I made this, Straights and Flats, in Photoshop. It’s kind of in the style of Mondrian. I wrote about Klee and Mondrian three years ago under the title Surely It Should Be Mondrian-ex, if you get the joke.
When I was a teacher, we taught bases in mathematics with pieces of wood. We had sets of them in boxes – little cubes, and lengths divided with grooves to indicate that they were notionally made up of many cubes. And flats with grooves to indicate a grid of cubes, and blocks with grooves to indicate a lattice of little cubes.
For younger children, the school had coloured lengths of wood to indicate 1,2,3, etc. each length had its own colour and the length and colour corresponded to a number. So the blue rod might be two bits long and that would represent the number two, and so on.
I taught eight and nine year olds, so I didn’t ever use the coloured pieces of wood, which were for the youngest children just starting school.
One of the teachers in the team told me about visiting his niece and her parents. His niece was painting, and was stumped because she didn’t have a colour for the grass.
So he pointed out that she had blue paint and yellow paint and asked her what she would get if she mixed them. And she said ‘five’.
Is it really a good idea to add an extra, arbitrary step between the thing and the understanding of the thing?
It’s important teach the difference between convention and logical necessity. A simple game would be to invent new single squiggles to represent numbers past 9 and add them up and take them away. It’s a test of creativity, or remembering the values assigned to numbers, and of the convention that is base 10.
We are living in a time where we are surrounded by things people make and names they make up, especially in the digital world. And those inventions and invented names are coming thick and fast.
It’s fun and interesting to hear your story again about that little girl’s misconceptions, although I hope someone finally taught her correctly – and if the artist who designed the art for that Kleenex box didn’t have Mondrian in mind, I’ll eat my hat! 🎩
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