Thursday, September 17, 2015

The Lessons of Puzzles

            When I was in elementary school I took part in a gifted and talented program at my school. Once a week several of us were pulled out of our regular classrooms to come together and work on things that we might not normally get a chance to do. This program was by nature experimental. The whole point was not so much to push kids further forward through the standard curriculum but to stretch their thinking wider within that curriculum. Exactly what that stretching meant depended both on what the students could handle and what the teacher could imagine.
My memories of the classes themselves are fragmentary. I know that at some point we did a unit on archaeology that I really enjoyed. In second grade, I remember trying to record notes in my notebook with my left hand after breaking the wrist on my right. I remember the location of the classroom – right off the gym in the back right corner just before you went behind the stage. For one of the projects my group filmed a war movie in my backyard. In another I tried to construct a working model of a maglev train. For her class, my younger sister created a fake episode of the nightly news to talk about what she’d learned in a unit about Australia. It included headlines from the day, a weather report, and even a commercial for Vegemite, a dark, yeasty spread that Australians use on breads and sandwiches.
            My strongest memory from this program, however, came from an exercise that didn’t work. During one unit on puzzles that we did in the fourth or fifth grade, the teacher read us a set of stories in which something mysterious happened, and we were supposed to piece together a solution to the mystery from the clues buried in the story. Unfortunately, we just couldn’t do them. There was a leap of imagination or a trick of logic in them that was beyond our capabilities. The story I remember most clearly involved a man who had hung himself from the highest rafter of an empty room, and no one could figure out how he got up there. The only clue was the presence of a puddle of water underneath him. We conjured all kinds of ways this man might have gotten up there – a pulley, a secret trapdoor in the ceiling, climbing the rope. Our teacher kept leading us back towards the water, clearly annoyed that we weren’t getting it. She kept telling us to think about the water, that the water had to have something to do with it, but we couldn’t think what that might be and thus kept spinning off in other directions. Finally with time running out and all of us tired and frustrated, the teacher gave us the answer: ice. The water had been a tall block of ice that the man had used it to get up to the rafters. After a while the ice melted leaving behind the puddle of water.
            I always thought the teacher could have done that exercise better. There had to be a halfway point somewhere along the way where she could have told us something more than to just look at the water. It was clear this wasn’t enough. It was clear that we needed another step, not just to help solve the problem but also to give us ideas about how to solve such problems in the future. Perhaps if she’d taken us into a further discussion of the properties of water or maybe helped us organize our thoughts in a different way we would have gotten there. Regardless, there was a moment there for teaching something else, for teaching ways to attack a problem when the answer isn’t immediately obvious, but the teacher failed to grab it.


            Polly brought home an exercise from her weekly gifted and talented session at school last Wednesday. The exercise contained three challenges, each of which involved taking a shape made from toothpicks and moving a couple of sticks around to make a new shape. They had done the first two problems at school and after showing them to me and having me try them out, Polly proudly told me their solutions, one of which she had come up with all on her own. The third problem was intended for her to work on at home. Feeling confident, she dove in and fiddled with the toothpicks, moving them in and out and around for a good ten to fifteen minutes without success. Eventually she got frustrated and walked away. She said that she’d try it again tomorrow, but I wasn’t sure she actually would. She was stuck and couldn’t see a way forward. I had a flashback to a man hanging from the rafters with a puddle of water beneath his feet.
            The next day after school, I asked Polly if she wanted to try the puzzle again. When she demurred, I knew what would happen. She wouldn’t touch the puzzle again until the following week when the teacher or some other student would present the solution. Then Polly would bring it home to us, and happily show us how it’s done, having learned from the exercise that if you wait long enough, someone else will give you the answer.
            That was not the lesson I wanted her to have, so I had her sit down with me and together we worked through the problem. While I knew what the answer was, I wasn’t that concerned with getting her immediately to it. I wanted to walk her through the process of thinking, to give her some directions about how to map out a systematic breakdown of the problem when her first brainstorming stabs did not meet with success. Ultimately, she already knew what she needed to do – take each stick in turn and move it around until she found the one that made the shape work – but she needed me to help keep her focused on doing that process one complete step at a time.
Eventually we found the right stick. The moment she slid that toothpick into place Polly could see the shape emerge in front of her, and she jumped up from the table to do a little dance. She was so proud of what she’d accomplished, proud that after being frustrated by the problem the day before she came back to it and was able to find the solution, proud of the idea that she was a person who could solve these kinds of problems.
I don’t know whether in that moment of exaltation she consciously remembered exactly how she’d gotten to the solution, that it wasn’t an act of magic but one of systematic elimination that had finally gotten her there. She’s six years old and even for adults such distinctions can vanish very quickly. However, it gladdened my heart to find her working a jigsaw puzzle later on that weekend and filling in the pieces line by line.

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