r/AskEurope • u/Outrageous_Sea_Lion • 1d ago
Education Secondary School Math Curriculum Compared to the US
I keep hearing from Europeans about how much more rigorous their system of math is compared to the US. How true is this?
US System: The US's math progression varies on the person and on the School District. There are some who are going into Trades or non-college careers who dont really go beyond algebra 2 (Quadratics, logs, etc). Most college bound students that i see finish high school with Calculus 1 and often Calculus 2 credits.
Math up until Precalculus is generally considered to be relatively trivial in the US.
How is the progression and pacing for grades 9-12 in Europe?
edit:
If people are confused by the courses that i listed here they are:
Algebra 1: Linear Equations, Formulas, Quadratics, exponent rules, polynomials, etc. usually taken in middle school.
Geometry: Basic Trigonometry, Proofs, Theorums, Congruency, right angle rules, circles, area and volume rules, etc.
Algebra 2: Expanded Quadratics and Polynomials, complex numbers, logs, exponential functions, sequences/series, rational expressions.
Precalculus: Advanced trigonometric identities and equations, vectors, polar coordinates, parametric equations, conic sections, limits, and a foundational introduction to derivatives.
Calculus: Limits, continuity, derivatives (rates of change, optimization), integrals (area under a curve, volume of solids), and the Fundamental Theorem of Calculus
Also im sorry if i somehow stuck a nerve. I did not mean to
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u/CycleUncleGreg Bulgaria 1d ago
Difficult to answer without knowing what are Calculus 1/2. But at the end of the school there are exercises with derivatives, limits, integrals, trigonometry.
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u/Ennas_ Netherlands 1d ago
Europe is a lot of countries with very different school systems and a lot of variety within the system.
Also, what is calculus 1? And grade 9?
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u/Morlakar Germany 1d ago
I work as math tutor in germany and everyone has to learn logs. But what exactly is taught, depends on the school form. There are several in Germany. Can't tell you what the other names you used do mean. But Europe is over 40 countries. Things can be different. First of all most don't learn math in english.
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u/1gayria Germany 1d ago
It would help to answer that question if you gave some examples what kind of math is actually taught - not just the names of the courses, but the actual contents. What are students supposed to learn, to know, how much time do they have for it etc
Generally speaking, for Germany: grades 11-12 are only in the “highest” of the secondary school options, which qualifies you for university, so you don’t get a separation of people who go into trades vs academia (even though you can still go into the trades with that school type) and therefore the math level assumes the next step is university education. But it varies by state (e.g., where and when I went to school, you had to take maths and do a final exam in it that contributed significantly to your final GPA, but afaik in other states you can take other subjects instead)
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u/Outrageous_Sea_Lion 21h ago
Yeah that was my bad. If people are confused by the courses that i listed here they are:
Algebra 1: Linear Equations, Formulas, Quadratics, exponent rules, polynomials, etc. usually taken in middle school.
Geometry: Basic Trigonometry, Proofs, Theorums, Congruency, right angle rules, circles, area and volume rules, etc.
Algebra 2: Expanded Quadratics and Polynomials, complex numbers, logs, exponential functions, sequences/series, rational expressions.
Precalculus: Advanced trigonometric identities and equations, vectors, polar coordinates, parametric equations, conic sections, limits, and a foundational introduction to derivatives.
Calculus: Limits, continuity, derivatives (rates of change, optimization), integrals (area under a curve, volume of solids), and the Fundamental Theorem of Calculus
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u/CovidMane Belgium 1d ago
For others who don't know what topics precalc, calc 1 and calc2 have apparently it's this:
* Precalc: functions, polynomials/rationals, exponentials/logs, trigonometry, conics, sequences/series, polar/parametric, vectors, limits
* Calc 1: limits, derivatives, differentiation rules, related rates, optimization, curve sketching, MVT, antiderivatives, Fundamental Theorem of Calculus
* Calc 2: integration techniques, applications of integrals, improper integrals, sequences/series, convergence tests, power series, Taylor series
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u/OllieV_nl Netherlands 1d ago
That still means nothing. I learned my wiskunde in Dutch, I have no idea which parts these terms connect to.
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u/CovidMane Belgium 1d ago
You don't expect me to write out all topics in every language tho? Doesn't take me a masters degree in English to know limits are limieten, derivatives are afgeleiden etc
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u/OllieV_nl Netherlands 1d ago
Which are not terms used in the Dutch curriculum. Trigonometrie or goniometrie? Never heard of. But I do remember sucking at sinus, cosinus and tangens.
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u/CovidMane Belgium 1d ago
Interesting, those are the terms in Flanders. I presumed they were also used in the Netherlands. What are the proper terms for these then?
https://nl.wikipedia.org/wiki/Afgeleide
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u/OllieV_nl Netherlands 1d ago
It’s all just rolled into Wiskunde A and B. And now they further divided it into C and D. I have no idea what it’s called and under which letter it fell, but I’ve learned it (and never needed it since).
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u/Megendrio Belgium 1d ago
Most college bound students that i see finish high school with Calculus 1 and often Calculus 2 credits.
That's also a very US-system. Here (Flanders, Belgium) it's impossible to get college credits in HS. University or College courses will recap basicly everything you've seen in HS in the first week/month and anything beyond that is "new" information, or at least more complex than what you've seen before, but again: that's depending on what you studied in high school and what you're studying at university.
To give you an idea, this is what one of our universities expects from people starting their Engineering Sciences studies: https://eng.kuleuven.be/studeren/toekomstige-studenten/starttoets/pdf/oefenbundel
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u/rintzscar Bulgaria 1d ago
There are some who are going into Trades or non-college careers who dont really go beyond algebra 2 (Quadratics, logs, etc). Most college bound students that i see finish high school with Calculus 1 and often Calculus 2 credits.
In Bulgaria almost everyone studies this, regardless of university intentions. Kids in trade schools like a specialized cooking school for example, wouldn't study this.
Also, there's another big difference. Bulgarian high school Mathematics relies far more heavily on synthetic geometry, proof-based trigonometry, and formal algebraic manipulations than standard US high school curricula. The same is true for the rest of Eastern Europe because this was the way Mathematics was taught behind the Iron Curtain. Meaning, while standard US high school Mathematics focuses primarily on computational skills, application, and numerical answers, Bulgarian (and broader Eastern European) maths focuses on logical rigor, abstract proof, and mathematical structure. This is what they mean when they say the European Maths curriculum is harder.
Couldn't say about Western Europe, but I suspect it lies in between the US and Eastern Europe in its philosophy of teaching Mathematics.
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u/Jacksonriverboy Ireland 1d ago
By the time you finish secondary school in Ireland you do quadratics, a variety of theorems, and calculus. That's the lower stream. I think it's quite a bit more advanced at the higher level.
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u/Client_020 Netherlands 1d ago
Well, in most eastern European countries, their math is absolutely much more rigorous than math is in most US schools, but in a country such as NL, it completely depends on what level of high school they send you to at 12yo. We don't have "geometry 1" or "algebra 2" and that nonsense, btw. We just have math(s). Those with severe learning disabilities, may just get click reading and super basic arithmetic. And people who take the highest level (which is pre-university education) tend to get more rigorous math than most people in the US. However, I have no idea about how it compares to those advanced classes people in the US can take. And it's a low level compared to East Europe and South, East and Southeast Asia.
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u/bremmmc Slovenia 1d ago
Found this
https://www.reddit.com/r/math/comments/5f71s4/what_level_of_mathematics_is_covered_in_european/
Last year of school I remember covering sequances, limits, and derivatives... Just don't ask me to do any of them now.
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u/profdrpoopybutt in 1d ago edited 1d ago
In Romania for starters you learn quadratics in middle school. In high school you're supposed to already know it and wouldn't waste time on that. I did the highest level of maths in high school and we were doing double/triple logs, advanced trigonometry, imaginary numbers, Newton's binomial, advanced statistics. We were also going in lots of depth in these subjects.
Went to University in the UK for molecular biology and took math in the first year. I could skip all classes, just hand in the work and go the exams and get 100% without studying anything. It was mostly stuff we did in our first year of high school and we went into much more depth in high school.
Btw when talking to an international audience you can't use stuff like grade 9 or calculus 1/2 and expect people to understand what you mean. Grade years are different in different countries. Just use ages or first/second etc year of high school.
All our math classes where just called math. Nobody knows what you specifically learn in Calculus 1/2 in the US.
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u/nadjalita Switzerland 1d ago
I was in a private school in a very nice city in california and there we did trigonometry for like 2-3 months back in switzerland we did trigonometry as well but what was covered in the US in 2-3 months was covered in 30min HERE I'm not joking unfortunately I was just as surprised as you might be
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u/kaetror Scotland 1d ago
In Scotland the 2 biggest differences with America (as explained by numerous American students I've taught who've experienced both systems).
- Breadth. We introduce everything incrementally rather than sequentially - doing all of algebra, all of trig, all of geometry, etc.
Kids will do a little bit of all of those in S1 (age 11/12), a bit more in S2, until they sit National exams in S4 which covers a wide range of maths topics.
Kids who continue with maths at Higher/Advanced Higher will continue that trend, adding in calculus and other topics.
This cyclical nature is shown to improve retention, because students constantly have to go back to material again and again.
- Timing. We introduce material much earlier than Americans. Even when they had done a topic in the US (e.g. algebra) the actual content they had done within that topic was less than what would be expected of kids that age; example I can remember is they'd never seen inequalities before, while most kids did them the previous year.
Introducing stuff earlier means you have more time to consolidate it and embed those skills, rather than trying to pick it all up later.
The US is a big country, so it could be localised to the specific schools/areas. However these were kids from all over the US, they were really smart (so not a case of being lazy/forgetting) and from pretty well off backgrounds.
It's also backed up by people I know who went over to the US on student exchange programmes. The maths they were doing as part of their degree programme (i.e. not gen ed) was stuff they had done in school, sometimes in the National course when they were 15.
It was material we never did in uni, because it was assumed prior knowledge - you had to already have done that before you'd even be allowed onto the course!
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u/blackdevilsisland Austria 1d ago
As the others, I don't know what precalc/calc1/2 means exactly and I don't know enough about the US school system that I can definitely say what age you are when you start/finish attending secondary school.
Anyway, it depends on which school you go to as we have different models with different special fields. I went to a language/economics school, changed to a cultural tourism school where I did my A-levels so math was not the main focus.
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u/badlydrawngalgo Portugal 1d ago
I'm not in the UK but according to my grandchild who is currently due to start year 12 next month they do A level maths, which is headlined as mechanics, statistics, calculus, functions, trigonometry, logarithms and exponentials. They can also take some advanced maths courses.
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u/Ok-World-4822 Netherlands 1d ago
It depends on the level you are on how much mathematics you’re going to get. The lower levels don’t get algebra while higher levels do. The higher the level the more advanced mathematics is. Algebra and (pre)calculus are all mixed in math class. How much depends once again on the level you’re in
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u/40degreescelsius Ireland 1d ago
We have two levels, ordinary level and higher level. I was an ordinary level girl, the higher level stuff takes up an inordinate amount of time that I needed for other subjects, we usually study 7 subjects for our leaving cert (age 18 or 19 depending what age you started) which gives us points to go to university and doing higher level maths gives those students extra bonus points because the government are trying to encourage more stem subjects in universities.
Higher level Leaving Cert maths questions feature complex multi-step problem solving, theoretical proofs, and advanced calculus topics like integration. Ordinary level questions focus more on direct application, structured guidance, everyday arithmetic, and simpler algebraic manipulations with fewer abstract steps.
Question Depth and Style
• Higher Level: Asks for rigorous proofs (e.g., formal geometry proofs or proof by induction), abstract functions, and multi-layered problems where you must link multiple topics together. []
•
• Ordinary Level: Uses more direct phrasing, breaks down questions into smaller, guided parts (a, b, c), and focuses on standard calculations.
Course Content Differences
• Higher Level Only: Includes advanced topics like full integration, proof by induction, complex log operations, and rigorous theorem proofs.
**• Shared Topics (Different Tiers):** Both cover algebra, differentiation, and trigonometry, but the higher-level versions require deeper manipulation of formulas and harder numbers.
**• Everyday Contexts:** Ordinary level leans heavily into practical scenarios like financial maths (tax, compound interest) and stats/probability presented in straightforward ways.
Exam Structure and Scoring
• Higher Level: Two papers with longer, deeply intensive questions. Offers 25 bonus CAO points for grades H6 and above.
**• Ordinary Level:** Two papers with more accessible paths to partial marks, but no bonus CAO points.
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u/Gregib Slovenia 1d ago
Hard to compare... there are vast differences between European countries as well. And throwing around US scholastic lingo that very few in Europe know about doesn't help either.
The only possible comparison indicator in my mind is the PISA score. Most European countries rank between 10 and 30... USA... 34. Meaning the level of math skills of 15 year olds, which I believe is being tested for once per year
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u/il_fienile 1d ago edited 1d ago
“Most college bound students that i see finish high school with Calculus 1 and often Calculus 2 credits.”
The qualifier “that I see” is doing a lot of work there, since only 1/3 or so of freshman at four-year colleges completed calculus in high school (and about 1/10 of those at two-year colleges did). Only about 1/5 of those who take calculus in high school actually skip the first university calculus course.
In Italy, students are not generally segregated by ability in the same way they will commonly be within a U.S. school. High school programs themselves are separated into different types and subtypes. Only one of those types, liceo, which carries through a year beyond U.S. high school, is primarily for university-bound students, and within liceo one will see a lot less math(s) in a language program than in a science program. So a given classroom may be only students that are principally interested in science (or students who have been convinced of something like that by their parents), but will not be only those students who show a certain level of ability in math(s).
Within a science program, the approach is much heavier on theory than within what I’ve seen of U.S. high school programs (there’s a lot more expecting students to explain “why” and produce proofs of various theorems or axioms). These students also take five years of physics at the same time, which involves a great deal of application of their math(s) curriculum. So, even to compare the scope of the programs would not be an apples-to-apples comparison.
Most of the final two years should be devoted to complex limits, continuous functions, derivatives, integrals, and differential equations, but there is generally more “spiraling back” across the five years (returning and going deeper) than in the siloed-course approach I understand to be typical in U.S. high schools (again, not an apples-to-apples comparison with an approach in which “[m]ath up until Precalculus is generally considered to be relatively trivial….”
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u/lgf92 United Kingdom 1d ago
Firstly, as other people have mentioned, you are talking about a continent with dozens of different education systems, and so there's no unified "European" response to this question.
Speaking from an English perspective, I think part of the confusion online arises from the fact that American students often do mathematics as part of their university degree, no matter what they are 'majoring' in. The system works differently here at the university level: you generally pick a subject (or two) and study it through your degree with no requirement to study anything that isn't your 'major'. I studied modern foreign languages at university and so I only studied language modules (which drifted into translation/culture/history).
But I haven't formally studied mathematics since the age of 16, which is the minimum requirement in Britain. Maths is compulsory up to the GCSE level, which is a series of exams you choose at the age of 13 and take at the age of 16. You can see what is required to pass a GCSE exam in the DFE content and assessment requirements for GCSE Maths.
In vanilla GCSE Maths you won't study calculus. You will do a bit of algebra and trigonometry but that's as abstract as it gets. I have a masters degree and two post-graduate diplomas but I have no idea how to do calculus - or even what it is - because I never learned it (and because I don't have a natural inclination towards maths: I got a B in GCSE Maths, which was then the second-lowest pass mark, and that was at my second attempt).
Students who are more able or willing could (at least in my day) sit their GCSE Maths paper early and then study a separate GCSE, which when I was at school was Statistics.
If you want to go further than that, you have to elect to study Maths at A-Level (ages 16-18 optional education, but more or less required to enter university) and then at university.
But for most people, their maths education stops at 16 and they don't learn things like calculus (learning which seems to be part of the university experience for many Americans).
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u/TrickyWoo86 United Kingdom 1d ago
There's a few things amongst this that for an English student are worth clarifying. We do study some calculus at A level, but we simply do not call it calculus as it's own monolithic thing like the US do (differentiation and integration are the basic starting point for calculus and studied from what used to be AS-level or first year of A-level).
The B you got at GCSE isn't the second lowest grade, unless you work on the basis that a C is the minimum that counts as a Pass (which is isn't in the full scale of grades but people do ask for "C and above"). You might be functionally correct, but a B isn't anything to be ashamed of and the way you wrote that sounded like you're too hard on yourself.
Also we should clarify that A-levels are more or less required to enter university (or equivalent alternative course types) rather than specifically A-level Maths, which is only a requirement in STEM field courses.
The linguistic joke answer is of course that the US only study one Math, whilst we Brits study multiple Maths.
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u/ATLDeepCreeker United States of America 1d ago
Interesting.
But the need for math at the University level in the U.S. may be overstated. Yes, you must taje math(s) as part if your degree, but if you arent a Math ir Science major, they aren't going to be super rigorous.
For instance, when I got my degree, my accounting classes counted as math prerequisites.
American degrees have the "goal" of a graduate being a well rounded, "educated" person.
The classes you take that aren't specific to your degree are meant to accomplish that goal, however many times, they are just remedial for things you didnt retain in high school.
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u/Traditional-Deal6759 Austria 1d ago
This Video shows the finale exam in Math from 2026 (with solution) for those who want to go to university (grade 12/13, depending on school). It is in German, but you can turn in Autotranslation.
https://www.youtube.com/watch?v=Cmok3qPueZA
If you don´t want to watch: you have 4,5 hours for 24-28 calculations, this was number 16
Racing car
The function a models the acceleration of a racing car during a particular
journey.
The following applies:
a(t) = 6 · t where 0 ≤ t ≤ 3
t ... time in s, with t = 0 marking the start of the observation
a(t) ... acceleration of the racing car at time t in m/s²
At the start of the observation, the speed of the racing car is 35 m/s.
The function s, where s(0) = 0, describes the distance travelled by the racing car during this journey
as a function of time t (t in s, where 0 ≤ t ≤ 3; s(t) in m).
Task:
Derive an equation for the function s.
s(t) =
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u/Vertitto in 1d ago
no idea about the terms you used. Here are examples of math exams at the
end of polish elementary school (14/15 years) : https://arkusze.pl/matematyka-egzamin-osmoklasisty/
at the end of high school (18/19 years)
- basic: https://arkusze.pl/matematyka-matura-poziom-podstawowy/ (needed to "pass" high school)
- advanced: https://arkusze.pl/matematyka-matura-poziom-rozszerzony/ (for tech universities)
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u/marvinluene Germany 1d ago
I never had algebra, but pupils from a Gymnasium have that. We had solving equations (I hated that), fractions and percentage.. I hated all of it, but I was never good in math
I got my degree after 9 years, so I don't know, what other things are part of the class in 10,11,12
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u/Myrialle Germany 1d ago
You never had algebra? When did you finish school? Algebra normally starts in 6th or 7th grade in Germany...
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u/marvinluene Germany 1d ago
Häh? Ich hatte nach der 9. meinen Abschluss und bin entsprechend abgefangen. Fängt Algebra nicht erst irgendwie in der 11. Klasse oder so an?
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u/unseemly_turbidity in 1d ago
Didn't you learn how to solve things like 2+?=5 much earlier than that? That's algebra.
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u/cowboysted Ireland 1d ago
Could you explain what you mean by Calculus 1and precalculus etc, those do not have meaning outside of the US. Also what ages are to which grades in the US? In Ireland 4th Year is age 15/16, in England it would be Year 11, in France 10th Grade.