Tonight while putting the 4-year-old to bed, he told me that he didn’t think he knew math. He said that he thought his 7-year-old brother was very good at math, but that he was not. Oh my. We need to nip this kind of thinking in the bud. But best to be careful about how to nip it so as not to cut off more than intended.
“Why do you think that?” I asked.
“Because I don’t know what 10 and 5 is, and James does.”
“Oh. Hmm. You’re 4. I don’t think you should know what 10 and 5 is.”
“Mom. What is 10 and 5?”
“15.”
“And what is 20 and 1?”
“21.”
“And 30 and 2?”
“32.”
And so on and so on. It was bedtime, and he’s 4, so I gave him the answers and didn’t bother with creating a way to coach him to discovering the answer for himself. For a while he kept quizzing me, always with numbers that followed the pattern of just tacking the second number on to the first to get the answer. Then…
“Mom, what is 30 and infinity?”
“Infinity.”
“No. No, it’s not. It is thirty-infinity.”
“Hmm. Yes. That answer does seem to make sense.”
“And what is 0 and 13?”
“I would say 13.”
“No, Mom. It’s zero-thirteen.”
“Ah. I think I understand now. That seems right.”
“Am I right? Is that right?”
“Yes, I think you are. A lot of people won’t say the zero first, but it doesn’t seem wrong to me.”
“Oh. Hmm.”
Pause for thought.
Then…
“Mom. Will you come with me to school when I am a teenager so that I can find my room?”
“You bet.”
Then he rolled over to go to sleep, leaving me to marvel at the workings of his mind.
(Mathematically…I wasn’t leading him astray or coddling him. He noticed a pattern. Then he applied his observation to new situations. THAT was the mathematical learning. At a developmentally appropriate age, he will discover that not all addition problems follow that “just tack on” pattern. In the meantime, we had a nice mother-son conversation, and he has hopefully shifted his “I don’t know math” thinking.)
mathy moments 
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