About seven years ago …
“Look, Mom, I broke my pecan in half.”
“Mmm-hmmm. Does it taste better that way?”
“Now I broke both halves in half. Now I eat them!”
“Wow! Do you know that when you break a half in half, it’s called a fourth?”
“Yeah, look. I’ll break this pecan in half, and then both halves in half. How many pieces do I have?”
“One, two, three, four.”
“Right, four. So each piece is one-fourth. Get it?”
Without responding, she eats the pecan. Okay, maybe it’s a little over her head; she only just turned five. We eat a few more pecans, then …
“Look, mom! This pecan is in thirds!”
Sure enough, there in her hand is one pecan in three pieces.
So does Nova, at five years and three months of age, understand fractions? No. But is she gaining a good basic understanding of real world math? Yes.
Will she remember this tomorrow? Unlikely. But has she gained a concrete experience of fractions that she can build on when fractions show up again in her young life? Absolutely.
Did I set out to teach her fractions? No. Did I use a concrete opportunity to help her put a name to something she is beginning to understand intuitively? Yes.
Will I run out and find some fraction worksheets to help her build on her knowledge? Not on your life. Will I keep an eye out for more concrete, real-world experiences that I can use to help her expand her own world? You bet.
Not bad for a Christmas Eve morning, sitting in your mom’s lap eating pecans, and wearing your dad’s sweatpants as a shawl.