Once upon a time, while in college, I decided to take my first intro-to-proofs class. I was so excited. "This is it!" I thought, "now I get to learn how to think like a mathematician."
You see, for the longest time, my mathematical upbringing was very... not mathematical. As a student in high school and well into college, I was very good at being a robot. Memorize this formula? No problem. Plug in these numbers? You got it. Think critically and deeply about the ideas being conveyed by the mathematics? Nope.
It wasn't because I didn't want to think deeply. I just wasn't aware there was anything to think about. I thought math was the art of symbol-manipulation and speedy arithmetic computations. I'm not good at either of those things, and I never understood why people did them anyway. But I was excellent at following directions. So when teachers would say "Do this computation," I would do it, and I would do it well. I just didn't know what I was doing.
By the time I signed up for that intro-to-proofs class, though, I was fully aware of the robot-symptoms and their harmful side effects.