Join the Dots

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Join all the dots
using only 4 straight lines and
without taking your pen off the paper

I often use the nine dot puzzle when I’m working with teachers. It helps us consider how thinking can work, why it can be really hard, and how differently people react when they are given something they can’t easily do. Faced with this puzzle, and told to work on it alone and in silence, some people will stare at the dots, trying to imagine what the answer could be. Others will start scribbling immediately, in an effort to find out how it works, not caring how many failed attempts they make. A few people might switch off pretty quickly because they decide they won’t be able to do it, or they can’t be bothered. And others may want to be told the answer almost immediately. (A handful of any group will know the answer already, so I ask them to come up with alternatives to the ‘classic’ answer.)

When we are asked to work something out, rather than just being told it, we have to think harder than we normally would. We don’t know yet, so we have to figure out how we could find out. I suppose this is why the human mind seems to like puzzles – trying to work something out is like aerobics for our brains.  Even though we know there is an answer, we get a buzz if we can work it out for ourselves. When I use this puzzle with teachers, I help them get the solution to the puzzle by giving them clues. The first, most important clue is that it gave rise to the saying “Think Outside the Box”. This puzzle is a great example of how, when the human mind is given a box, we tend to stay inside it. As soon as you let people chat in groups about the puzzle, they quickly start to build on each other’s thinking, and pretty soon someone has figured out the answer.

For me, though, the most interesting thing about the nine dot puzzle is not that there is a ‘correct’ answer, but about how many alternative solutions I can devise. Can I come up with a solution that no one has ever thought of before? Is there a more interesting way to solve this? I feel this way about education at the moment. I worry that if we are told that we have to find the one correct answer, we might stop looking for alternatives. And the alternative solutions to the nine dot puzzle? Well, try this. Holding your pen on the paper, fold it up, so that you can connect the dots in a stroke or two. Or this. With your pen still on the paper, grab a pair of scissors and cut out the dots, rearranging them to complete the task. Perhaps my favourite alternative answer of all is not to do with the dots at all, but with the tool I am using. Because all I need to do is to find the world’s fattest marker pen, and I can join the dots in a single line.

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