Here's an odd one of mine:
The Trachtenberg Speed System of Basic Mathematics
I checked this out from the Scottsdale library when I was 11. I'd learned all the usual algorithms to multiply and divide and do basic arithmetic, but like most kids, I assumed that those were the only ways to do those things - that the steps we learned were truly fundamental and the one and only way to get the result.
Then I read Trachtenberg and learned that there were other procedures you could use to get the very same results. The techniques we'd learned were not the only ones!
Oh, there were tradeoffs - you might have to remember more stuff and more special cases - but once you had those down you could zip right through a calculation that would have taken a long time otherwise.
So that's how I learned that there was more than one way to do it.