I don't seen how quantitative intuition and precision are somehow opposed to each other. 4*5 is 20. Not 21. Not 18. 20.
That is logical, and it's vitally important in the understanding of all future concepts. You don't need to understand advanced calculus to grasp the concept that 2 3/4 oranges + 2 1/3 oranges is not 5 oranges altogther, but actually more, and that left over bit is in fact meaningful and relevant.
It's when you start to play with abstractions that mathematics becomes confusing, not when you are being precise.
I think you misunderstood my example. My point was that knowing that there is 5 1/12 oranges (as opposed to 5) is the important precision, and it works logically to a child's mind.
It's quite a bit more complex to expect the child to discard the 1/12 and suggest there are 5 oranges. It's not that the 1/12 is useful for anything, it's the fact that it exists, and is accounted for.
That is logical, and it's vitally important in the understanding of all future concepts. You don't need to understand advanced calculus to grasp the concept that 2 3/4 oranges + 2 1/3 oranges is not 5 oranges altogther, but actually more, and that left over bit is in fact meaningful and relevant.
It's when you start to play with abstractions that mathematics becomes confusing, not when you are being precise.