Most students in these countries don't end up college track.
1. College Matriculation rates are low. Only 36% of Germans aged 25-46 have attended Tertiary Education (University as well as Vocational School) [0]. This is a similar story in the UK and Canada as well.
2. In countries like Germany and UK, college track HS admissions are competitive. Attending a Gymnasium or a uni track independent school or public school requires having a mix of high scores in grades 6-8 or competitive exams.
3. Calculus is not in the default curriculum. For example, in Canada Advanced Functions only teaches a bit of Calculus for a semester. The course is optional, only allowed at Grade 12, and sometimes isn't offered in HS. This is a similar case in the UK with "Further Maths" as an optional A-level and Germany with the Maths curriculum in Realschules.
I see India and China missing from your rebuttal, that is close to half of the worlds population and likely more than 2/3rds of all students who go to college.
Because for this conversation, I felt like talking about comparable first world countries and explaining the Chinese and Indian education system to a (fellow) American is annoying and tiring.
Points 1-3 are the same for India and China as well.
In China, Gaokao (college admissions exam) is only allowed to those who attend College Track high schools (Sr Secondary School).
To enter a Sr Secondary School (10-12) in China, you need to pass the Zhongkao, which is de facto limited to the top 40% scorers of the exam.
Zhongkao is not mandatory btw, and a number of (often rural or migrant) students end up failing to take the exam.
If you don't pass the Zhongkao, your options are either expensive private schools or going to a vocational school which will technically count as a tertiary program by giving a diploma and an extra year, but doesn't include as rigorous STEM classes as the Sr Secondary Schools.
This is similar to India as well, where Calculus isn't introduced in the CBSE or a number of State Board Exams. ICSE introduces Calculus at Grade 12, but ICSE is limited to elite private schools and elite/competitive public schools.
In both India and China, Tertiary education is low (it's difficult to get exact statistics as both countries have now begun obfuscating tertiary level with vocational programs). That said, given the Gaokao filtering, it probably doesn't exceed 30% in China, and India is most likely half of that given the 15-20 year head start China had on India.
CBSE is literally just the limits and basic derivatives. It's literally Pre-Calculus as it is taught here in the California (Pre-Calculus with Limits, Ron Larson).
With the Chinese curriculum, same story if not at a Sr Secondary School. Here's the curriculum for the Secondary Vocational Schools (aka the schools most Chinese students end up attending) - http://www.moe.gov.cn/jyb_xxgk/s5743/s5744/A07/202001/W02020...
> That said, given the Gaokao filtering, it probably doesn't exceed 30% in China
* Zhongkao Filtering, not Gaokao filtering
Also the Zhongkao IS mandatory, but heavily limits admissions into Sr High School (college track) Programs
Also, since 2022, Senior Vocational School students can now take the Gaokao, but given the curriculum in a Sr Vocational School as shown below, it's highly unlikely they'd meet the scores required to get into a university in China.
1. College Matriculation rates are low. Only 36% of Germans aged 25-46 have attended Tertiary Education (University as well as Vocational School) [0]. This is a similar story in the UK and Canada as well.
2. In countries like Germany and UK, college track HS admissions are competitive. Attending a Gymnasium or a uni track independent school or public school requires having a mix of high scores in grades 6-8 or competitive exams.
3. Calculus is not in the default curriculum. For example, in Canada Advanced Functions only teaches a bit of Calculus for a semester. The course is optional, only allowed at Grade 12, and sometimes isn't offered in HS. This is a similar case in the UK with "Further Maths" as an optional A-level and Germany with the Maths curriculum in Realschules.
[0] - https://gpseducation.oecd.org/CountryProfile?primaryCountry=...