We were packing for a trip recently. I have developed a system for getting the kids packed. It is beautiful. Here’s how it works:
- Send kids to basement to get suitcases.
- Keep suitcases on first floor.
- Send kids upstairs to get one type of item at a time. E.g. Three pairs of underpants. Then three pairs of socks. Et cetera.
- Kids throw each type of item in the suitcase.
- Repeat steps 3 and 4 as often as necessary.
- Done.
Seriously. It’s awesome.
I made an observation with Tabitha partway through.
Me: Isn’t it strange how a pair of socks is two socks, but a pair of underpants is only one thing?
Tabitha (six years old): Yeah. It should “a pair plus one” because there are three holes.
Me: Wow. I hadn’t thought of that. So how many holes does a shirt have?
T: Three….No four!
Me: How do you figure?
T: The one you put your head through, the arms, and the head hole.
If you are like me, you may be a bit behind the curve on her language here. “The one you put your head through” is the one that ends up at your waist once your shirt is on. I had to think about this for a moment.
A few days later, I was curious to probe her thinking a bit further. She was getting dressed (a process which is always slow, and occasionally very frustrating for the parents):
Me: Do you remember how you said a pair of underpants has three holes and a shirt has four?
T: Ha! Yeah!
Me: I was thinking about that and wondering whether there are any kinds of clothing that have one hole or two holes.
T: Socks have one hole!
Me: Oh. Nice. Sometimes Daddy’s socks have two holes, though.
T: Yeah. When they’re broken.
By this time, she finally has the underpants on and her pants are being slowly pulled on.
Me: Wait. You need socks!
She goes to her dresser and proceeds to sort through the very messy sock drawer.
T: There are no matches.
I find what appears to be two socks balled up together.
T: No! Those aren’t socks! Those are for putting over tights to keep your legs warm.
We look at each other.
Big smile.
T: Those have two holes!
Overthinking my teaching 
I love these!
Heh heh… The guy named “teachbarefoot” likes a post about doing math with socks… That’s kinda funny…
I tried to like your response, but then I realized WordPress doesn’t let me do that, haha.
Nice. The counting is a bit off from what topologists use, though. They would argue that socks have no holes, the leg warmers have 1 hole, the underpants 2 holes, and the shirt 3 holes. I wonder if that numbering convention could be explained to Tabitha.
Really it’s counting boundary components, which is a perfectly natural thing to do and topological. If you want to be algebraic-topological about the distinction between boundary cycles and “holes”, you’re going to end up with some delicious ambiguity in where the holes really are.
Good point, Jesse.
Great post — I loved hearing about your kids’ excitement and creative take on life, math, and the intersection between them. Wait, are those socks broken, or are they just legwarmers?
jesse and gasstation, you do understand that we are dealing with a 6 year old here, right? I’ll let you two do the disambiguation when she gets to your courses in college!
ProfJohn, they are legwarmers. Nice pick up on the broken socks idea, by the way.
Yes, I was aware of the age (the title of the post includes it, after all). Six is not too young to start counting at 0 rather than at 1. My son was counting in binary on his fingers by that age (though we had to warn him about 4, 128, and 132 being rude gestures).
I agree that counting the boundary elements is a lot simpler than what I was taught in the one topology course I took decades ago and is certainly the more sensible thing to be discussing with a 6-year-old.