I am totally the opposite. I can work through complex algebra proofs, but ask me to work out 2 x 3 + 21? Good luck.
I am like this as well for the most part. I'm going to need a lot of paper in order to do complex math (and I was a math minor in college), none of it in my head except the derivative of e^x^.
That said, on rare occasions -- twice in my half a century life -- my brain has instantly popped out the answer to a math puzzle and I was correct. But do I know how I arrived at that answer? Nope. My brain told me and that's all there is that I'm consciously aware of. One of those instances was the winning point for my team in a Math Olympics type competition.
Sounds like my math experience.
I find showing my work and proving things super fun! It's a puzzle for me, to show how things work. I'm doing a master's degree in physics and I excel at the most rigorous classes and suck at the more heuristic ones.
I do everything in my head. I write only the outcomes of parts of my calculations, to not forget them or do errors.
This was why I fell off with math in high school and never got my mojo back. My mental math skills were above average but once discipline and showing work and “proofs” (especially proofs) came into play I was out
My older daughter does this. You tell her a math problem. She'll blurt out the answer. Ask her how she got it, she doesn't know and can't explain it.
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