While driving on the highway, my wife had the following exchange with my three year old son, Timon.
“Mom, what’s three plus three?”
“Mom, what’s four plus four?”
“So… three plus four is seven.”
My wife was so stunned, she told me later, she almost stopped the car to tell me.
Timon asking us questions about addition is nothing new. He’s been trying to participate in a similar game my older son plays with me. What’s remarkable here is that Timon has derived the addition fact for three plus four.
Timon also recently noticed that one plus three and two plus two both equal four and showed me on his fingers why he knew it was true. He’s playing with addition of small numbers, sometimes asking me what the sum is, sometimes showing me by counting out on his fingers. He has yet to count on from a number he knows (he starts counting at one each time) but he does recognize groups of objects up to four and sometimes five in size without counting directly.
My point here is to pay attention when your children discover ideas on their own. They might just surprise you.