Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.

I agree that it's easier to learn that way, but it's not much use when solving real-world problems; you can learn the techniques relevant to the solution once you know what they are, but, if you haven't met them before, you won't recognise that they're the right ones.