Nobody answered directly to my questions in the public school forum. I found this thread
https://www.dcurbanmom.com/jforum/posts/list/101940.page and figured this is probably a better forum to get help from. Critical thinking & problem solving seem to be thrown around a lot nowadays, but many schools do not even know what they are. The math "problem solving" has zero word problem, only math calculations. The "critical thinking" projects are just glorified craft projects with no explanation of 'how' or 'why,' no concepts or laws behind it.
Can anyone explain what exactly "critical thinking" is? I know about the Socratic questioning method, but how do you use it and critical thinking to do something useful?
How do the schools teach it? What do you teach it with assuming it is not something that can be taught as a separate skill? How do you transfer the critical thinking skills taught in a controlled environment (classroom) to use it across the board in other subjects and in the world?
How do you teach the students what questions to ask, which statements to question (theory statement) and which statement not to (law statement)? How do you teach them information literacy and reasoning tools? Is there a program for it?