sequence is the whole point, and the middle stage is where almost everyone rushes. Move a student to symbols too early and they memorize a procedure with no structure underneath it, which works right up until the problem changes shape. Build from experience to representation to abstraction and the understanding survives contact with unfamiliar problems.

The bar model. This is the specific technique that most descriptions leave vague, and it deserves naming.

Take a problem: Tom has three times as many marbles as Sam, and together they have 48. Draw one bar for Sam and three identical bars for Tom. Four equal units now account for 48, so one unit is 12. Sam has 12, Tom has 36.

That is a simultaneous equation solved by a nine-year-old with a pencil and no algebra whatsoever. More importantly, the student has been forced to ask what relationships are actually at work before touching a calculation, which is the habit that separates people who can do math from people who can follow steps.

Depth over breadth. Fewer topics, developed further. Students explain their reasoning, compare strategies and justify conclusions, and an answer without an explanation is treated as incomplete.

Worth being precise here, because this is the one most often misapplied. Depth over breadth means actually cutting topics from the year. It does not mean covering the same enormous list more slowly, which is what usually happens and which produces the worst of both.

What happened when England tried it

England did not dabble. It committed at national scale, sending teachers to Shanghai, hosting Shanghai teachers in English classrooms, and building a network of Maths Hubs around the approach. The government has allocated around £76 million to teaching for mastery.

The longitudinal evaluation by Sheffield Hallam University found inconclusive evidence that participating schools improved their Key Stage 2 results, and stated plainly that there was no quantifiable evidence that the teacher exchange, or East Asian informed teaching alone, was raising attainment at Key Stage 2 compared with other schools. Pupil attitudes toward math did not shift either.

That is a discouraging headline, and anyone selling you Singapore math should have to answer it.

But read further and the picture gets more useful. The researchers found that not all participating schools actually went on to implement the pedagogy. Among the ones that did, there were positive impacts at Key Stage 1, and an exploratory analysis of sixteen schools that sustained a Shanghai-informed approach across two years did find a low positive effect.

So the method is not the problem. Implementation is. Which raises the obvious question of why implementation kept failing.

The part everyone skips

Here is the detail that explains most of it, and it surfaced in the British debate almost as an embarrassment.

Shanghai math teachers typically teach two lessons a day. Two. Their colleagues in England and the United States teach five or six, plus supervision duties. The Shanghai teacher spends the remainder of the day inside a teaching research group: planning lessons collaboratively, observing colleagues, being observed, and picking apart individual lessons in detail with other specialists. Primary math is taught by people who specialize in math rather than by a generalist covering everything.

That structure is not a nice extra sitting alongside the pedagogy. It is what produces the pedagogy. The precise questioning, the carefully chosen examples, the anticipation of exactly where a class will go wrong: those come from a profession organized to develop them, over years.

The evaluations noticed this. The professional development architecture, with its regular group observation and its habit of actively critiquing practice, was repeatedly identified as the major strength of the Shanghai system.

So a school buys the textbooks, keeps the six-lesson timetable, gives teachers no shared planning time and no subject specialism, and then concludes after two years that Shanghai math does not work. What did not work was importing the visible half of a system and leaving the machinery behind.

Which is good news if you are not a school

Notice who is not bound by any of that.

A home educator working with two or three children has no timetable problem. A tutor working one to one has all the planning time in the world relative to the teaching time. A small independent setting can decide to specialize.

The constraints that defeated a £76 million national program are constraints of scale and staffing. They do not apply to you. The pedagogy is published, the bar model is free, and the thinking time that Shanghai buys with a two-lesson day is something a parent at a kitchen table already has.

How to actually use it

Do not skip the pictorial stage. It is the one under time pressure and it is the one carrying the load. If a student can solve it with a diagram but not with symbols, they are mid-process. If they can solve it with symbols but not draw it, they have memorized something.

Learn the bar model properly before teaching it. An afternoon is enough. It handles part-whole, comparison, ratio, fractions and percentage change, and it builds algebraic thinking years before algebra arrives.

Practice with variation, not repetition. This is the piece most often lost in translation. Twenty near-identical problems train a procedure. Twenty problems that each change one feature train the concept, because the student has to notice what changed and what it did.

Require the explanation every time. An answer alone is incomplete. This costs you nothing and it is the single highest-return habit on the list.

Cut the topic list. Depth over breadth is only real if something comes off.

In a mixed-age setting, run one concept at several levels. One student works the bar model visually while another extends the same relationship into symbolic form. Same idea, different sophistication, same conversation.

The honest caveats

Two things get left out of most enthusiastic write-ups.

First, the test scores of high-performing East Asian systems are not produced by classroom teaching alone. They sit on top of a large private tutoring sector, long study hours and significant exam pressure, with documented costs to student wellbeing. Anyone claiming the method alone produces those PISA numbers is not being straight with you.

Second, Shanghai is Shanghai. It is a wealthy, selective, urban region, and it was reported separately in PISA for that reason. It is not a national average and should not be quoted as one.

None of that invalidates the pedagogy. Concrete-pictorial-abstract, the bar model, variation practice and demanded explanation are good instructional design on their own merits, and they were good before anyone noticed the rankings. But the honest claim is narrower than the marketing: these are strong methods, they need real teacher subject knowledge and real planning time to run well, and the test score gap has other causes stacked underneath it.

Math taught this way is not mechanical. It is a language of logic, and logic cultivated carefully supports sound judgment well outside the math lesson. That is worth the trouble. Just go in knowing what the trouble actually is.

Okay, Mister, So how does TPA use this?

Fair question, and there is a version of that answer that is just an advertisement. Here is the other one.

Depth over breadth is the strongest match, and it is enforced rather than encouraged. TPA's academic units never re-teach. Week twelve assumes week six and does not revisit it. Each six-week arc carries a single named mathematics spine, decided before a word of the arc is written, and the four mathematics days in every week introduce it, extend it, complicate it and deepen it. There is no review week to fall back on, which means depth is structural rather than aspirational.

Concrete to abstract is handled by a dedicated component. Every academic week carries a math supplement in six parts: the skills that week used, worked examples, a middle section where the student either finishes a partly worked solution or finds the deliberate error in one, pencil-and-paper drill, then story problems requiring them to read a situation, pull the numbers out, work them, and put the answer back into the story. That final move is the one most programs skip, and a number with no meaning reattached is where math instruction usually stops.

Explanation is required. Task ladders end in constructing and defending a claim, response sheets carry a line asking what would change the student's mind, and every arc ends in a spoken defense. An answer on its own is treated as incomplete.

The no-repeat rule creates an obvious problem, so it is answered directly. Each skill names the earlier week where it was first met, with an instruction to go back and look if it has gone. That converts a trap into deliberate spaced retrieval with a pointer home.

Answers live at the back of the student's own book, showing the working rather than just the number. Hiding answers from a child assumes the point is the score.

Now the part that matters more.

The Shanghai advantage that no publisher can sell you is professional, not instructional. Two lessons a day, subject specialists, and years spent developing teacher knowledge inside a structure built for it. No set of materials supplies that, and TPA does not pretend to. A parent or tutor working through these units still has to understand the mathematics well enough to see exactly where a student's reasoning broke, and nothing in a PDF fixes that.

What good materials can do is narrow the gap: sequence the ideas properly, supply the worked examples, show the errors worth spotting, and demand the explanation every time. The rest is still the adult in the room, which is the honest position and the reason the England program produced so little from so much money.

Sources

Boylan, M., et al. Longitudinal Evaluation of the Mathematics Teacher Exchange: China-England. Sheffield Hallam University for the Department for Education. https://assets.publishing.service.gov.uk/media/5c49b38340f0b61717193d2d/MTE_main_report.pdf

Boylan, M., et al. (2018). "The Mathematics Teacher Exchange and 'Mastery' in England: The Evidence for the Efficacy of Component Practices." Education Sciences, 8(4). http://shura.shu.ac.uk/23973/

"Policy Transfer and Isomorphism: A Case Study of the England-China Maths Teacher Exchange." British Journal of Educational Studies. https://www.tandfonline.com/doi/full/10.1080/00071005.2021.1926915

OECD (2012). PISA 2012 Results.