It’s interesting to see how quickly America is being dumbed down by stupid policies.
College level science and engineering education doesn’t make sense without a understanding of at least basic calculus.
Students in other countries in the world (for this assumption India, China, Canada, UK, Germany given my experience with the following) are tracked and/or calculus is optional.
We've traditionally had tracking within the US system (hence why AP and Honors classes matter) which helped filter students accordingly.
The issue is our "Hail Mary" pipeline - community colleges - are unnecessarily viewed as negatively, even though they help students remediate any knowledge gaps they might have.
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=...
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.
Here's the curriculum for CBSE. https://cbseacademic.nic.in/web_material/CurriculumMain24/Sr...
Most state boards are similar to this.
Similarly most Chinese students end up learning calculus in school.
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...
Notice how it caps at permutations.
* 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.
That doesn't actually mean that you need to cover calculus in high school. The calculus needed for the first year of college science and engineering can be easily taught early in the first year in the classes that need it.
That's how it worked at Caltech when I was a student (late '70s and early '80s). Around 75% of an incoming class had no calculus. It only took a lecture or two in Phys 1 to cover all the calculus that would be needed for the rest of first year science and engineering.
That calculus taught in Phys 1 wasn't rigorous and proof based, but high school calculus usually isn't either. By second year everyone had a year of Ma 1, which was rigorous and proof based calculus.
For computer science, imagine learning about logic gates and VLSI in the same year.
This question is relevant to me because we are deciding what to teach our kids and I haven’t yet been able to come up with a good argument for why to spend time gaining the skill of pen and paper mechanical calculus algorithms.
Are there professional scientists or engineers out there that do calculus on paper?
Yes.