Crawling comes before walking . . . usually. Words come before sentences . . . usually. Even at the most basic level, learning doesn’t always follow the order that seems logical to us.
The ducklings are pretty normal, but even so they come up with learning sequences that leave me scratching my head. In doing puzzles, I had rather assumed that small children, being more hands-on, would be interested in poking the pieces into place first, and only later would they figure out how to find the right place to put the piece. Maybe that assumption is wrong, but both the ducklings are much better at spotting the right hole than they are at turning the piece around to get it in the right place. I do sympathize with them . . . I hate tinkering with things, too. Sometimes the eye is quicker than the hand.
D1 is still in process of learning to count. Various books I had read on brain development indicated that this followed a pattern: first learning to rattle off the sequence, then to touch one item while reciting one number, then to realize that the last number uttered is the total, and ultimately to recognize symbols that go with the number. She did learn to recite the numbers first, but she still doesn’t see the importance of one-to-one correspondence, although I think she does realize that the final number recited is the total.
And she already recognizes most of the numerals, so if I ask her how many in a book, she’ll look over at the numeral rather than try to count. I think we need to do counting outside of books. As an alternative to reading the numeral, she’ll count in groups. Show her a page with five, and she’ll say it’s "two and three." That should make addition easy to teach–and even multiplication, since for an even number she might say, "two twos." But I still can’t figure out how to get her to slow down and count one object at a time.