As a student, I know what it takes to get good grades. Essentially, you want to be able to reproduce the work that is taught in class during a test. You don’t need to be creative or original in your work. Rather, you simply need to understand the procedures and apply them (for the most part).
This is rather straightforward. After all, if you’ve worked through the homework in your class and have studied the material, it’s not too difficult to do fairly well in a given class. Questions become variations on a theme, so getting good grades is almost algorithmic.
However, one type of question in my classes that is more tricky to answer is the conceptual class. This means that the question requires some sort of explanation and reasoning, rather than a calculation. It might not seem like it, but this is by far the more difficult type of question, since it is so ambiguous. There are the usual issues of not knowing if you’re explained enough, but the real difficulty is that you can’t go through an equation to necessarily give you an answer. That’s why I (and I assume many others) dread conceptual questions.
Additionally, it’s simply not easy to conceptually understand a topic in mathematics or physics, instead of being able to reproduce it. Just because I can calculate the change in entropy for a certain physical situation does not mean I can explain why the entropy increases or decreases in that situation. In other words, I can reproduce the calculation, but I might not be able to really explain it.
You might guess that this makes me nervous. Indeed, when my goal is to get good grades in a class, conceptual questions are not what I usually want to see in a test. They are tricky and less straightforward than calculations, which means I will tend to make mistakes more frequently. As such, I try to avoid this type of question.
I think that you can also guess that this isn’t a good thing. If you’ve read anything from me, I’m sure you’ve gotten the impression that the one thing I want people to have is the conceptual understanding instead of only the computational ability. Of course, you’d be right, and that’s what I want to talk about today.
In my mind, conceptual understanding is critical1, but the problem in school is one of alignment. The reward systems in school don’t favour trying to ask conceptual questions, because they punish creative thinking in favour of being “right”. However, if the students never get to test their common sense and intuition about various subjects, why should we expect them to do well on a test with these kinds of questions?
One thing that I think everyone can agree on is that having a misconception about a subject is something we want to avoid. Put another way, we don’t want students to go through a subject with an incorrect view of a phenomenon, and then proceed to carry this incorrect mental picture with them for years later. Any teacher will tell you that they don’t want this to happen to their students. But the irony is that we do allow this by simply not asking enough conceptual questions to students!
The educational model in physics in particular isn’t set up for this kind of question. As such, we seem to ask fewer conceptual questions because they aren’t easily graded and take up time. The cost is that we let students make their own conclusions regarding the phenomena they learn about, and I am certain that students don’t get it right 100% of the time. Judging from my experience, it’s not even close. Consequently, we end up going through a course thinking that we know enough about the subject, only to be stumped by a conceptual question that either has us scratching our heads or confidently saying something that is incorrect.
The solution is obviously to tackle more conceptual questions when you are learning, but this isn’t as easy as it seems. While I think this is the answer, it’s not a practical suggestion at present, since it punishes students unfairly in terms of grades for attempting a question and being incorrect in their formulation. In my mind, this isn’t something that one needs to be tested on. Instead, conceptual understanding comes from years of engaging with the topic, but this lesson isn’t being taught when students have the mentality of “remember for the test, and then forget”. I know many of my friends who go through school with this mentality, and it’s something we need to work to discourage. Instead, I think conceptual questions need to be asked more, but not necessarily graded on. I’m thinking of a weekly question that gets students thinking about a topic more deeply. Personally, I will be trying to do this with my own learning. If I come across a conceptual question I cannot answer, I will make sure I find the answer so that I can explain it easily.
I think physics is one of the few subjects where you can really dance between the rigour of mathematics and the simple explanations of intuition. As such, I think it’s useful to not be married to the former approach only, and to be able to explain topics without simply resorting to the mathematics. I think you know that I’m by no means against using mathematics, but doing the computation can sometimes evade the more difficult part of explaining2.
Indeed, if you only want computational ability, than I would suggest we teach everyone how to program calculations into a computer so that we don’t have to keep on doing them by hand. ↩
Of course, this same idea can be applied to mathematics, though everything gets a bit more abstract. In mathematics, it’s the difference between saying you know something and can prove it, versus merely being able to compute it. ↩