If I fetch three logs for the fire, subtracting from the wood pile and
adding to the stove, is that quantitative sense or number sense?
It depends on if you were aware that you got "3" logs.
If I was asked to "get three logs" and obey, is "number sense" now in
the foreground? Is "counting" alone enough to establish "number
Yes, if someone asked you to go get a particular number of logs and you did so, repeatedly with different numbers, then you have number sense. You can count.
When I see two people each have half a load of hay, or half a loaf of
bread, I am seeing that they have copies of "the same thing" (loaf of
You are seeing "sameness", it isn't number sense.
By the way, here is the chimp "counting"...
I would say that this chimp has better quantitative sense then you or I. Almost savant like. Unfortunately, for counting, it tops out at 8.