I’ve taken multiple classes in trigonometry and calculus and I’ve done well in them. I’ve taken a course in linear algebra and while I don’t know what that is, I know it means that I’ve learned some high level math. And that leads to some strange biases, like believing that knowing math isn’t that important.
In my everyday life I don’t use calculus or linear algebra. Until I stop and think about it, I’d tell you that I don’t really use math at all. I’d tell you that learning math is nowhere near as useful as it used to be and that computers can do that work for us now. What’s the point in learning it?
But all my knowledge of math is making me forget what it is like to not know it. I can’t think like a beginner. This is the bias we all fall into when we know something well. It’s one of the stages of learning – you start knowing nothing, then you learn more and more until you know enough to be useful, and then master it. And the master doesn’t know how much she knows.
I’ve encountered this before but I only applied the idea to software development. I tried to start teaching someone programming. He had never been exposed to any programming concepts, although he was fairly technical. I kept starting with a topic that I thought was fundamental and then finding out that I needed to go back further to something more fundamental. I found that I had no idea what the fundamentals were because I had so many layers of knowledge.
So no matter what you know, just know that you know more than you know. Find a way to share it with those that don’t.