I write and say this to myself over and over again, but it’s always worth repeating: we cannot obsess over work that is slightly imperfect. While it is nice to think of alternate scenarios or instances where we should have improved, the reality is that learning is the process of transforming those things that I’ve done wrong to things I’ll do right the next time. It’s never fun in the moment, no, but in the long run you’ll be able to solidify the lesson.
The reason I revisit this so often is that I am frequently reminded of things I have done wrong as a student. It’s the natural way of things. If I knew all the material, I would be given credit for the class and wouldn’t have to go. Therefore, I’ll make many mistakes and incorrect assumptions as a student. The goal of each class is to slowly eradicate them.
That becomes the question, then. How can one know that they have learned what needs to be learned in a particular class? There are different ways to go about answering this question. Tests are the obvious one, of course. As a physics undergraduate, I take tests in all my classes where the goal is usually some kind of computation or manipulation of variables and data. Therefore, I’m used to the stresses of tests and the knowledge that my mark on a test becomes more or less a quick measure of how I’ve understood a particular segment of the class. And despite most of my teachers acknowledging that this is the case (and that having a bad test can reflect a myriad of issues not related to how well one understands the material), we still have the traditional tests. They aren’t going to go away for the time being, so that is why students will undoubtedly stress about their mistakes on these tests. (I can personally vouch for this. I’ll frequently spend a whole day after a test is completed thinking about where I might have made mistakes.)
The second way to answer the question is much more subtle, but I believe it is much more indicative of learning. Unfortunately, it also is the one that is difficult to measure. The way it works is that I’ll catch myself in another class using the material I used in a previous class. In my mind, this is the essence of learning. The prime example for me is my progression through mathematics. When I first entered CÉGEP, I had virtually no idea what limits, continuity, and derivatives were. My background knowledge concerning calculus was essentially zero, and so learning the subject was a whole different situation than what I was used to. When I first took my tests concerning how to identify limits and what an approximation for the tangent line to a curve was, my knowledge was mild at best. I still did well (particularly well, according to some people) on tests, but the foundation wasn’t built. I could do the assignments, but I don’t know if I would call myself a master at the material. In essence, I was learning, but I hadn’t learned the whole subject.
Now that I am removed from that time by two years, I have a whole different perspective on the knowledge I gained in those first calculus classes. Instead of being somewhat sure of the concepts, I feel like I can explain them with minimal help. Indeed, I may even be in the position to tutor some students who are at that stage in their lives, and it’s exciting to see how far I’ve come.
Additionally, the main way I see that I have truly learned the concepts from years ago is in how I apply them every day. I like to stop and marvel at times how I’ve gone from being tested on derivatives and limits to simply applying these ideas in more advanced problems. I remember first learning about the power rule for derivatives and how it seemed almost magical at the time, but now it is a routine occurrence. Derivatives and calculus has become a daily fixture in my life. Even the more complicated ideas like the power rule are now something I am expected to whip out of my toolkit at a moment’s notice. The fact that I can do this is a testament to the fact that I have learned what there was to learn in those first calculus classes.
Evidently, you’re probably thinking: that’s great, but there’s no way you can actually test this in a way that is practical. And unfortunately, you’re probably right. I don’t know how we can move away from traditional tests, but what I remind myself whenever I begin getting hard on myself for making stupid mistakes on a test of assignment is that the tests don’t matter to my long-term development. As long as I get through the course and work hard at understanding, I will learn the content. Having a better mark than someone else doesn’t make me better than them, and it certainly won’t matter in the end.
Being hard on yourself is something I see too many students (including myself) do, and I want us to acknowledge the fact that it is almost never as bad as we make it out to be. Sometimes, getting just good enough on a test is alright, and the world won’t end.