Way back when I taught math, I remember having a student in one of my junior high mathematics for college students classes who pulled out her calculator to do 8

Way back when I taught math, I remember having a student in one of my junior high mathematics for college students classes who pulled out her calculator to do 8+9 (that's the exact calculation, I remember it remarkably clearly). And yet, she was able to manage the symbolic manipulation around the rest of the algebra problem she was solving. The thing I took away from that is that while we tend to think of arithmetic as a prerequisite for algebra, the skill sets are largely orthogonal. I kind of wonder if this was part of how the child of two math professors¹ was taking upper-division college level math classes at Harvey Mudd as a high school student. It's not so much that he learned K5 mathematics quickly and was on to pre-algebra and algebra as that he was likely introduced to algebraic concepts much sooner than his peers. ⸻⸻⸻ 1. I never met him, his time was a little before mine, but I recall someone who had met him saying that his parents taught him a lot of mathematics but not so much by way of social skills.