Author here - like one of the other commenters said, I don't think there's anything wrong with your approach, or any way of thinking for that matter. I don't think there's anything particularly "right" or advantageous about the way my brain works either. I don't have any reason to believe I'm better at math than the average engineer - definitely not a math prodigy or super genius or something like that.

With that being said, trying to think a different way for the challenge of it is definitely interesting. Reading through some of the other comments here and trying to taste words or replicate other people's minds is a weird, fun exercise :)