Here’s another comment on that New York Times piece:
“mystery number game …. ‘I’m thinking of a mystery number, and when I multiply it by 2 and add 7, I get 29; what’s the mystery number?’ “
See, that’s what I mean, the ubiquitous Common Core approach to math teaching these days wouldn’t allow for either “games” or “mystery”: they would insist that your son provide a descriptive narrative of his thought process that explains how he got his answer, they would insist on him drawing some matrix or diagram to show who that process is represented pictorially.
And your son would be graded on his ability to provide this narrative and draw this diagram of his thought process, not on his ability to get the right answer (which in child prodigies and genius, by definition, is out of the ordinary, probably indescribable).
Actually, I do often ask CJ to talk out his process after we do a mystery number. I share with the commenter the worry of slipping into a classroom regime where students are graded on their ability to recite the “correct” process. But in general, I think asking about process is great. For one thing, I learn a lot about how arithmetic facility develops in the mind. I asked CJ the other night how many candies he could buy if each one cost 7 cents and he had a dollar. He got the right answer, 14, not instantly but after a little thought. I asked him how he got 14 and he said, “Three 7s is 21, and five 21s is a dollar and five cents, so 15 candies is a little too much, so it must be 14.”
How would you have done it?