Try to Actually Learn
February 28, 2022
I've met too many students whose primary goal is to Get Good Grades rather than Actually Learn. There are plenty of reasons for this: not enough time, the importance of grades, fear of failure, etc. But if you're reading this and you're in school, then I want to discourage you from having this attitude. Instead, I suggest that you try to Actually Learn.
What does it mean to "Actually Learn"? It's when you, well, actually learn. It doesn't necessarily correlate with your grades, and it certainly has nothing to do with how you stack up against your peers. Instead, it refers to how much your understanding of the material has truly improved. It doesn't even have to be strictly from the course material: if the instructor is teaching advanced calculus, but your understanding of elementary algebra improves, then you have Actually Learned.
Actually Learning usually doesn't involve tons of memorization, or calculations (though they have their role). Instead, it should feel mentally stimulating and satisfying. Pieces of new information should fit together with information you already knew. Your knowledge and abilities should expand in a lasting way, after you've taken the final exam. Of course, vague notions like this aren't easy to measure or completely define, but I think you get the point. Actually Learning typically occurs when the learning process feels natural, not forced.
It's easy to fool yourself into thinking that, because you got an A in some course, you've Actually Learned something. While it's true that you probably Actually Learned something, it's unlikely that you've Actually Learned all of the course material. But that's okay, because Actually Learning an entire course's worth of material requires repeated exposure.  And remember, how much you succeed at Actually Learning depends on your improvement in understanding, which is independent of whatever the course covers. Your final grade may or may not reflect this improvement, because your graders don't know where you started.
The problem I've witnessed is that many students leave a course without Actually Learning much at all. Here's a common situation:
- A student looks at a homework problem and doesn't know what to do.
- They come to my office hours, transcribe whatever I say, and submit that as their solution. (Or worse, they copy their friend's solution. Or even worse, they search online.)
- The grader (somewhat reluctantly) gives them a decent grade, since they did manage to convey the gist of the correct solution.
- So for their next homework, the student goes straight to office hours, and the cycle continues.
If they beat the average on a few exams by a sufficiently large amount (correctly answering 80% of questions often suffices), then they'll leave the course with an A. But as far as I can tell, it's possible that this "A" student didn't Actually Learn very much. In fact, Ken Bain describes a notable example in What the Best Colleges Teachers Do (which I reviewed here):
After the term was over, the two physicists gave their examination once more and discovered that the course had made comparatively small changes in the way students thought. Even many "A" students continued to think like Aristotle rather than like Newton. They had memorized formulae and learned to plug the right numbers into them, but they did not change their basic conceptions... Perhaps because they were focused on grades rather than on understanding the physical universe, they didn't care enough to grapple with their own ideas and build new paradigms of reality.
But who cares if the student doesn't Actually Learn, right? The student might think, "Nothing my professors teach me will Actually Help my career or my life, so why should I 'Actually Learn' or whatever? If I need to know something someday, then I'll learn it in my own time. For now, my primary goal is to Get Good Grades, because that's Actually Useful (and measurable), unlike Actually Learning. Besides, it's not my fault that nobody, including the professor, Actually Cares about anything that happens in the class. Who are you to tell me what I should Actually Do?"
This hypothetical student is rather snarky, but they make some good points. I don't know everyone's situation, background, and goals, so I can't make any blanket recommendations. Here's the thing though: I believe that in most cases, it's much better to focus on Actually Learning than Getting Good Grades. And by "better," I mean that you'll learn more, and your grades will improve. 
To see what I mean, let's consider a hypothetical student named John. (I've seen many students like John.) He's sitting in office hours, and after receiving a bunch of hints from the teaching assistant (TA), he finally writes a solution. But this solution is, as described earlier, basically a transcription of everything the TA said. It's missing details, and in some parts, the logic is out of order. He asks the TA, "Is this correct?" and the TA doesn't know what to say. On the one hand, it does contain the right ideas since, after all, it's what the TA said. On the other hand, the presentation is atrocious, it's not thoroughly written, and it isn't even John's own work.
The TA points out a few areas to improve, and John immediately asks for elaboration. It sounds like he's genuinely curious, and close to understanding the solution, but he actually has no idea what's happening. The TA senses this, says a few words, and walks away to help another student. John scribbles those words down, as if they were the secrets of the universe. Then he waits a few minutes out of politeness (and to give the impression that he's Actually Trying), and asks the TA to check his "work" again.
This debugging process repeats itself for a while. John "runs his code" by asking the TA if his solution is correct, and the TA responds by pointing out a "bug." After 50 minutes, maybe there aren't any bugs left, or the TA has gotten tired of being treated like a debugger. Regardless, office hours are finally over, and the homework is due tonight, so the TA is relieved. But based on the questions that John has (and hasn't) been asking, the TA suspects that John hasn't Actually Learned anything.
Again, I've seen many students (from different demographics) exhibit John-like behavior to various degrees, and I can't really blame them. They might face a host of challenges like mental illness and family pressures. Their mathematical background, established well before college, often has fundamental gaps. Some of them simply don't like the course material. And maybe the teaching staff, including myself, aren't that helpful. But the student has likely been pressured into taking this class, so they're not interested in Actually Learning. They just want to survive.
Yet even with all of these factors working against John, I believe that a shift in his attitude from "Treat the TA like a debugger" (in order to Get Good Grades) to "Try to Actually Learn" would substantially improve his situation. Here are a few things he can do:
- Mentally process the hints that the TA gave, and ideally, refrain from asking the TA anything for at least 12 hours. Use this time to apply the hints to the problem statement.
- Construct a small example for the problem, and try to solve it. This might illuminate why the TA's hints could be useful. At the very least, hopefully it shows why the problem has been difficult to solve.
- Recall how similar problems were solved in lectures, recitation, and previous homework assignments. Perhaps the solution to this problem uses a similar strategy.
- Read the textbook(s) and watch related videos. It can't hurt John to strengthen his understanding of the material, even if it doesn't seem directly relevant to the problem he's trying to solve.
- Work with someone else who's also trying to Actually Learn, and exchange ideas with them. If the group figures out the solution, each member should write it down independently.
I'm not suggesting that all of this would be easy for John. While it might not require a lot more time (since he's no longer idly sitting in office hours), it certainly requires more mental effort. So he might worry that in the worst case, he spends this effort on Actually Learning, doesn't learn anything, and his grades get worse. In response to this worry, I'd tell him that there's a whole bunch of literature on growth mindset that he might find inspiring. Also, the TA can probably tell that he's been trying to Actually Learn, and this motivates them to help him achieve this goal. Finally, grades probably don't matter as much as John thinks they do. In my opinion, it's much better to Actually Learn and get a B-, then fake and fumble your way to a B+. 
Let's say John goes for it, and tries all of the things listed above in an attempt to Actually Learn. Right away, the whole office hours experience would be less frustrating for everyone. (In fact, John wouldn't even need to attend office hours quite as much, because he wouldn't feel compelled to query the TA every 5 minutes.) Moreover, I'm pretty sure his grades would improve because, although grading is a messy topic, I think they generally scale with true mastery of the material. Most importantly, by doing these things, John is more likely to Actually Learn something, and that should feel inherently rewarding.
 In this post, I'll mostly be thinking about the topic of algorithms (see here, here). I've been exposed to the material for years (as a student, teaching assistant, and instructor), and each time I see it, I still feel like I have a lot to Actually Learn. (See spaced repetition, Feynman Technique.)
 In some cases, it really is a lot easier to Get Good Grades than to Actually Learn. Maybe you have access to all of the answers, so Getting Good Grades is a breeze. Or maybe the material is extremely boring/useless/difficult, which makes Actual Learning a nightmare. But I don't think these cases constitute a majority of situations. Besides, I'm just trying to help; you don't have to Actually Listen!
 For pretty much any topic, there are plenty of non-grade-related reasons to study it, and I think a good instructor should provide these reasons. For the topic of algorithms, here are a few reasons that I've given.