We learn when we are challenged, when we struggle, when we push ourselves. If you’re not stuck you’re not learning.
Nobel laureate physicist Richard Feynmann said of scientific research: “It’s a very difficult and unhappy business. And so most of the time you’re rather unhappy, actually. You can’t penetrate this thing. We’re all some kind of apes that are kind of stupid, trying to figure out to put the two sticks together to reach the banana and we can’t quite make it. And I get this feeling all the time, that I’m an ape trying to put the two sticks together, so I always feel stupid. Once in a while, though, the sticks go together on me and I reach the banana.”
Research and learning is thus by necessity. If it’s not a struggle you’re not doing it right.
Andrew Wiles, who became perhaps the most famous mathematicians in the world when he proved Fermat’s Last Theorem, describes research similarly: “Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark.”
You always need to challenge yourself. When the lights are on there is no use sticking around. Always find a dark room. Otherwise you are not making progress.
So also for students. Confusion is not a sign of failure, it’s a sign you are on the path to progress. In mathematics, if you look at a problem and instantly know what to do then you are not learning. If the teacher tells you exactly what to do then you are not learning. Yet this is exactly what many people expect to happen in a mathematic class.
The biggest obstacle to learning is shutting down in the face of resistance. Unfortunately this is a very common reaction. As children we may yell “I don’t wanna” and go watch cartoons. Later we become more subtle about it. Instead of acting like a child, which at least has the virtue of honesty, we concoct self-serving rationalisations that enable us to keep being quitters, only without having to admit it to ourselves.
The key to such self-delusion is to always blame external forces when things do no go our way. It’s all someone else’s fault. There’s nothing we can do about it. In mathematics this comes in two main forms.
The first is to say: this is hard, I obviously don’t have the “math gene,” so I should just give up. This is associated with the notion that in mathematics you are supposed to know what to do immediately upon seeing a problem. This very harmful and inaccurate notion is unfortunately deeply ingrained in many people through many years of conditioning during their basic mathematics education.
The second is to say: this is hard, the teacher didn’t show me an example exactly like this that I could copy, so the teacher sucks. This is associated with the “monkey see, monkey do” teaching paradigm, which is again a very harmful notion that is unfortunately conditioned into many people throughout their early years of mathematics education.
In both of these cases students have found an excuse to give up that does not involve taking any responsibility of their own. They didn’t have to do anything hard, and nothing was their fault. Win, win.
Learning is about attitude more than aptitude. We are defined as learners by how we act in the face of adversity. When something is challenging, how do we react? If we see it as proof that we can’t do it, or that the teacher is poor, and therefore give up or try to cheat our way out of it, then we have ensured by our attitude that no learning will take place. Instead we should look at the challenge and say: ok, this is where learning begins. Let’s roll up our sleeves and see if we can figure this thing out. Let’s have the courage to try and fail and try again, because that is what learning looks like.