My daughter is pretty excited about math right now.
She begs for us to give her math problems, I have heard doing sums out loud sometimes after she goes to bed. I heard her add 2 plus 2 = 4 plus 4 = 8....up to 2048 the other night (wtf how do I get the plus sign to show up). Pretty swell for a 7 year old.
I try not to do a bunch of raw calculation with her and instead focus on ideas, patterns, graphs and math language. What time is it if it's a quarter to 4 or half past 2. Isn't it queer that the clock has 60 min and a quarter of an hour is 15 minutes while a dollar is 100 pennies and a quarter is 25 cents? I run out of ideas and am damn tired of it sometimes but it's fun to see her wrestle with stuff and get excited.
I've mentioned negative numbers and maybe she's seen some in a graph and what not. She's never had any on her homework (her home work is addition and subtraction with some sneaky multiplication mixed in). I can' say that I've never taught her anything about them.
She had a sheet with a number line and some addition subtraction problems that she had written out that had a bunch of problems with negative numbers on it. I asked her where she learned to use negative numbers.
"Let me show you she said," and proceeded to draw a number line which was opposite the typical orientation 3 2 1 0 ? (with an X through it) -1 -2 -3. "I was thinking," and she writes on the paper "We can not start at the end! Thar is a infinaty of nubers. (Spelling is her own). And from there she just up and started to manipulate simple math over the conceptual chasam that is 0.
Fucking blew my mind...
I don't think she's a math genius or anything but she's clever at it and has a natural inclination to engage in challenging ideas. I'm impressed and surprised. I hope she doesn't rederive the fundamental theory of calc at 14 or something, it be a daunting responsibility to keep her stimulated. She's an average math student in class but I suspect that is mostly her being inattentive at raw calculation. I don't think with 31 kids in the 2nd grade class the teacher has a lot of time to gauge how well any given student can grasp big ideas, she just sees how many little sloppy mistakes my kid makes and my my child rushes everything and is sloppy as hell with details.
We have started working on fractions and decimals with Legos and cut up pieces of Halloween candy. She's picking up on them pretty quickly.