I still have summer on my mind, so I thought I’d share a math in the wild story from way back in July.
“I’m bored. What should I do?”
So said my seven year old son while we lazed about a gorgeous Massachusetts beach. In the deepest recesses of my mind, my mother’s words echoed, “Only boring people get bored.” Then I thought to myself, “You need something to do? I’ll give you something to do!”
“See that rock over there?” I asked pointing to one edge of the small beach. “Go there and tell me how many heel-to-toe footsteps it will take you to walk to the complete opposite side of the beach.” I fear it would be irresponsible for me to tell you I promised him a dollar if his estimate was within 20 steps of his actual measurement.
He took a look across the beach and gave me a number, 150 steps. I said, “Okay, let’s see.” And so he (having enlisted a buddy to walk alongside him) started to walk across the beach heel-toe, heel-toe, heel-toe. He got about a third of the way and had already reached his estimated step count.
And so he said, with great disappointment, “Oh, I—you know what, I know I’m going to be wrong.”
And so I said, “Well, guess what? Take this opportunity to revise your estimate. How are you going to do it?”
He had a look back to where he started, forward to where he was going. “It’s going to be, I don’t know, maybe 400 or something?” I asked him how he came up with it and he said “Well, I know that I have already gone my 150 steps, and I am not even halfway.” He kept walking.
Around 300, he looked ahead to his destination and said, “I’m not going to do it. I’m not going to do it.”
I didn’t want him to give up because this was a good activity, it was mathematically rich.* And so I said, “Yup, and you have another opportunity to revise your estimate. How are you going to do it?”
He really wanted that dollar. He thought for a bit and said, “Well, I know I went 300 steps and I think I am around halfway now… I’m going to double it.”
And in my head, my internal math teacher said, “Woohoo! Amazing!”
And so he doubled his estimate and kept going. And, you know, he really wasn’t within 20 steps when he got to the end, but he wasn’t out of the ballpark either.
And I said to him, “That was really awesome.”
And he asked, “Well, do I get the dollar?”
*Just how mathematically rich? Here are some of the formal concepts tucked into that informal moment on the beach:
Eyeballing the Distance is an example of visual/spatial estimation.
Walking heel-to-toe and keeping a running count is an example of accurate measurement by iterating a nonstandard unit, as well as data collection.
Checking Course at Milestones is an example of iterative estimation & the use of visual benchmarks or landmarks to make a smarter guess.
Doubling at Halfway is an example of multiplicative thinking and proportional reasoning.
Learning from mistakes and persisting in revising our work is an example of a productive math mindset!
And finally: Daily life looks a lot messier, of course. For every moment of ‘mathematical perfection’ in my world, there are probably a hundred moments of pure chance and beautiful chaos (still math!).