My son is 8, and yesterday he came home from school and said, "I'm not above grade level in math." He sounded a little disappointed, but not too much; he also s

My son is 8, and yesterday he came home from school and said, "I'm not above grade level in math." He sounded a little disappointed, but not too much; he also seemed to be asking if that really means anything. We had a really interesting conversation. I've been a middle and high school math teacher most of my life, so this is quite familiar ground for me. Over dinner I asked him how he would go about measuring whether a kid is "above grade level". He got really animated and started to tell me what he thought second graders should know and be able to do, and how third graders should expand on that, and what he thought he'd start to learn in fourth and fifth grade. I told him I could start to teach him some of the operations and skills he'll learn in the coming years, but that it probably wouldn't mean a whole lot. Instead I asked him what ideas he's already familiar with that other kids his age don't know about, because we talk about math almost every day. "I know what phi is, and pi!" Yes, and we've also talked about limits, calculus, negative numbers, fractions, decimals, and he's looked at pages of math that's well beyond my understanding as well. I told him that when he gets to middle and high school classes, he's going to see higher level math and it's going to sound familiar because we've already been talking about the ideas for years. He's going to watch other kids fail and drop out of those classes because the ideas and the skills will be too new and too difficult for them to take in. I said we're probably much better off just continuing to talk about fun and interesting areas of math for the time being instead of worrying about "grade level".