Earlier this week, I had the opportunity to read at my youngest son's school for their Community Reading Day. This sort of thing almost makes paying for my own health insurance worth being self-employed. He's in the third grade and has a great class with plenty of sharp, friendly kids. Unbeknownst to me, though, Community Reading Day involved more than just reading.
Although the program coordinator had given me the book (The Bee Tree) I was reading to the class almost a week beforehand, I, of course, didn't open the packet until 1:00am the night before (technically the morning of, but you know what I mean). Inside the packet was the book (not surprisingly), some poorly photocopied coloring pages, and a note telling me to prepare a suitable related lesson to accompany the book. Woops.
Fortunately, I was a teacher for long enough (and invariably never prepped enough for class since I was too busy being Captain Computer Tech at the same time) that I can pull a lesson out of nowhere pretty quickly. Those lessons were for high schoolers and I was always in awe of elementary teachers, but this was Community Reading Day, not Ex-Teacher Reading Day, so I figured I'd be all right.
It was my kid's class, though, so I wanted to do something interesting, something that they wouldn't learn otherwise. And it needed to relate to bees (hence, The Bee Tree). As I pondered what might be a cool third-grade appropriate lesson there at 1:00 in the morning, a presentation that I'd heard in a graduate calculus course came to mind. No really.
Bees, as it turns out, create a completely optimal space for their honey, raising their young, and storing food. The hexagonal shape of honeycomb cells actually maximizes interior volume while minimizing surface area. Since bees must eat about 8 times the volume of honey for a given volume of wax that they need to create their hives, wax is a precious commodity, so optimization is key. Obviously I wouldn't expect the third-graders to be able to handle calculus-based optimization problems (in fact, the so-called Honeycomb Conjecture, or idea carried forward from the ancient Greeks that honeycombs were optimally arranged, was only proved about 10 years ago).
However, if the third-graders were meeting the math standards outlined for their grade here in Massachusetts, they should know enough geometry to be able to have a pretty cool discussion about hexagons and other shapes that might fit together with the smallest perimeter and largest surface area. My wife, when I mentioned the next morning what I'd be talking about, thought I was nuts. "There's no way they're going to get that stuff!"
Any my oldest son? "Uh, yeah, you're really going to have to dumb this stuff down."
Well, what did I have to lose? It's not like I had an evaluation riding on it. So I headed into the class, read the story, talked about bees and made them learn the word onomatopoeia because there was just so much of it in the story, and then launched into my geometry lesson. I explained about how much work it took to make wax and all the ways that bees used space in their hives. Then I broke them into groups and had them brainstorm shapes and talk about how they would fit together.
The groups presented their favorite shapes and we talked about how we'd calculate perimeter and area for each of them (the many-sided polygons and ellipses we just talked about in general). We talked about wasted space, edges, and even the idea that circles are just regular polygons with an infinite number of sides. And guess what? They got it. They were excited. They were competing with each other to figure out the right answers and were debating in their groups about why certain shapes would make the most sense for a honeycomb. They knew the words infinity, perimeter, and area without me defining them. They rocked.
I raised the bar quite a bit higher than my wife thought I could, they reached for it, and they hit it.
The whole time, of course, I was silently thanking their teacher whom I've known for quite a while. His quiet adherence to the standards and deep subject matter expertise had prepared them to stretch and extend (and his standardized test scores confirm that year after year).
The point here, though, is that it's OK to raise the bar. Kids will reach as high as we expect them to. Sure, we need to give them the tools and scaffolding to make it happen and we can't start spewing calculus at them in the third grade, but these kids are sharp and hungry to learn. We damn well better tap into that while we still can, instead of waiting to push them in high school (if at all). By then, they've settled happily into mediocrity.