I was speaking more tongue in cheek. But I agree with you that math being taught in the US is not up to par. I'm not convinced that 'integration' is the key.
I am, at this very moment, long term subbing for pre-calculus, teaching about annuities, compound interest, difference between continual compound and discrete compounding, etc. The new-age modality in this district is to rely heavily upon work sheets and self discovery in mathematics, with teacher re-enforcement of core principles.
I disagree with this.
I think this kind of teaching works if the student enters having a previously firm foundation in the prior principles, but sucks if there's any sort of hole. Which there often is, because the variability in quality is a very real deal.
What seems to be a breath of fresh air to these students is a simpler approach - introduction of the topic, multiple examples, and common trouble spots associated with the topic. It saves valuable time for students (which is increasingly rare for high performers, as they often have 4-6 hours of homework per night due to AP hell) and it allows exposure to diverse problems as they're not sitting their hitting their face on a table for 3 hours trying to solve something simple.
Additionally, most math teachers I've met knew enough math to slither by and take the CSET, qualifying them to teach in the state, but they lack themselves the foundation necessary to teach as sometimes it takes more than proficiency with the textbook and current modalities to teach a weaker student.
