Singapore Math vs Russian Math, and what to use after Singapore
“Singapore Math” and “Russian Math” are both labels coined in the US. Behind each is a real school tradition with its own textbooks. Singapore’s elementary books teach with visual models and a structured routine, and they do that well. The Russian Math textbooks, the course A. P. Kiselev wrote for Russian schools, do something they don’t: they prove every rule, and they don’t stop at grade 8.
How each teaches
The Russian Math textbooks give a definition, prove the theorem, then set the problems. A child learns why the order of addition doesn’t matter and why long division works, and later why the angles of a triangle add up to two right angles. Singapore moves from objects, to pictures, to symbols, and uses bar models to solve word problems.
| Feature | Russian Math textbooks | Singapore Math (US editions) |
|---|---|---|
| How far it goes | Grade 4 to grade 12, ending with Kiselev's Calculus | Ends at grade 8 (grade 5 or 6 in some editions) |
| Why rules work | Proved: Kiselev's Arithmetic proves why long division works, read with a child of nine or ten | Shown with visual models |
| Geometry | A full proof-based course in plane and solid geometry: Kiselev’s Geometry, Book I and Book II | Middle-school geometry |
| Hard problems | Separate problem books with full solutions: Rybkin, Shaposhnikov & Valtsov | Workbooks and extra practice books |
| The next step | Same author, same notation, from arithmetic to calculus | A different publisher and a different method |
Already using Singapore? Where to continue
You don’t have to choose one or the other. When your child finishes Singapore’s elementary levels, or wants to know why a method works and not just how, the Russian Math textbooks take over. The Where to start page places your child by age and by what they have already done.
Questions parents ask
- Is Russian Math harder than Singapore Math?
- It asks for a different effort: following an argument rather than a model. Children who ask "why?" usually find it easier, not harder.
- Do the Russian Math textbooks work without a teacher?
- A parent reads the arithmetic with a child of nine or ten. From algebra on, a motivated student can work alone.
- Do they cover high school?
- Yes. Kiselev’s algebra, plane and solid geometry and calculus, with trigonometry and problem books from the authors who taught alongside him. They do not teach statistics or school-level probability.
- Can we switch from Singapore partway through?
- Yes. Each book covers a defined stage, so you can buy one level at a time. The Where to start page places your child by age and by what they have already done.
Find your child’s starting book →Which book for which school year →All books →Compared with AoPS, Math Mammoth and Beast Academy →