Imagine you are asked to learn about something, and the only way someone can help you understand it is with words, because there are too few examples of it around to actually see it for yourself. You think you know what it is they are talking about, but you keep getting confused because your image of what it is seems so much different than what the other person is describing.

It gets worse because most of the other people you talk to haven’t really seen it before either, and are relying on a story they read about it once before in a book or occasionally on their attempts to tell the story to other people. They sometimes contradict each other, and then other people come in and start telling a totally different story. In fact you aren’t listening to just one story, but many different stories all at once.

When you were growing up the story you were told was pretty different. None of your friends or family knows this new story. In fact, you were never told this story in school or even university. You don’t even really understand why you are being asked to listen to this story because as far as you are concerned, the story you had growing up was a perfectly nice story. Why come up with a new story?

You try and tell the story yourself, but it turns out the story is so different from any stories you have ever heard that it is hard to remember all of it at the same time. You make a lot of mistakes telling the story and feel discouraged and decide you should just stick with your old story. It’s a lot easier to do, and virtually everyone you know seems to value it a lot. Gradually you stop trying to tell the story, and stick with the older story that you undersntand very well.

 

This description pretty much exactly summarizes a reason why I think math education is so hard to change. The narrative around the changes necessary is often just too different than people’s personal experiences of learning mathematics.