How Countries Teach Math
10 countries. 10 different philosophies. One subject. Here's what makes each approach unique — and how PISA scores compare.
PISA 2022 math rankings: 🇸🇬 Singapore (575) > 🇨🇳 China (591 in 2018) > 🇯🇵 Japan (536) > 🇰🇷 South Korea (527) > 🇫🇮 Finland (484) > 🇬🇧 UK (489) > 🇩🇪 Germany (475) > 🇫🇷 France (474) > 🇺🇸 USA (465). Key differences: Singapore uses CPA + bar models; Japan uses hatsumon (problem-posing); Korea adds private hagwon; Finland bans tests until 18; China requires rote multiplication tables by age 9.
The Full Comparison
| Country | PISA 2022 Score | Core method | School age | Formal algebra age | Calculator policy | Number naming | Decimal separator | Order of ops mnemonic | Signature feature |
|---|---|---|---|---|---|---|---|---|---|
| 🇸🇬 Singapore | 575 #1 | CPA (Concrete-Pictorial-Abstract) + Bar Modelling | 6 | 13 (Secondary 1) | No calculators until age 11 | Short scale (billion = 10⁹) | Point (3.14) | No acronym — concept taught directly | Bar model visualisation — solves algebra problems without algebra |
| 🇯🇵 Japan | 536 #4 | Hatsumon (problem-posing) + structured whole-class neriage | 6 | 13 (中1, junior high) | Limited in primary; used in secondary | Myriad system — 万/億 (groups of 10,000) | Point (3.14) | No acronym | Jugyo kenkyu (lesson study) — teachers refine one lesson over weeks |
| 🇰🇷 South Korea | 527 #6 | Intense drilling + private hagwon academies | 6 | 13 (middle school yr 1) | Limited in primary | Myriad system — 만/억 (groups of 10,000) | Point (3.14) | No widely used acronym | Hagwon culture — students study until 10 PM in private academies |
| 🇫🇮 Finland | 484 #16 | Play-based, inquiry learning, individual pace | 7 | 13 (grade 7) | From primary | Long scale (miljardi = 10⁹, biljoona = 10¹²) | Comma (3,14) | No acronym | School starts at 7 — latest in OECD. No standardised tests until 18. |
| 🇨🇳 China | 591 #1 (B-S-J-Z 2018) | Whole-class Shanghai mastery + rote fluency | 6 | 12–13 (初中 / grade 7) | Not in primary | Myriad system — 万/亿 (groups of 10,000) | Point (3.14) | No acronym; 九九 table chanting | 九九乘法表 (9×9 multiplication table) memorised by rote by age 9 |
| 🇩🇪 Germany | 475 #25 | Structured curriculum, Abitur preparation, formal proof | 6 | 11–12 (Gymnasium kl. 5–6) | From secondary | Long scale (Milliarde = 10⁹, Billion = 10¹²) | Comma (3,14) | Punkt vor Strich (× before +) | Abitur requires calculus from every student; long-scale "Milliarde" naming |
| 🇫🇷 France | 474 #25 | Formal proof culture + Grandes Écoles elite track | 6 | 11–12 (collège, 6e/5e) | From collège (age 11+) | Long scale (milliard = 10⁹, billion = 10¹²) | Comma (3,14) | No acronym; French students prove rules directly | Classes préparatoires — world's most demanding undergraduate math preparation |
| 🇬🇧 UK | 489 #22 | Mastery approach (imported from Shanghai since 2014) | 5 | 11 (Year 7, KS3) | Varies; GCSE allows calculator papers | Short scale (billion = 10⁹) | Point (3.14) | BODMAS / BIDMAS | GCSE 9-1 at 16; A-Level maths (calculus, statistics, mechanics) |
| 🇮🇳 India | N/A* N/A* | NCERT curriculum + Vedic math supplements | 6 | 11 (Class 6, NCERT) | From secondary school | Indian system — lakh (10⁵) / crore (10⁷) | Point (3.14) | BODMAS (follows UK tradition) | Vedic math (16 sutras) + lakh/crore number system |
| 🇺🇸 USA | 465 #26 | Common Core State Standards, discovery/conceptual learning | 5 | 13–14 (Algebra I, grade 8–9) | Often from grade 3-4 | Short scale (billion = 10⁹) | Point (3.14) | PEMDAS (Please Excuse My Dear Aunt Sally) | PEMDAS; Common Core's "explain your thinking" approach |
*India has not participated in recent PISA rounds. China figures are for Beijing-Shanghai-Jiangsu-Zhejiang (BSJZ) — not nationally representative. OECD average: 472.
The Key Dimensions Explained
Age formal algebra starts
Symbolic algebra (working with variables like x) is introduced earliest in England (age 11, Year 7), France (collège, 11–12), Germany (Gymnasium, 11–12) and India (Class 6, age 11). East Asian systems — Singapore, Japan, South Korea and China — formally begin algebra around age 12–13 at the start of secondary/junior high. The USA is the latest, with Algebra I typically taken in grade 8–9 (age 13–14), though many students meet pre-algebra concepts earlier.
Calculator use policy
Policy splits sharply. Singapore and China keep calculators out of primary school entirely (allowed from roughly age 11+), prioritising mental arithmetic and fluency. Germany and France introduce them from secondary/collège. Finland and the UK permit calculators from primary school, and the UK even sets dedicated calculator and non-calculator GCSE papers. The USA often allows calculators from grades 3–4.
Number naming (billion vs milliard)
Three different systems are used. Short scale (billion = 10⁹) is used by the USA, UK and Singapore. Long scale is used by Germany (Milliarde = 10⁹, Billion = 10¹²), France (milliard / billion) and Finland (miljardi / biljoona) — so the German "Billion" means a million million, a notorious source of finance-translation errors. East Asian countries (China, Japan, South Korea) use a myriad system that groups digits in tens of thousands (万/萬 = 10,000, 億/亿 = 10⁸). India uses the lakh (10⁵) and crore (10⁷) system.
Decimal separator
The USA, UK, Singapore, Japan, South Korea, China and India write decimals with a point (3.14) and group thousands with a comma (1,000). Continental European countries — Germany, France and Finland — write decimals with a comma (3,14) and group thousands with a space or point (1.000). This reversal is a common cause of data-entry and spreadsheet errors across borders.