The problem is teachers! One of my relatives is taking Community College level math right now. I was helping her with some homework, which was multiple choice. The problem was simple, find an area of a triangle. We did the problem, and the answer was not among one of the possible solutions. I quickly double checked my work, making sure I was right, and we decided to mark none on the problem sheet and give the right answer + show work. The teacher said that in this case you should always guess what the closest right answer is, and just mark that. WTF. The actual answer was roughly 65, the closest number to that on the answer sheet was 73.
Math in USA is taught like religion, you have to believe what you are told, and god save you if you ask for proof. I remember in School we were reviewing Pythagoras Theorem. I asked the teacher to explain why it worked. She proceeded to draw on paper a triangle with sides of 3 and 4 inches, and then measured the long side, and said ‘see,’ with a very proud tone in her voice. When I asked if there is any more definitive proof, she replied that “it’s a theorem, there is no proof, that’s just the way it is.”
I spent the first 6 grades of my education in Ukraine, admittedly in the communist equivalent of prep schools. There we were given math problems, and we were expected to solve them OR prove that they were unsolvable. At least one problem on every test was unsolvable, and they actually expected you to provide proof. My experience with college level math on US was the same, the teachers were smart and taught well. But Middle School and High School level math in USA is pathetic, in my experience.
It sounds like you just had a bad math teacher. The Pythagorean Theorem has quite a few proofs, a number of which are understandable to students with only basic geometry knowledge. I'm almost certain I had to prove it in my math class at the time.
I think students (who are themselves a product of their parents and their culture) are also part of the problem. When students don't try, they fall behind, and when they fall behind, they have no choice but to make silly guesses.
Math in USA is taught like religion, you have to believe what you are told, and god save you if you ask for proof. I remember in School we were reviewing Pythagoras Theorem. I asked the teacher to explain why it worked. She proceeded to draw on paper a triangle with sides of 3 and 4 inches, and then measured the long side, and said ‘see,’ with a very proud tone in her voice. When I asked if there is any more definitive proof, she replied that “it’s a theorem, there is no proof, that’s just the way it is.”
I spent the first 6 grades of my education in Ukraine, admittedly in the communist equivalent of prep schools. There we were given math problems, and we were expected to solve them OR prove that they were unsolvable. At least one problem on every test was unsolvable, and they actually expected you to provide proof. My experience with college level math on US was the same, the teachers were smart and taught well. But Middle School and High School level math in USA is pathetic, in my experience.