Your first point begs the question that people learn those topics from school. They are taught them, but the question is if they learned them. Seems as likely

Your first point begs the question that people learn those topics from school. They are taught them, but the question is if they learned them. Seems as likely that what little people do know if those topics was mostly learned by popular culture's use of them. Such that, I don't think you would get disagreement from the people that you are writing towards.