Free research atlas · Russia ↔ US · counting to PhD

How Russia teaches mathematics, and how it reaches further by 17

We mapped the Soviet–Russian school tradition against the US system, age by age, from first counting to graduate research. Every concept sits where each system introduces it, where children become fluent, and how it is taught, with the strength of the evidence marked on every claim.

No sign-up needed for the atlas. Works on phone, tablet and desktop.

0to100math.com/atlas · Two clocks
The atlas's Two clocks view: at age 10, the Russian and US classrooms side by side with a chart of concepts at fluency by age
381concepts, counting → graduate research
813curriculum topics mapped (328 RU · 485 US)
53same-age problem pairs, original Russian text
37known bottlenecks, with remedies
24teaching principles, evidence-graded
What the research found

Not earlier. Deeper, broader, and built on a different primary school.

Six bottom lines from the atlas. Each carries its evidence grade, and each opens the part of the atlas that backs it.

01Inferred

Russia is not mainly earlier. It goes deeper and broader by 15–17.

At age 11 both systems have about the same number of school concepts at fluency. After 12 they separate. For a concept both teach, timing usually differs by a year or less.

See the two clocks →
02Secondary

Primary school builds something different in kind.

Multi-step word problems with schematic models, letter equations from grade 1–2, and "=" read as a relation. Motion and work problems are fluent in Russia by 10–11; in the US they appear as Algebra 1 exercises.

Compare the problems →
03Secondary

44 concepts reach fluency in Russia's standard track but not in the US standard track.

24 of them by grade 9: number theory, Vieta, rational expressions, three years of axiomatic geometry, vectors. The reverse holds too: 17 US-fluent concepts, mostly statistics and modelling, that Russia leaves thin.

Where the gaps are →
04Secondary

The mechanism is structure, continuity and teachers, not genius.

Daily mixed oral review, one coherent textbook line per stage, 5–6 math lessons a week in grades 5–9, and proof for everyone from 13. The best-evidenced pieces also work in US classrooms.

How it is taught →
05Secondary

Strong on curriculum tests, average on applied ones.

TIMSS 2019: Russia 567 / 543 vs US 535 / 515 at grades 4 / 8. PISA 2018: Russia 488, near the OECD average. We show both, along with the critiques.

Weigh the evidence →
06Secondary

The best path gates on understanding, not on the calendar.

Fraction knowledge at 10 predicts algebra at 16. Ages 9–12 look like the highest-payoff window. Calendar-based "algebra for all" has not raised achievement in two large studies.

The optimal path →
School concepts at fluency, standard tracks

Even at 11. Apart by 15. Further apart by 17.

Count of school-level concepts each system's standard track brings to fluency by a given age. Counts depend on how finely topics are split, so read them as direction, not precise size. The US accelerated track reaches 190 by 17.

RussiaUSInferred
Inside the atlas

One interactive map of how math is learned, from 3 to research.

Explore by age, by strand or by concept, in English or Russian. Click any concept to see what it builds on, what it unlocks, and how each country teaches it.

The concept map

Every dot is a concept, placed at the age a child reaches it. Violet is Russia, ochre the US, and the line between them is the gap. Trace any concept back to its prerequisites and forward to what it unlocks.

Open this view →

0to100math.com/atlas · Concept map
Concept map: strands of mathematics by age with Russian and US placement of each concept
The 0 → 100 path

Sixteen stages, from counting to research.

Drawn from the Russian sequence and the learning-science evidence. Each stage ends in a mastery gate: move on when the gate is passed, not when the calendar says so.

  1. 1age 3–5

    Quantity before number

  2. 2age 5–6

    Measure and the number line

  3. 3age 6–7

    Additive structures within 100

  4. 4age 7–8

    Place value and multiplicative foundations

  5. 5age 8–10

    Multi-digit operations, unit fractions, rates

  6. 6age 10–11

    Fractions and decimals as numbers

  7. 7age 11–12

    Ratio, proportion, negatives

  8. 8age 12–13

    Algebra I: expressions, identities, linear functions; proof begins

  9. 9age 13–14

    Algebra II: quadratics, rational expressions, reals; similarity

  10. 10age 14–15

    Functions as objects; sequences; probability; trig in triangles

  11. 11age 15–16

    Trig functions, exponents and logarithms, stereometry

  12. 12age 16–17

    Calculus foundations and parameters

  13. 13age 17–19

    Rigour bridge: logic, proof, ε–δ

  14. 14age 18–20

    Core undergraduate structures

  15. 15age 19–22

    Abstraction: algebra, analysis, topology

  16. 16age 22+

    Graduate frontier

Red-ruled stages mark the window the evidence points to as highest-payoff, roughly ages 9–12: fractions as numbers, "=" as a relation, and letters as variables. See every gate in the atlas →

How 0to100math will teach

Research-proven methods, with AI that notices where a learner is stuck.

The atlas is the map. The adaptive trainer, now in development, walks a learner along it.

Mastery gates

Each stage has a gate to pass. Strong learners move ahead faster, and nobody is pushed past a gap.

Daily mixed review

Short interleaved practice, the Russian habit of daily oral review. It is among the best-evidenced techniques in learning science.

Schematic models

Word problems drawn as diagrams first, then equations. This is how Russian primary school makes later algebra cheap.

Bottleneck detection Soon

The trainer reads the error patterns behind 37 known stumbling blocks and re-sequences the path for the learner's level.

Adaptive trainer · waitlist

Be first to try the trainer.

It places a learner on the 16-stage path, finds the bottleneck, and builds the next session around it. Parents, teachers and students are all welcome.

We store only what you type here. We use it only to tell you when the trainer opens, and we'll delete it whenever you ask. For adults, or students 13 and older.

How sure are we?

Every claim carries its evidence grade.

Comparative education research is full of confident claims built on thin data. The atlas marks which is which.

Verified

Checked against a primary source: a federal standard, a textbook, an exam specification, or a peer-reviewed study.

Secondary

From reliable secondary sources or consistent expert accounts, not yet traced to a primary document.

Inferred

Our own judgement from the curriculum data. Useful for direction, not for precise size.

Open

Listed in the uncertainty ledger, with what it would take to settle it.