That was one of the fun parts of my previous career, observing and assessing cognitive development in children of different ages. The concepts, like counting with one-to-one correspondence, appear in fairly predictable sequence, all as laid out by Piaget.
One of my favorite moments came early in my career. I was doing a 3-year reevaluation on an 8YO boy diagnosed with Downs. The first question on the Information scale of the WISC-R involved holding up my thumb and asking, "What do we call this finger?"
The boy's face broke into a huge grin as he imitated the gesture and shouted, "Fonz! Ay, ay, ay!"