My schooling system meant the first 7 years of rote learning, and the next 5 years of examining what we learnt and explaining it. I don't think we were ever taught critical thinking. It just showed up in the essays whether you had it or not.
That said, I don't think that the American syllabus is particularly good. I also don't think that critical thinking can be taught. I think it's innate.
The system that is generally thought to teach critical thinking is where you check the information you are given, compare it with other information, check its sources, etc.
There is no way in this lifetime of new data every three minutes that it is possible to do it.
I believe., though, the fact that I had to learn solid data for the first seven years of my life, gave me a good foundation, in that it enabled me to compare whatever data was coming in against that.
For instance, if i was taught that 2+2=4, and then someone told me that 2+2=6, I would immediately know it was wrong.
Many of the issues today go back to people being taught wrong information, plus been given a wrong value system.
All kids are going through a similar education system - it's what the world does - teach them to read, the write, to add, to subtract, and various other bits of data. The people who do well afterwards either had wealthy parents, had the right contacts from the word go, or were talented in some particular way.
My opinion.