By David Starshaw–Mathematics Teacher–High School
How does someone become an expert? This is a driving question for teachers as we guide our students from being relative novices to relative experts in a specific area. But it’s also relevant for all of us in any area of our lives where we try to become more proficient. How do I win at this game? How can I run faster? How can I be more confident with public speaking?
Many of us intuitively understand that practice is a key ingredient of expertise. You have to practise to get better. As the saying goes, “practice makes perfect” (or alternatively, “practice makes better” or “practice makes permanent”).
In 1973, William Chase and Herbert Simon performed an experiment where a chessboard was set up with around 25 pieces positioned as they might be during a game. They asked a chess master and an amateur to look at the chessboard, cover it up, and recreate the setup of the pieces on another chessboard. They could go back and peak at the original chessboard as many times as they needed to. Unsurprisingly, the master took far fewer looks than the amateur – 4 compared to 8. But then the researchers rearranged the pieces in such a way that would never occur in a real game. This time, the master was no better than the amateur.
The masters weren’t better at chess because they had a better memory in general, higher IQ, or “natural talent.” Instead, they had seen lots and lots and lots of chess games. Experts have experienced a staggeringly wide variety of previous attempts and have learned what to do when similar situations happen in the future. These can be thought of as if-then statements. If I see my rook cornered, then I move my pawns forward. If I see a quadratic equation, then factorising it will likely be helpful. If I fumble a line in my speech, then going back a sentence helps me to recover. These if-then statements become totally automatic for the expert – like a reflex. They don’t need to consciously think about them which frees up their working memory for thinking about the big picture. I really like one of Niels Bohr’s quotes in which he says “An expert is a person who has made all the mistakes which can be made, in a narrow field.”
So when people tell me they are “good at maths” or “bad at maths”, what I hear is that they either have or haven’t built up a good library of these if-then automatic reflexes. And just like any reflex, it can be improved with focused practice. Once you have a lot of these automated, everything starts to fall into place as you travel further along the road from relative novice to relative expert in a specific area.