Depends from the school and the textbook. My math textbooks didn't even mention the Fibonacci sequence and it wasn't until Project Euler that I found out about it.
I learned more about Fibonacci and the golden ratio in nature and art through my high school Art History course than I ever did in a math course. Though I had played with fractals a little bit before that course so the fractal geometry of nature and Fibonacci-fractal relationships weren't a complete mystery to me. http://fractalfoundation.org/OFC/OFC-11-1.html
Same here, I learned about the golden ration in my high school Art class. Weird, because it was never mentioned through my college years despite how important and ubiquitous it is.
This probably has a bunch to do with how the Fibonacci sequence is attributed with a lot of mysticism and attributes it doesn't actually have.
The golden ratio does not depend on the Fibonacci sequence, it depends on the recursion equation, and it's only ubiquitous if you add error margins of 10% or so so that it covers ratios like 3/2 and 7/4. Nautilus shells aren't described by the Fibonacci sequence, and the golden box isn't all that pretty.
It's a great and motivational story, but it's not the magic bullet some authors make it out to be.
