Children seem to have this innate sense of the sweet spot between practicality and abstraction which is well suited to mathematical thinking.

Given the Roman number II, the integer 2, the real number 2.0, the word pair, children seem to understand the relationship between them.  Children seem to know how two chairs and two people are the same.  In the bath last night, my two-year-old asked for one of her “guys” and when I gave it to her she pointed at the other one and said “two guys.”  Then she pointed at herself and said, “I’m two!”

What is the sameness between those two guys and the two years she’s lived and the two fingers she holds up proudly each time she uses that word?  Where does that sameness break down?

If I give her three sticks and she counts them, she counts to three.  If I break one of the sticks in half, she understands I haven’t added or subtracted any substance from her stick pile, but she also understands that predicates are needed when we talk about the four sticks we now have: two whole sticks and two half sticks.  If I ask “how many sticks are there?” she could answer a bunch of different ways: 4, 3, 2, or some other answer I haven’t thought of.  In order to settle on the same answer, we have to have a conversation about what we mean by “stick” – just a whole stick?  any part of a stick?  the number of sticks before one was divided?

Mathematical logic in children seems to be something that develops early and is surprisingly capable without too much intervention.  Wonder what it is that we do to change that?