# Misaligned Incentives

There’s a saying among students regarding preparing for an exam. In short, it goes like this: *Study a lot before the test, and then you can forget most of what you know.*

There’s a saying among students regarding preparing for an exam. In short, it goes like this: *Study a lot before the test, and then you can forget most of what you know.*

Everyone solves problems differently. Some like to work directly with the mathematics head on, while others prefer to have a more intuitive approach. This includes studying simpler cases of a problem, or looking at examples in order to really understand what’s happening. These are all valid approaches, but the point I want to highlight is that these are all *strategies*. There’s a certain method to tackling a problem. It’s not that you can’t solve a problem through trial and error, but if you want to solve more problems more quickly, your best bet is to figure out a strategy.

Why is it that some students will pick up new subjects in mathematics and science relatively easily, while others will struggle for weeks on end getting just the simple concepts down? As a tutor, I see this all the time. In fact, I would almost wager to say that *most* students I work with aren’t actually having difficulty with the topic they say they don’t understand. So what’s going on?

I’m currently studying both mathematics and physics in university, and I have to admit that it can be difficult to straddle the line between the two. Both are similar, yet demand different mindsets in terms of how to think about tackling a problem and actually coming up with a solution. In mathematics, not only is the right answer desirable. Every step along the way should be rigourously justified. That’s because the conclusion that one wants to get to rests on the arguments that come beforehand. Without those arguments, you don’t have anything. This is why mathematics classes require students to create proofs that carefully apply definitions. I’m not saying that there isn’t any playfulness involved, but when it comes down to making an argument, the clearer the supporting propositions, the easier it is for others to become convinced of the truth of your claim.