I have to look up in B’s old portfolio how B used to do arithmetic when he was still getting comfortable with which numeral what which. I think he used to use counting, being my ears boy. But M surprised me yesterday when he showed me how he has been calculating his addition in the first Miquon book. He likes his rod track number line, because he can look up the numerals and remember where they come in the sequence. I though he was looking them up, then using Cuisenare rods to figure the addition. Actually, he was looking up the numerals, placing a finger on each of the addends, then eyeballing the sum on his rod track. It works well for him with small numbers, but when he has a large sum, he can get off in his estimates. I’m not really surprised, M has quite the eye.
This is the boy who asked me last year how exactly did you know how many things there are? I replied, "you say the name of the numbers in order as you sort each thing you are counting. The last number name you say as you finish sorting is how many things you have all together."
"Oh, that’s how you do it." he replied.
I never expected to have to explain counting explicitly, I just figured everyone picked it up by example. M keeps surprising me.