Top math countries don’t schedule more math. Many parents just buy more.

The world’s strongest math systems schedule about as much classroom math as American schools report, or less. What several of them add is an exam that decides a child’s next school years before college, and a second shift of lessons that parents pay for after school.

We read their laws, timetables and spending surveys and set them beside TIMSS 2023, the international test given at grades 4 and 8. The first five rows are the top five scorers at both grades. England and Ireland speak English and beat America anyway, and even the closer one, Ireland, leads by 29 points at grade 4 and 34 at grade 8. The strongest trial of any method here costs nothing, shuffled homework beating sorted homework 61% to 38%, and the last two sections have it along with a one-line test you can try tonight.

Read the minutes column with one eye shut. Taiwan, South Korea (grade 4, grade 8) and Japan show what the state sets, and schools can adjust it. Ireland’s primary figure is a suggested minimum published in 2023, and the fourth graders tested that year had learned under an older framework that said 250. England and the U.S. have no national rule, so theirs are reported figures, from inspectors in 2023 and, for third and eighth graders, principals in 2011-12.

The age column means the first exam most children face that decides where they go next. Selective schools can test earlier, as England’s grammar schools do. Paid-lesson figures cover all academic subjects, and Japan’s cover public schools only. They come from different years and different questions, so ignore a gap of a few points.

Japan’s law gives an eighth grader half the math minutes an American principal reports

Japan’s school regulations set 175 math lessons a year in grade 4, at 45 minutes each, and 105 in grade 8, at 50 minutes, over at least 35 weeks. That comes to 150 minutes a week for an eighth grader, the low point of junior high, since grades 7 and 9 get 140 lessons. American public school principals reported 300 minutes in 2011-12, a 14-year-old answer. Japan’s eighth graders scored 107 points higher in 2023.

One side of that comparison is a legal standard and the other a survey answer. Principal and teacher reports in TIMSS 2019 put both on one ruler, at 105 hours a year for Japan’s grade 8 and 154 for America’s, a smaller gap in the same direction. On that ruler, the only rows above America are Singapore at grade 4 and Taiwan at grade 8, by 1 and 3 hours, both within sampling error.

England’s curriculum sets no time per subject, and a 2023 report by its school inspectors found 3.5 to 4 hours a week in most secondary schools they visited. Hong Kong suggests a share of lesson time. Singapore told parliament in 2020 that it recommends about 5 to 6 hours a week in grades 3 to 6, bracketing America’s figure.

Chicago doubled algebra periods for below-median ninth graders in 2003, and a 2009 study found test scores rose while grades moved only modestly. A 2013 follow-up found students near the cutoff 8.7 percentage points more likely to graduate in four years, though not the average student placed in it. Minutes still matter for some students, then, and America has no national rule on them. Your child’s school is the only place that can say how many minutes a typical week holds and what was cut to make room.

South Korea’s paid math peaks at 57% in grades 7 and 8, years before the college exam

South Korea counts paid lessons by subject and grade, which no other survey we read does. Its 2025 survey has 33% of first graders in paid math lessons, 46% of fourth graders and 57% of seventh and eighth graders. By the final year of high school, the year of the national college exam, the share is back to 32%, counting vocational schools.

An eighth grader in math lessons cost 301,000 won a month, about $222 at the Treasury’s rate for September 30, 2026, which converts every figure below too. All private lessons, arts and sports included, came to 27.5 trillion won in 2025, about $20.3 billion. Asked why, the most common answer for academic lessons was keeping up with school, at 49.5%, ahead of studying ahead at 22.7% and admissions at 16.2%.

Japan’s ministry found 39% of public elementary families and 66% of public junior high families paying for cram school in fiscal 2023. Paying junior high families averaged 349,000 yen a year, about $2,222. (The ministry reissued its tables after finding errors, so even math superpowers have a bad spreadsheet day.) Taiwan’s ministry counts 53% of elementary and 56% of junior high students in cram school subjects, in surveys for 2019-20 and 2020-21.

Singapore told parliament in February 2026 that it does not track the share of students in tuition by subject. Its household survey shows tuition at S$104.80 a month per resident household in 2023, about $82.

Hong Kong’s official count dates from 2004-05, at 36% of primary and 28% of lower secondary students, and a 2018 note for its legislature said other surveys suggested 50% to 75%. America’s federal figure, for 2006-07, is nearly as stale. It has about 11% of public school students in tutoring other than free programs, and in most schools about two-thirds of those households paid in whole or part.

Does the second shift produce the scores? A 2011 study of Taiwanese junior high students put the average effect of math cram school as fairly small, and a 2024 study of Korean panel data found that tutoring raises college-exam scores and widens inequality. A 2020 study of Japan points out that its fourth graders already score high with little cram school behind them. We could not find a randomized trial of paid after-school math lessons in any of these systems on ERIC, the federal education research database. Nobody can tell you how much of East Asia’s lead the second shift buys.

The firmest tutoring evidence sits elsewhere. A 2024 review of randomized field experiments pooled tutoring’s effect at 0.29 standard deviations, the researchers’ unit for how far a group moves against the normal spread of scores. The largest effects came during the school day, at least three days a week, a long way from a weekly session at a storefront.

England trailed America by 34 points at grade 4 in 1995 and led by 35 in 2023

NCES’s trend tables have England’s fourth graders rising from 484 in 1995 to 552 in 2023, while America’s went from 518 to 517, no measurable change. At grade 8 the two were tied at 515 in 2019. England led by 37 in 2023, mostly because America fell 27 points in four years, while England’s 10-point rise was not statistically measurable. NCES flags five of the table’s eight systems, these two included, for coverage, sampling or reliability problems.

England’s paid tutoring looked small in 2023-24, and no count we read covers the years of its rise. In a May 2024 Department for Education survey, 10% of parents of children in Years 1 to 11 reported paid private tuition that school year, and in its December 2023 survey, 13% of secondary pupils reported private tutoring the year before, against 24% tutored through school while a national program ran.

Ireland looks similar at age 13, with 4% in extra or private tuition, in mothers’ answers about their child’s supports in 2021-22. Then the exam arrives. In the year of the Leaving Certificate, at 17 or 18, 49% of students were taking what Ireland calls grinds, with 63% in the top income fifth against 33% in the bottom, in a 2016 report.

The gap narrows on the test of 15-year-olds. In PISA 2025, the U.S. scored 463 in math, level with the average for the OECD’s mostly wealthy members, with no measurable change since 2022 and 20 points below 2003. The UK scored 488 and Ireland 480, against Singapore’s 563 and Japan’s 525. Only 45% of sampled American schools took part before replacements, which NCES says leaves some potential for bias.

A table of countries cannot tell you what caused what. England and Ireland still sit well below the East Asian rows, so they don’t show tutoring is useless. On those surveys, they do show a system can clear America by about 30 points on TIMSS without a bill on that scale, at least below the final exam year.

Governments say they want less exam pressure, and their moves point both ways

Singapore’s primary leaving exam comes around age 12, and secondary school posting follows its results. Hong Kong gets there earlier in effect, scaling school marks from the end of Primary 5 and sorting children into three bands for secondary places. Japan’s prefectures run public high school entrance selection and Taiwan’s ninth graders sit a national exam each May that helps rank them for high school, both around 15. America requires state tests in grades 3 to 8 and once in high school and has no national exam that places a child.

Singapore dropped mid-year exams by 2023 and moved its primary exam to coarser score bands in 2021. Hong Kong has scaled with a separate sample test since its 2005/2007 allocation cycle, it says to reduce drilling and pressure. Taiwan’s ministry says its exam’s fewer score levels are meant to lower pressure. South Korea’s middle schools keep a semester with no school-wide written exams, during the years when math lessons peak, but its 2022 curriculum cut that semester’s activities from 170 hours to 102. England’s curriculum review calls time in its national exams at 16 excessive, at 24 to 31 hours, while rejecting calls to scrap them. The government has promised a cut of 2.5 to 3 hours and, in the same response, a new national reading test in Year 8, at ages 12 to 13, with every school expected to check math progress that year.

Surveys also ask how children feel about it. In TIMSS 2023, 61% of Taiwanese eighth graders, 60% of South Koreans and 59% of Japanese, English and Irish landed in the test’s “do not like learning math” group, against 51% of Americans. Singapore and Hong Kong are the exceptions, at 39% and 44%.

Singapore math, mastery and lesson study rest on few trials and small effects

In America, Singapore math means a program built on Singapore’s textbooks. A 2016 randomized trial of one such program, 22 grade-level teams in 12 schools, grades 3 to 5, found gains of 0.11 to 0.15 standard deviations. A federal review of a related curriculum, updated in December 2015, found no studies that met its design standards and drew no conclusions.

Mastery teaching covers fewer topics in more depth. England tested it in two trials reported in 2015 covering 127 schools and 10,114 pupils. Primary schools gained 0.10 and secondary 0.06, neither statistically significant alone, and 0.07 pooled, about a month’s progress by the report’s own conversion, after one year.

Lesson study is Japan’s habit of teachers jointly planning and critiquing a lesson. A 39-team U.S. trial in 2017 found gains with a fractions resource kit. An 80-team trial in 2024 found average fractions scores did not rise, with a possible gain in one state.

Shuffling the homework beat sorting it, 61% to 38%

Mix the practice. In a 2020 trial whose plan was registered in advance, across 54 seventh-grade classes over four months, students whose assignments mixed problem types, so no two in a row used the same strategy, scored 61% on an unannounced test a month later. Students whose assignments were grouped by skill scored 38%. That is one trial, and its authors say important caveats remain. At home, pull 8 problems from the last three chapters and shuffle them. At school, ask how much of the homework is mixed.

Copy England’s check at home. England’s multiplication tables check gives children 25 questions at 6 seconds each at the end of Year 4, around age 9, weighted toward the 6, 7, 8, 9 and 12 tables. There is no pass mark. We found no trial of the check itself. The closest evidence is a 2021 federal practice guide for elementary students who struggle with math, which rates short timed activities as strong on 27 studies, when they run 1 to 5 minutes, cover what has already been taught and let children chart their own scores. It warns against merely handing out timed worksheets. The official practice site is for schools only. Write your own 25 on tables your child has already learned, keep it short, and let your child chart the score.

Move the equals sign. In a 2015 experiment, 166 second graders were randomly given workbooks that wrote facts as ☐ = 4 + 3 instead of 4 + 3 = ☐, among other small changes. They understood equivalence better 5 to 6 months later, with no observed loss in computation. A 2011 study of 90 children found a benefit from the reversed format alone, and a 2023 trial with 132 California teachers found that a fuller package, which teaches the equals sign before arithmetic, beat reversed practice alone. All of this measured understanding of the equals sign in young children and says nothing yet about later math scores.

One line of arithmetic split Hong Kong’s 88% from America’s 47%

NCES posts real TIMSS questions for free. On page 22 of the 2011 grade 4 booklet is one built as a sum, an equals sign, then a box plus a number. In 2011, 88% of Hong Kong’s fourth graders and 85% of Singapore’s got it right, against 47% of Americans. England’s got 29%, and two years later its new national curriculum put missing-number problems such as 7 = ? − 9 in Year 1, at ages 5 to 6.

Tonight, try the same shape with your own numbers. Write 5 + 7 = ☐ + 4 and say nothing else. An 8 means your child is balancing both sides. A 12 means stopping at the sum, the pattern answer-on-the-right worksheets can train, and a 16 means adding everything in sight. One question is not a diagnosis. If you see a 12, the next move costs a pencil. Tomorrow, write the sum with the box on the left.

The tables we built and the calculations we ran on this page are free to reuse under Creative Commons Attribution 4.0: credit Kidsomnia and link here. Government figures inside them stay under the agency’s own terms.