A short story, courtesy of BE/bfx (whichever you prefer):

Once upon a time I spent some of a summer studying abroad at a technical school in France. Think of it as being somewhat similar to a UC or other state run institution. While my courses were not math based (language and economics based), I did manage to expose myself to some of the math that was being taught there through becoming friends with some of the professors. They were more than happy to share some of their calculus material and homework assignments with me.

The language barrier was easily overcome, but the interesting part was the content. The content was the same material that I had been taught, or was taught back at university following this study abroad. That did not change. What did change was the problems that were being asked, and how to approach them. These problems were much more challenging than what I had experienced in the United States, even at a high-ranked engineering based university. They required a deep understanding of calculus, algebra, and trigonometry in ways that were not taught to me. While I was able to solve a lot of these problems, it was more challenging than it should have been. From that I inferred that either the rigor of the course at this university in France was stronger than that of my university in the states, and that material is likely being taught with a greater emphasis on understanding and comprehension as opposed to identifying patterns and systems that lead to an answer without as much understanding of the significance of the math in between.

"I was very good at following obscure steps to manipulate mysterious symbols, without any real understanding of what I was doing.”

It is scary just how true that statement can be, and I was able to see the educational differences that lead to that firsthand.