Jeremy Côté


Reading a Solution

When you have a lot of homework, it’s awfully tempting to just look up the answers. After all, you’re only doing it because you want to get other homework done, right? And if you take the time to read through the solutions, it’s good enough. You aren’t just copying down answers. You’re following the work that is done.

While the above situation sounds good in theory, in practice it is a terrible way to try to learn. It’s easy enough to find solutions to mathematics and science problems online, but finding them obviously diminishes the value of the problems.

If we compare the learning that happens due to working through a problem and the learning the happens due to reading a solution, I’m sure our intuitions will be correct. Working through a problem is a much better use of our time, even though it isn’t particularly efficient.

We’ve all been there: gazing intensely at a problem, frustrated that the answer won’t present itself to us. Then, usually just a few centimetres away lies a device that can find the solution for us. Why struggle when you can get through the small hurdle and continue on the problem?

My answer: tests.

Sure, it is nice to be able to look up just a “hint” to help you complete the problem that has been frustrating you for the last half an hour. However, the issue is that the “hint” most likely gave away the crux of the problem. Rarely are problems created only to test your ability to calculate one thing. Instead, they’re usually made to tackle specific concepts and make sure a student can recognize and deal with them. By turning to hints and help every time those points of confusion are reached, you’re robbing yourself of the skill needed to come up with an insight during a test.

Let’s consider an even more extreme idea: only reading a complete solution to a problem instead of even attempting it. While I am certain you will understand the solution (as you should, since that’s the point of a well-written solution), your ability to have gotten to the answer without any help has not improved. Instead, you’re fooling yourself into understanding how to do a problem, when really you only understand someone else’s solution to a problem. Therefore, reading a complete solution will make you think that you understand everything, but it’s more likely that you don’t know how to do it on your own.

Still, these online resources are good for something. I use them to verify my answers when I am done working on a problem. I rarely do what I described in the preceding paragraphs, because I know that when I reach a point of difficulty on a test, I can’t just magically skip to the next line of my solution like I can do when reading a person’s full solution. That blank space needs to be overcome first, and making the effort to practice writing full solutions by yourself without help is the key to being able to solve problems on your own.

Don’t just read solutions. Get good at making them.