Now and then I buy my lunch or a snack in Pret A Manger and it usually costs around £5 or less. Things move quickly in Pret but my brain isn’t so speedy working out my change. Over the last few months I've tried to use these outings as a way to improve my mental arithmetic which is quite poor.
The queues build fast and the sales assistants work quickly. The sandwiches aren’t labelled so the staff occasionally get it wrong. A simple subtraction is no trouble (such as £2 from £5). I can also manage £2.50 because I know it’s half of £5. But if I have to split 10 pence into pennies it's more difficult. £2.25 from £5 is trickier – my brain rounds down the 25 pence to 20 pence, so it assumes I’ll have about £2.80 change. I sort of know that the pence part needs to end in five, but is my change £2.85 or £2.75? It should be easy but like a dyslexic with words, the numbers get scrambled in my brain. It's hardly a huge sum of money but who likes being short changed?
A few years ago I discovered that calculation depends on something called working memory - the ability to hold all the relevant components in your head while the brain works on them. At least one other person I've talked to about this empathises, so I’m guessing others suffer from this too, though perhaps not as badly as me.
I wondered if creating and memorising a visual representation of the money might help my working memory. My brain vaguely sees the money spent and the change left as two pieces of a jigsaw puzzle; they make two distinct shapes which interlock. I thought I'd try an experiment.
The picture above shows I spent £1.76 and received £3.24 in change. I like the solid blocks of colour but it doesn't really work for me because it's too ‘busy’. I tried a simplified version (below), but without the text it’s hard to ‘read’, but it gives a sense of proportion and the division of pennies is clear which is the bit that gives me most difficulty:
The third representation has been reduced to a few lines. Each little rectangle represents 10p.
Then I tried Cuisenaire rods to do some different calculations. Each rod represents a different number; an orange rod is the longest and represents ten, a blue nine, brown eight, a black seven, dark green six, yellow five, pink four, light three, red two and white one. In the pictures below I have used tens, sevens, twos and ones. Unhelpfully, my tens rods appear red in the picture.
The picture above shows five orange rods. Each rod represents 100, or one pound, so that's five pounds in total.
This picture shows my first calculation. The two orange rods at the top represent (10s) 200p, the black rod (7) 70p, the green rod (3), 30p. So I've spent £2.70 and I receive £2.30 change. But what if I spend £2.25? The smallest rod I have is a white (1) or 10p. I have nothing to represent pennies.
This is how I did it. The picture above shows I spent £2.20 (and something) and received £2.30 (and something). The 'something' is represented by the white 10p cube.
Above I have split the 10p into pennies - 5p at the top and 5p at the bottom. Here I can see that if I spend £2.25 I'll get £2.35 in change. OK, so I've developed my own Cuisenaire symbology but as the white cubes are outside the rectangle I see them as having a separate function.
What method did I enjoy most?
I'd have to say it was the Cuisenaire rods because I enjoyed handling them - the wood is so light and smooth and makes a beautiful sound when it's placed on a hard surface. Using sound, touch and sight seems to make a greater impression on my brain. However the Cuisenaire colour coding needs to be memorised and the standard shades don't represent my synaesthetic colours. I haven't let that bother me though - I guess it's like learning a new language. I need to play with these a little more to see if I can imprint the images in my memory!
