2 + 2 = Fish

E has made something of a name for herself in our household as our resident puzzle-solver, so the events at our breakfast table one sunny morning were a wide-eyed surprise.

See that pic up there? Go give it a minute or two. I’ll wait.

Back? Super.

H  – our resident dyscalculic – looked at this and got it, literally, in about one second. Seriously. Through a mouthful of cinnamon roll, her immediate comment was, “you flip the shape around and stick it together, so two 2’s make a fish, two 3’s make an 8, and two 7’s make a triangle.”

Sleepy E arrived at the table minutes later to find the iPad at her place, and frowned. And then her ‘working’ face went on, and I could see the gears starting to whirl and steam starting to rise. I could literally watch the permutations and insinuations get examined, one by one, and discarded.

“I don’t get it,” she sighed.

The real revelation for us was that it was literally impossible for E to discard the symbolic freight of numbers as mathematical fact. She was trying mathematical possibility after mathematical possibility, analogy after analogy – do fish have four fins? Does a triangle relate somehow to the number seven? – without success.

It’s a rare moment when H’s issues in subitization become a gift. They’re not numbers first to H; they’re shapes. If I gave you a set of squiggles that, mirrored and docked, became recognizable shapes, you could probably solve that problem as fast as she did. (And maybe you did anyway.) But load down a graphic with meaningmathematical meaning in this case – and E’s traditional problem-solving machinery grinds into motion instantly. I had to point out to E, as a hint, that if you began by thinking of them as numbers, the puzzle actually became more difficult to solve, at which point she ‘got it’ – but whole minutes had gone by.

This strikes me as particularly important having watched (again) the video entitled Future Learning, in which one of the most important skills for next-generation success is the ability to reject doctrine, to slip dogmatic bonds and free the mind to approach problems freshly, with what amounts to that child mind. As I marveled at what H had done, I wondered to myself: are there fish and triangles in my own daily challenges that I’m not identifying and addressing correctly? And how do I teach ‘machinery’ like E’s to start with the ‘child mind’ when we approach problems like this one?

One response to this post.

  1. I’ve just spent the last two evenings reading your blog, from the most recent posts back to this one, and, suffice to say, I find it fascinating! We don’t have any formal diagnoses in our house – here in New Zealand they are sadly often considered the height of parental desperation and/or pretension, so are uncommon and expensive – but this post made me smile, because when we came across that particular puzzle, I, an excellent candidate for dyscalculia, saw the intended answer immediately just like your H did, whereas my partner, who is the resident math fanatic, spent at least 10 minutes on the same sort of processes as your E, before looking at me and asking whether he was doing it all wrong! But then our eldest daughter, then aged 5, who is great at math but also has very dominant imaginational intensity, got the solution straight away, and then proceeded to rattle off alternative ‘products’ for the same questions, and more numbers and letters that you could apply the same treatment to. It’s interesting how such a simple concept can inspire so many different approaches!


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