How Russia teaches mathematics, and how it reaches further by 17
A side-by-side map of the Soviet–Russian school tradition and the US system, by the child's age, from first counting to graduate research. Every concept is placed where each system introduces it, where it becomes fluent, and how it is taught. Evidence strength is marked on every claim. The short version: in school, timing differences for shared topics are small; the difference is depth (proof for everyone from 13) and breadth (number theory, equations, stereometry, calculus), built on a primary school that trains multi-step reasoning.
The concept map
Each dot is a concept, placed at the age a child reaches it. Lanes are strands of mathematics. In "Both", the violet dot is Russia, the ochre dot the US, and the line between them is the gap. Click a dot to trace what it builds on and what it unlocks; click a lane name to focus it.
Two clocks: what a child studies at each age
Slide the age. Left is the Russian classroom at that age, right is the American one. Chips are concepts; darker means deeper (exposure → introduced → developed → mastery with proof). Red rings mark what is new or deepened that year.
Coverage heatmap
Each square is one concept at one age: top half Russia, bottom half US, shaded by depth 0–4. The last column is the gap in years at fluency (negative = Russia earlier). Pick a strand.
Where the gaps are
Average difference in the age at which each system's standard track brings a concept to fluency. The lead is concentrated in particular strands, and some strands run the other way.
Fluent in one system only (standard tracks)
Russia only
US only
How it is taught: the principles behind the sequence
What a Russian classroom does differently, the cognitive mechanism, how strong the evidence is, and how an adaptive app can use it.
Teaching systems
The enrichment ecosystem
Why it works, and where the claims are weak
Time on task, international results, controlled studies and the strongest critiques, in one place.
Scheduled math time per week
International benchmarks
Studies
Critiques and counter-evidence
Same age, different problem
Representative problems from both systems at the same age, with the original Russian text. The bars rate demand from 1 to 5. Most Russian items are written "in the style of" a named textbook, so the evidence badge matters here.
Exams and the olympiad ladder
What each system tests, at what age, and the hardest thing on the paper.
Russian olympiad ladder
US competition ladder
The optimal learning path
Sixteen stages from age 3 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. This is the backbone the adaptive trainer will follow.
Acceleration: what the evidence says
Engine hooks for the adaptive trainer (next phase)
Bottlenecks: where children get stuck
Known conceptual stumbling blocks, why each is hard, how each system handles it, the error patterns that reveal it, and a remedy sequence.
How far the concepts go: university and graduate school
Where school mathematics leads. Russian placements come from the Moscow State mech-math study plan; US placements from typical major curricula and PhD qualifying exams. Most depth values in this tier are expert judgement.
A short history of both systems
From Kiselev's textbooks and the Kolmogorov reform to Common Core and the new federal program.
Research library, glossary and uncertainty ledger
The full research notes behind this atlas, every primary source, a Russian–English glossary of all concepts, and an honest list of what is still unverified.