Japan’s Tokushu-san vs. the World: Why No Other Country Teaches Math This Way

In my previous article, I introduced “Tokushu-san” — the curious set of special math problems that Japanese children encounter around the age of ten. They include Tsurukame (Crane-and-Turtle), Traveler’s problems, and Kabusoku (Excess-Deficit). These problems appear almost nowhere else in the world, yet in Japan they are considered an essential part of elementary arithmetic.

At first glance, Tokushu-san looks like a collection of clever puzzles for test preparation. But the reality is far deeper: these problems serve as a bridge between concrete arithmetic and abstract algebra, long before algebra is formally introduced. The question we will explore here is simple but profound: Why does only Japan have Tokushu-san? And what do other countries do instead?

To answer this, we need to step outside Japan and examine how mathematics is taught in the United States, the United Kingdom, Singapore, and Finland. By comparing their systems with Japan’s, we can see not only how different the methods are, but also why Japan’s approach is unique.

The United States: Word Problems without a Canon

In the United States, mathematics education is organized state by state, but since the 2010s the Common Core State Standards (CCSS) have provided a shared framework. The guiding principles are focus, coherence, and rigor. Students encounter fractions and decimals in the middle grades, and proportional reasoning in the upper grades.

When it comes to thinking skills, the U.S. system emphasizes the eight Standards for Mathematical Practice. These include “reason abstractly and quantitatively,” “construct viable arguments and critique the reasoning of others,” and “look for and make use of structure.” In other words, logical reasoning and abstraction are strongly encouraged.

But here is the key difference: there is no fixed canon of puzzle types like Tokushu-san. American students practice solving complex word problems that may require multiple steps and strategies, but the problems are not standardized into recurring formats. For example, a child might face a problem about mixing paint colors or sharing pizzas among friends. Each problem is unique, and success depends on reading comprehension, flexible thinking, and step-by-step reasoning.

For advanced learners, there are math clubs and contests such as the Math Olympiad, where students tackle non-routine problems. However, these are extracurricular and not part of the mainstream curriculum. In everyday school life, American children do not meet an equivalent of Tsurukame or Traveler’s problems.

The United Kingdom: Mastery and the CPA Approach

In England, the mathematics curriculum is structured into Key Stages. Key Stage 1 covers ages 5–7, while Key Stage 2 spans ages 7–11. The 2014 reform of the National Curriculum emphasized higher expectations, such as requiring all students to master the multiplication tables up to 12 × 12 by Year 4.

The philosophy behind British math education is often described as the Mastery approach. The idea is that every child should achieve a solid grasp of fundamental concepts before moving on. Instead of racing ahead, teachers ensure that the entire class moves forward together, revisiting topics with increasing depth.

A hallmark of this approach is the Concrete–Pictorial–Abstract (CPA) progression. Children first manipulate physical objects (counters, blocks, or measuring cups), then represent problems visually (pictures, diagrams), and finally move to abstract symbols and equations. This gradual transition helps secure deep conceptual understanding.

Reasoning and explanation are also central. Students are encouraged to articulate not only what answer they obtained, but also why it works. Teachers prompt them to justify their solutions and to critique others’ reasoning. This emphasis on dialogue builds a habit of mathematical communication.

Yet here too, we find no equivalent of Tokushu-san. The U.K. curriculum does not offer a set of standardized puzzle types that all students practice. There are certainly challenging problems—for example, through the UK Mathematics Trust (UKMT) competitions—but these remain optional enrichment rather than a shared national canon. In everyday classrooms, British children practice fluency and reasoning without ever encountering a Traveler’s problem or a Crane-and-Turtle puzzle.

Singapore: The Bar Model Method and Problem-Solving Culture

Among the countries often compared to Japan, Singapore is the closest when it comes to structured approaches to word problems. Since the 1980s, the Ministry of Education has emphasized a spiral curriculum, where concepts are introduced in a simple form and revisited with increasing sophistication at later grades. By the end of primary school, students have already encountered percentages, ratios, and even introductory algebraic expressions.

Central to Singapore’s pedagogy is the Bar Model method. When students face a word problem, they are taught to draw rectangular bars to represent quantities. For example, if Alice has twice as many apples as Ben, children sketch two bars for Alice and one bar for Ben. This visual representation makes it easier to reason about ratios, differences, and totals without immediately resorting to algebraic symbols.

In this sense, the Bar Model serves a similar role to Tokushu-san: it bridges arithmetic and algebra before formal algebra is introduced. However, there is an important distinction. Tokushu-san consists of fixed problem types—Tsurukame, Traveler’s problems, and so on—whereas the Bar Model is a general tool. It can be applied to almost any arithmetic word problem, from sharing sweets to comparing speeds.

Singaporean students also undergo high-stakes assessments, most notably the Primary School Leaving Examination (PSLE) at the end of Grade 6. This exam includes complex word problems that require not only computation but also creative problem-solving. As a result, children spend years honing their ability to dissect problems using heuristics such as “work backwards,” “look for patterns,” and “draw a diagram.”

In short, while Singapore cultivates similar skills to Japan—abstract reasoning, bridging arithmetic and algebra—it does so through versatile strategies rather than through a fixed canon of puzzle types. If Tokushu-san represents Japan’s cultural “math drills,” the Bar Model represents Singapore’s cultural “problem-solving toolkit.”

Finland: Slow Pace and Phenomenon-Based Learning

Finland is frequently celebrated in international discussions of education, thanks to its consistently high rankings in global assessments and its reputation for child-centered learning. Mathematics in Finnish primary schools looks very different from both Japan and Singapore.

The national Core Curriculum provides broad goals, but teachers enjoy wide autonomy in how to implement them. Progression is intentionally gradual: for example, fractions and decimals are introduced later than in most systems, often in the middle grades rather than the early years. The aim is to ensure that all children build confidence and conceptual clarity rather than racing ahead.

A distinctive feature of Finland’s approach is phenomenon-based learning, introduced in the 2016 reform. Instead of treating mathematics as a siloed subject, students sometimes study it through real-world themes such as climate change, population statistics, or economics. For example, they might learn percentages and ratios while analyzing energy consumption or voting data. In this way, mathematics is embedded in social and scientific contexts.

Assessment also differs. Finland has no nationwide standardized testing at the primary level. Teachers rely on continuous observation and provide descriptive feedback rather than numerical rankings. Retention is rare; struggling students receive additional support through special education services rather than being held back.

When it comes to problem-solving, Finnish classrooms often include open-ended tasks and puzzles. Yet, like the U.S. and U.K., there is no canon of fixed puzzle types comparable to Tokushu-san. Children are encouraged to explore and generalize from experience, rather than practice a set of codified methods. In other words, Finnish mathematics nurtures flexible thinkers, but does not provide the repeated, structured drills that characterize Japan’s special problems.

Japan: The Educational Role of Tokushu-san

Now we return to Japan, where Tokushu-san holds a central place in the upper grades of elementary arithmetic and, more prominently, in the competitive world of junior high school entrance exams. To outsiders, these problems may appear to be quirky test puzzles. But within Japan’s educational culture, they are valued as a unique training ground for mathematical thinking.

Consider the classic Tsurukame (Crane-and-Turtle) problem: “In a cage, there are cranes and turtles. Together they have 20 heads and 50 legs. How many cranes and how many turtles are there?” At first glance, it is a riddle. Yet beneath the surface, this is nothing less than a disguised system of linear equations. Children who have never seen algebra are learning to set up and solve simultaneous equations by reasoning about heads and legs.

The Traveler’s problem provides another illustration. Two people leave different towns at different times and speeds. Where will they meet? This problem foreshadows algebraic treatment of rates, time, and distance, but it is introduced through accessible narratives that ten-year-olds can grasp. By solving such puzzles, children practice reverse reasoning, estimation, and the coordination of multiple variables.

In effect, Tokushu-san acts as algebra before algebra. It provides young learners with the opportunity to manipulate abstract relationships long before they encounter the formal symbols of x and y. By presenting these relationships in the guise of animals, travelers, or baskets of fruit, the problems give children a tangible entry point into abstract structures.

This approach is more than mere test preparation. It is a cultural commitment to structured problem-solving, where specific problem types serve as mental training drills. Much like practicing scales in music or kata in martial arts, Tokushu-san provides a repertoire of standard forms through which deeper skills are cultivated: abstraction, logical inference, and problem decomposition.

Conclusion: What Makes Japan Unique

By comparing Japan’s Tokushu-san with mathematics education in the United States, the United Kingdom, Singapore, and Finland, a clear pattern emerges. All of these countries value reasoning, problem-solving, and abstraction. Yet none of them employ a fixed canon of puzzle types as part of their mainstream curriculum.

In the United States, children wrestle with diverse word problems, but there is no recurring structure to master. In the United Kingdom, the emphasis lies on mastery and dialogue, not on standardized puzzle forms. Singapore comes closest, with its Bar Model method and problem-solving heuristics, but even here the approach is a general tool rather than a set of fixed problem types. Finland, meanwhile, situates mathematics within broader social and scientific phenomena, avoiding structured drills altogether.

Japan alone has cultivated a tradition of structured problem forms. Tokushu-san are not arbitrary riddles; they are carefully designed training exercises that anticipate algebra, nurture abstraction, and sharpen logical reasoning. They are, in essence, a cultural invention—an educational heritage developed through decades of entrance exams and teaching practices.

This uniqueness matters. In an era where education systems worldwide are searching for ways to balance conceptual understanding with problem-solving fluency, Japan’s Tokushu-san offers an intriguing model. They show how a well-designed set of problem archetypes can accelerate the transition from arithmetic to algebra and provide young learners with mental tools that endure beyond the classroom.

Seen this way, Tokushu-san are not just “Japanese exam tricks.” They are a distinct contribution to the global conversation on mathematics education—evidence that cultural traditions can shape how children learn to think mathematically. And perhaps, they suggest that the world has something to learn from Japan’s peculiar yet powerful puzzles.

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