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> In short, no matter what the class's level, mathematics definitely needs to be taught from a more problem-solving, integrated perspective.

I'm always looking for examples of how this is done. How did you learn how to solve problems? (Did someone teach you?)

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I suspect the foundations of my mathematical problem-solving skills were laid when my parents signed me up for extracurricular math classes with teachers from the local Russian community, when I was in elementary and middle school. I started on competition-type problem solving with my middle school math team coach, an extraordinary teacher contrasted with the largely incompetent ones in the curricular program. However, the majority of the techniques I applied to competitions, and I suspect the majority of my overall problem-solving skills, I accumulated through self-study, not a small part of which was from the Art of Problem Solving books from the website linked in the original post. If those were used as textbooks and the teachers knew (and felt) the material, then I think the mathematical education in this country would get a significant boost. If some of the material turned out to be too hard for those less talented at mathematics, the approach would still be the one to use in simpler textbooks.

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