How I Wish I'd Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes

by Craig Barton

The answer of £75 probably came to you almost instantly, without you really being conscious of what you had done. You immediately and unconsciously recognised the percentage sign and what it means, and you know that 25% is the same as a quarter. You have automated this knowledge, and hence it takes up no space whatsoever in your working memory. You have also automated the procedure for finding a quarter of something, so you can quickly work out a quarter of £300 by halving and halving again without imposing too much strain on your working memory. You can do all of this because you are an expert. You could also probably do this calculation if music was playing in the background, your partner was asking why you haven’t done the washing up, and you were attempting to juggle. The fact you have automated much of the knowledge necessary to answer the maths question frees up space in your working memory to attend to other things.