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Last night something happened that I wanted to share with you. My daughter loves all kinds of math concepts like probability, geometry, topology - she will often make connections between "non-mathematical" things and series, square numbers, prime numbers, digital roots, mobius strips, angles, and the list goes on. However at age 8 she doesn't have basic arithmetic memorized. She will still add up on her fingers.
Last night she devised an "addition table" using dominoes. She arranged them such that you find the two numbers that need adding in their respective rows and columns, find where they intersect, and then count up all the dots on that domino. Most of us would find this more time consuming since we just do one-digit addition without much thought process. If she had learned addition by heart then would she have ever devised this addition table? She has arranged the dominoes in various patterns and I see that she is fascinated by the qualities of the different arrangements. There are mathematical concepts going through her head though I have no idea what they are and they might take a greater understanding of math or number theory to describe in words.
I bring this example up because when we talk about how unschooling facilitates learning at one's own pace, most people think it means that we need to be patient with "slow" learning but rarely we get an example of learning that is made possible precisely because something else was not yet learned or learned "slowly."
It reminds me of one of my favourite quotes of Wittgenstein, "Is my understanding only blindness to my own lack of understanding?" If we rush to "understand" addition, as indicated by correctly (and promptly) adding given numbers, we may miss out on investigating what addition is, and what numbers are.
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