What works actually it's the method of discovery, acquisition of knowledge, forming and amending scientific theories, and seeking the facts and the truth. Unfortunately, many Americans don't really understand what the scientific method is. There are several reasons for this. One is the strong influence of religion, which is much higher here than in other advanced countries. In addition religion has been meddling in education. Another reason is the failure of schools to teach what science and the scientific method is.
Education has to be knowledge, but what kind of knowledge? Memorization & repetition without understanding isn't the goal. Education, like science, should be a tool for knowledge. In this sense, it's more important how you thing than what you think about.
We may not be scientists but we must understand what science is and what it does. Democracy depends on the people's understanding of issues, engagement, and prudence. It's obvious that the quality of a system depends on the quality of the people involved. Ignorance doesn't serve the good political life--nor life in general.