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.
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Six bottom lines from the atlas. Each carries its evidence grade, and each opens the part of the atlas that backs it.
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 →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 →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 →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 →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 →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 →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.
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.
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.
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.
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 →
The atlas is the map. The adaptive trainer, now in development, walks a learner along it.
Each stage has a gate to pass. Strong learners move ahead faster, and nobody is pushed past a gap.
Short interleaved practice, the Russian habit of daily oral review. It is among the best-evidenced techniques in learning science.
Word problems drawn as diagrams first, then equations. This is how Russian primary school makes later algebra cheap.
The trainer reads the error patterns behind 37 known stumbling blocks and re-sequences the path for the learner's level.
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.
Comparative education research is full of confident claims built on thin data. The atlas marks which is which.
Checked against a primary source: a federal standard, a textbook, an exam specification, or a peer-reviewed study.
From reliable secondary sources or consistent expert accounts, not yet traced to a primary document.
Our own judgement from the curriculum data. Useful for direction, not for precise size.
Listed in the uncertainty ledger, with what it would take to settle it.