Russian math compared with Singapore Math, Art of Problem Solving, Math Mammoth and Beast Academy
Four programmes a homeschooling family is likely to be weighing, and what the Russian textbooks do differently. Each is good at what it is for; the question is what you want.
In one sentence
Singapore Math and Math Mammoth teach procedures through models and worked examples for the elementary and middle years; Art of Problem Solving and Beast Academy aim at competition mathematics from an early age; the Russian textbooks are the original school course of a tradition that proves every rule from arithmetic onward and runs, in one sequence, from arithmetic to calculus.
Coming from Singapore Math? Singapore Math vs Russian Math, and where to continue →
| Russian textbooks (Kiselev and others) | Singapore Math | Art of Problem Solving | Math Mammoth | Beast Academy | |
|---|---|---|---|---|---|
| What it is | Translations of the classic Russian school textbooks: one author's complete course, arithmetic to calculus, plus the problem books written to go with it | A programme based on the Singapore primary curriculum: textbooks, workbooks and teacher guides | A textbook series and online classes written for strong students and competitions | A worktext programme (text and exercises in one book) for elementary and middle grades | A comic-style curriculum with guide and practice books for grades 1–5, from the AoPS team |
| Approach | Proof-based: every rule is proved before it is used; definitions first, then theorems, then problems | Concrete → pictorial → abstract; bar models; procedures explained with visual models | Problem-solving first; students discover methods through hard problems | Mastery-based, self-teaching, procedure explained then practised | Puzzle- and story-led, aimed at keeping strong young students engaged |
| Range | Grades 4 through 12, into university analysis | Kindergarten to grade 8 (grade 5 or 6 in some editions) | Pre-algebra to calculus, plus competition books | Grades 1–7 (through pre-algebra) | Grades 1–5 |
| Sequence | One sequence, one publisher, one method, arithmetic to calculus | Elementary and middle only; a different programme after | Starts at pre-algebra; something else is needed before | Elementary and middle only; a different programme after | Elementary only; designed to lead into AoPS |
| Who teaches | A parent or tutor who reads alongside a younger student; older students work alone | Parent-led with teacher guides | Largely self-taught; online classes available | Self-teaching by design | Parent-led, then self-paced |
| Exercises | Graded exercises with answers in the course books; separate problem collections with thousands of problems | Workbooks and extra practice books | Many hard problems, full solutions in separate books | Built into the worktext | Practice books |
| Format | Paperback, hardcover, Kindle, reader-only digital edition | Print and online | Print and PDF | Print and online | |
| Cost | A single book per year or two; no consumables | Several books per year | Books plus optional classes | Low; one worktext per grade | Several books per grade; online subscription |
| Not covered | Statistics, probability at school level, coordinate transformations, vectors; the modern exam strands | Nothing beyond grade 8 | Nothing before pre-algebra | Nothing beyond pre-algebra | Nothing beyond grade 5 |
Which one, for whom
- A child of 9–11 beginning real arithmetic, with a parent who will read with them
- Kiselev's Arithmetic. Every rule is proved, which no elementary programme does. Singapore Math or Math Mammoth if you want a self-contained workbook routine instead.
- A strong student who wants competition mathematics
- Art of Problem Solving, with the Russian problem books (Problems for School Mathematics Circles, Shaposhnikov & Valtsov, Rybkin) as a second source of hard problems with full solutions.
- One sequence from arithmetic to calculus without changing publisher
- The Russian textbooks are the only option here that runs the whole way, written by the same author in the same notation.
- A student who learns best from worked procedures and visual models
- Singapore Math or Math Mammoth. The Russian books are text and proof; they expect the student to follow an argument.
- An adult relearning mathematics properly
- Rashevsky's Arithmetic and then Kiselev's Algebra and Geometry. The programmes above are written for children.
Before buying for an exam course, read what these books do not teach on the curriculum page. No book in this catalogue teaches statistics or school-level probability.
Where to start: the course in order →Which book for which school year →