Memorization in Education
Educators have unrealistic views about memorization.
If you’re reading this as a student, think about any time a teacher spoke about their thoughts on memorization. Unless the point of the class was to memorize certain facts, I’m guessing the teacher did not love the idea of memorization. In fact, for those who teach subjects such as physics or mathematics, they might have gone on a rant about how memorization is a terrible thing to do and one should focus on understanding the material. They might tell you that it’s not a problem if you forget a small detail in a formula. You know the concepts, so you should be capable of working out the details if you ever forget them.
If this describes a teacher you’ve had, they weren’t being fair at all.
Before you start thinking that I see myself as apart from this issue, don’t worry, I’m just as culpable. I’ve given reasons quite close to what I wrote above to students, even though on reflection I know it’s not true.
It’s a seductive message. If you know your core concepts, you can work out anything you forget. Therefore, you don’t have to be a “memorization machine”. You can focus on deeper understanding, not on memorizing formulas. It’s the dream of every teacher. It indicates the students are engaged with the material, not on passing. What more could a teacher want?
The problem is that our educational system does not reward deep understanding. Sure, deeper understanding can be good for the student in the long-term, but there is no incentive present in the system. This creates a dilemma for the students. Is it worth investing the struggle and the effort for deeper understanding, or should they only focus on getting good grades?
“But wait,” you might protest. “Getting good grades in school requires the student to have a deep understanding of the subject.”
This argument is incorrect. A student that has a deep understanding of the subject might do well, but it’s by no means necessary for success. From personal experience, I can say that getting good grades in a class did not mean I had a deep understanding of the subject. It just meant I did well on the assignments and the tests, which is what the grade reflects.
This is why most students don’t have deep understanding as their primary objective. They are making a calculation, and coming up with the answer that the most important thing is to get good grades. Since a deep understanding isn’t necessary for success in a class, students won’t seek it out. I’m not saying that they don’t want to have a deeper understanding of a subject. It’s just that they won’t be sad if it doesn’t happen.
The world rewards good grades, so that’s what students have learned to chase. It means that if they don’t understand a concept, looking for a deeper explanation may not be the first thing they try. Instead, a student may opt for memorization, because it’s the most efficient way to achieve their goal. As teachers or tutors, we can’t blame them for that. They’re acting in their own best interest (at least, in the moment).
So what’s the solution? As usual, I have no clue, but I do have some suggestions. First, we need to accept that memorization is how students choose to study in some classes. That’s not going to stop until our grade-crazy system is changed. Instead, we should encourage students to look at our explanations and ask themselves which is easier to remember. If it’s easier for them to memorize the information, than I don’t think we should do anything about it. A deeper understanding of a subject should end up looking “obvious” to students, in the way that memorization is not. After all, a deep understanding creates a sense of cohesion that pure memorization cannot.
The other suggestion is to create questions that don’t fit the cookie-cutter mold. By asking students about the concepts in a different way than usual, they won’t be able to just bring up a formula. Questions that aren’t only plug-and-play will reward students for doing more than memorizing. Plus, it should translate to getting good grades.
It’s a long road from memorization to deeper understanding, and the external incentives aren’t there to encourage students. However, there are long-term benefits of a deeper understanding, so it’s important to convince students that memorizing isn’t the only way forward.
What Counts As Cheating?
This sounds like an easy question, but I think I have a bit of a different perspective on it.
In science and mathematics programs, it’s not too difficult to cheat. I’m not talking about cheating on tests or exams, but on assignments. That’s because most professors don’t write their own problems. Instead, they assign them from textbooks. The upside is obvious: they don’t have to spend time crafting new questions every semester. Unfortunately, the downside is that textbooks questions tend to be posted online. No matter how obscure the book is, there’s a good chance that someone has taken the time to post the answers.
This presents a dilemma for the student. On the one hand, the answers to the assignments are right there, waiting to be looked at. On the other hand, is looking at those answers considered cheating?
I understand those who take the perspective that it is cheating. After all, the student isn’t doing the work themselves. They are outsourcing it to someone else online. Because of this, it should count as cheating. I think this is a good line of reasoning, and it makes a compelling case as to why students who use online answers are cheating.
But, I still disagree with this assessment.
I think I have a more nuanced view of the problem. As in most things in life, the truth is that it depends on the situation. It’s easy to slap a declarative statement on any discussion, but it often hides the complexity of the situation. I think this is the case here, and I want to make an argument for when looking at the answers online shouldn’t be considered cheating.
This is how a typical assignment goes. The teacher gives it to the students, along with a due date. The students then work on it during that period, asking questions if necessary. Most of the questions get answered, but some might not. The assignment is handed in, and is handed back perhaps two weeks later. By that time, the student has forgotten the content of the assignment, and going over corrections isn’t the most compelling thing (especially since there is new homework to do).
But what if instead the student works through the homework, trying all of the questions, and then looks online to check their work? By doing this, they can check their line of reasoning and make the necessary corrections to their argument before handing in the assignment.
I think this method has several benefits. First, it gives the student quick feedback on their work. Instead of waiting weeks before an assignment is handed back, they can check their work as they do it. This keeps the problem fresh in the student’s mind. Plus, it’s more motivating to do corrections during the time you’re working on an assignment than later on when you have other things to do.
Second, checking the answers online encourages deeper thinking about a problem. How so? Suppose you work through a problem, and think that it’s straightforward. You then compare your answer to one online, and you see that there’s a whole lot more to the question than you realized. This makes you stop and say, “Oh wait, I forgot about this particular aspect.” The result is that you go back and figure out what you did wrong. If you never checked your work, you would only see the mistake you made a few weeks later. By that time, you probably won’t put reworking through the problem high on your list of priorities. That’s why it’s worth checking your answers while you write them. It gives you a chance to dig deeper on a problem that you went through too quickly.
Third, checking your answers online helps you avoid losing marks. Yes, I know this is controversial. If you’re getting help online, did you really “earn” it? My answer to this is “yes”. That’s because I’m thinking about what the main purpose of school is supposed to be: to learn. Not to get things on the first try, not to produce the best work on your own, but to become competent in whatever subject you’re studying.
Tell me who you would consider to be “learning” more. On the one hand, you have a student who does their homework, doesn’t check their answers online, and gets decent grades. On the other hand, you have someone who does the questions on their own, then checks online and makes the appropriate changes before submitting their work, and gets great grades. I would say that the person who consults the answers online is doing more work. Not only do they try the problems themselves, they then do the extra work of making sure their answers are good and doing the necessary corrections. By the end of the assignment, I would say this person has thought more about the questions than the person who does the work themselves and submits it as-is.
Sure, the second student consulted the answers online. But in the grand scheme of things, I don’t think this should be a bad thing. The point is that they are invested enough in their understanding (and success) that they took the extra time to look at the answers and fix their own. By the time exams roll around, I would predict that this kind of student has had more experience with the content than the other person. This is why I don’t think shooting for better marks is a bad thing. The marks help you as a student, and it’s not the point of learning anyway.
Like anything, this perspective has some caveats. You can absolutely find yourself in a situation where you forego even trying the assignment because you looked at the answers online. As you can imagine, this isn’t in the spirit of what I meant. If you’re going straight to the answers online, you’re not learning too much (except how to find the answers you need). Likewise, if you finish your problems and “check” online by just copying the answers you find, that’s of limited use as well. The best way to do it is to slowly look at the answers online, and make sure they match what you have. Anytime something is different, don’t keep on reading the answer. Go back to your own work and see if you can spot an error in reasoning.
The reason I think my perspective here is a bit controversial is because some people might complain that you don’t end up “earning” your grades. I can understand that viewpoint. However, if I’m completely honest, I don’t think it matters in the long run. In my eyes, grades are a tool to get you where you want to be in your education. They aren’t really an indicator of learning. It’s unfortunate, but that’s the way it is. Therefore, I don’t put too much stock in my grades, preferring to see if I can explain the concepts I learn.
The ugly truth is that school doesn’t reward you for trying your best and learning through growth. The educational system rewards those who can perform well on the first try, which is why I actually think using the answers you find online isn’t cheating, but a good use of your time. Of course, you need to do this responsibly, but if you do the work first, I don’t think it’s a bad thing to check your work online.
Balance As A Student
As a student, there’s no shortage of things I could be doing to help my academic career. I could do some side research, I could read more about my field, I could network with other researchers, I could study more for my upcoming exams, I could work through another textbook, I could volunteer for any number of academic events, and the list goes on. There are so many things I could be doing to advance my career and invest in my future that I could be busy every day for the rest of my life. If I wanted to, I could fill my schedule up with these activities and never be done.
Let’s take a simple example: practice problems. If I wanted to do really well in my classes, I could do extra problems every night in order to be prepared for my exam. I wouldn’t get “rewarded” for doing this, except that my exam scores would probably be higher. I’ve done this before an exam, but I could do this throughout the whole semester in order to improve.
I won’t do this though. In fact, I do almost none of the things in the list I gave above. Even if those items would advance my career in academia, I forget about them. Why? Because if you don’t achieve balance in your life first, you won’t be able to do anything else.
Balance is more than just an athletic skill
The problem with that list is that it’s incredibly seductive. If I do just a few more things, I will be giving myself a much better chance at fulfilling my goals in the future. This is the thinking that leads to the slippery slope of spending too much time trying to “advance” your career as either a student or a researcher.
The truth is that your pursuit isn’t going to be fun all the time. There will be times when you’re frustrated, exhausted, and maybe even sick of your work. But if all you do is think about your work, you don’t have an outlet to ponder other things. You then end up telling yourself that you should be better and more disciplined, before soldiering through.
This may sound like the way to go, but it isn’t. Pushing through when things aren’t going your way is a good skill to have, but you can’t do it all the time. At some point, you need time to recharge. This is why balance in your life as a student is so important. You can’t just keep your focus on academics all the time, or else you will risk burnout. And make no mistake, burnout doesn’t mean you take an extra bit of time to recover. Burnout can be catastrophic, killing your desire to do the activity that you once enjoyed. I think it’s safe to say that none of us want that.
As a student, I feel this pull to do more all the time. Even now, when I’m still on summer break, I feel like I should take some time to start reading ahead and working through the material. My reasoning is that this will lead to better results in my courses, so it seems like a good investment. However, I’ve been fighting this urge for the last few weeks, because I know that I will have plenty of work to do as soon as the semester starts. Do I really want to inundate myself now?
The answer is clear: I want to enjoy my studies, not have them feel like a burden.
So what’s the fix? How can we avoid burnout and the urge to keep on working all the time?
There are two things that work for me. The first is to establish clear boundaries, and the second is to find side projects or hobbies that you enjoy doing.
The most important thing to do in order to protect your personal time from your work time as a student is to create boundaries. The clearer, the better. The goal here is to make sure there’s no question about whether it’s “work” time or “personal” time.
You might think this sounds simple, but I’m serious. For example, I know many students who say they are going to do homework in the evening. What this ends up turning into is a marathon session in which they work a little bit on homework while also doing other things throughout the whole night. By midnight, they find themselves still working on their homework, with no end in sight. This happens because homework tends to take longer than one session. But, if you aren’t careful, it can end up taking over your whole life outside of class.
I get it, homework is important. You don’t have to make a sale’s pitch to me about the importance of doing the homework in a class. That being said, I have strict boundaries on my time with respect to homework.
Here’s what that looks like for me. When I get home, I eat dinner. After that, I start doing homework, and I’ll work until 20:00. Once 20:00 rolls around, I stop working. I don’t say, “Oh, I’m almost done this problem. I’ll just do a bit more.” No, when it’s 18:00, I stop. I used to be bad at this, but now I’m at the point where I won’t go further.
What I’ve done here is set a clear boundary. There’s no question as to when it is “homework time” and when it is “relaxing time”. The boundary is at 20:00, and I stick to it. By doing this, I’ve made sure that I never do school work beyond that point. This is even true when preparing for tests and exams.
Why don’t I make an exception? The reason is that I find that people tend to work within their timelines. Give someone a week to do a project, and most will take that full week. Give them the same project but with only half the time, and chances are (assuming it’s reasonable) they will still get the project done on time. This happens because we fill our time within the constraints we are given. If I let myself work past 20:00, you bet I would end up working until later. But, I know two things. First, if I set myself some reasonable, sharp boundaries, I can get my work done. Second, I want to be healthy and prioritize other aspects of my life too. In order to do this, I need to acknowledge that my studies aren’t everything.
I also want to note that this isn’t my only boundary. I also have one in the morning, which is the period when I run. Therefore, I never do homework in the morning before class. I don’t finish assignments, and I don’t cram in some extra studying. Even if it’s the final exam and I know my classmates are spending their morning studying, I’ll be out on my run, because it’s what I do.
Setting boundaries is important, but it’s also crucial to plan ahead. What I mean by this is that you still need to get your work done. If you have projects or homework with deadlines, you need to work with those. Yes, sometimes those deadlines can be inconvenient. As such, you should have a system in place to accommodate that. For myself, this means doing homework in the evening, and also in-between classes or in the late afternoon. Despite my sharp 20:00 cut-off, I still spend a lot of time doing homework. It’s just that I make sure there’s an end in sight. If I leave it open-ended, I will naturally go past my usual time.
The worst thing you can do is try to get things done whenever you can fit them in. I’m not saying this can’t work, but it encourages you to work more than you should. If something isn’t done, it’s easy to tell yourself that you will spend another hour on it instead of figuring out a way to finish within the timeframe. By establishing clear boundaries and planning how you will accomplish things ahead of time, you’re ensuring that you won’t let your academic life infiltrate the rest of your life.
Take things in chunks
Related to the idea of planning ahead from the above section is to take things in chunks. What I mean by this is simple. If you have a week to do something, please don’t wait until a day before the deadline to start working on it. It sounds like a bad idea no matter how you say it. This is why many of my classmates end up having to work through the night in order to do homework. It’s not that they had to do that. It’s that they didn’t plan ahead to finish it during reasonable hours.
I want to take a moment here to acknowledge that not everyone is in the same situation that I’m in. I have the luxury of coming home to prepared meals and only having to worry about my school work. I don’t need to work a job on the side, and I don’t need to worry about a million other tedious tasks. I can focus on my homework from the moment I’m done dinner to the time before I go to bed. As such, I realize that I’m very lucky.
That’s why I don’t think it’s realistic to expect for everyone to take up my specific schedule and boundaries. Rather, it should be something everyone reflects about. Am I planning ahead of time? Am I establishing clear boundaries? These questions should be asked again and again.
Instead of waiting until a few days out to finish a project or homework, start it right away. Don’t wait until you’re pushed up against a deadline, because that’s when your boundaries start to break down (out of necessity). Instead, if you do a bit every single day, it becomes a lot easier to finish things on time and without worry.
In fact, I’m at the point where I’m done a lot of my homework way before it’s due. This may seem like overkill, but I like doing this because it lets me relax before a deadline comes. By being done super early, I can be comfortable with the upcoming deadline. If it turns out I need to make a change in my work, I can do that without a hassle. Plus, being done early lets me review my work so I can make it even better. For me, it’s the best scenario.
The point here is that you don’t want to take projects or homework as a huge commitment that you leave until the last minute to do. Instead, you want to break it up into chunks, because this lets you deal with small, manageable parts. Plus, it means you don’t have to worry about deadlines as much. The result is that the boundaries you have settled on won’t be tested, because you will be done your work on time.
Finding a hobby
Finally, if you want to achieve balance between your academic life and the rest of your life, it helps to have something to balance your studies with. This is where having a hobby comes in. The goal of a hobby is to let you relax and disconnect from your academic life. You shouldn’t be worrying about your projects and commitments during the time you dedicate to your hobby. Your hobby is the chance for you to enjoy yourself, without any expectations and pressure associated with it.
For example, my main hobby is running. I’ve been running for years now, and it has been a fantastic way to disconnect from my homework, upcoming exams, and any other stress. In particular, I enjoy that running is a physical activity which is completely different from my studies in theoretical physics and mathematics. I think this is a good way to go when choosing a hobby. Find something that is different than your focus in academia, since it will make the boundaries between the two clear. If you have a hobby that’s too close to your academic life, it could lead to thinking about your work all the time.
Of course, you can still make it work. Another hobby I have is writing here on my site. I write about a bunch of topics related to mathematics, physics, and academia, which is about as connected as can be to my education. Still, I make it work because writing is a different kind of activity than going through an intricate calculation. That being said, I think this arrangement works because my main hobby of running is so different from my other interests that it helps balance things out.
The other great thing about finding a hobby is that it lets you practice setting clear boundaries. If you commit to going on a run every morning like I do, there’s no possibility for doing homework or trying to fit in extra work time. Instead, you learn to plan ahead and make sure that every activity has its own time slot. This prevents your academic life from “spilling” into every part of your life.
Related to this is the fact that having multiple interests lets you “forget” about all of your commitments. When I’m out on a workout during my run, I don’t have the capacity to think about my upcoming deadlines or exams. I can only think of the effort I’m giving right now to move fast. I get to live in the moment, and forget about the rest. This feeling is quite liberating, and it doesn’t have to come from running. It only requires you to find an activity that demands your focus. Through the act of focusing, you learn to give yourself a break from all the rest.
A hobby also gives you something else to look forward to in your day. It gives you a way to look at the day as a “success”, even if other things go wrong. By running each morning, I get to start my day at school feeling that, even if everything else goes wrong, at least I have my run to be happy with. That can’t be taken away from me. In this way, my hobby lets me find other meaning in my life. Of course, this can also be found through family and friendships, but I wanted to point out that a hobby is a great way to find success as well. This doesn’t mean you have to turn a hobby into a “professional” success, but it means you can set yourself small goals and be proud as you achieve them.
Achieving balance between your academic work and the rest of your life isn’t easy. It’s an unstable equilibrium, where any small nudge can send the balance out of whack. In order to combat this, you need to be vigilant all the time about how you’re spending your time. Letting yourself drift through your life is a recipe for ruining the balance (if there was any to begin with).
Instead, you want to erect clear boundaries between different aspects of your life. Don’t let yourself be ruled by your commitments. Establish a plan and stick to it. This is helped by doing tasks in smaller chunks, since you won’t be in “panic mode” to get things done. Finally, it’s easier to balance your life when you have a hobby or some other pursuit to focus on. Ideally, it’s something outside of your academic interests, but if you’re creative you can still stick to your interests.
In the end, the goal I have for you, the reader, is to be happy with the way you spend your time. It might seem reasonable to “supercharge” your career by spending all of your time on it, but I would argue that this is a recipe for burnout. Sure, if we were robots that never needed different stimuli, we could do the same thing every day with zero novelty. However, we are human, and novelty is what we crave. I know as well as anyone else that it’s important to focus one’s attention if you want to succeed (whatever your definition of success is), but we need some novelty. This is why it’s important to find balance, or else you will quickly become disenchanted by your academic career. And, if you’re anything like me, this is something you don’t want. We all got into academia because we loved learning and asking questions. It would be unfortunate to leave because we did too much of it.
If you want to be in academia (long past being a student) for a long time without burning out, my suggestion is to find a way to achieve balance as quickly as possible. At the risk of sounding melodramatic, forgetting about this is risking your future health.
The Grit to Push Through
If you ask someone what the point of a mathematics or science degree is, chances are they will tell you a tale about becoming a great problem-solver and seeing the world through new eyes. This has become a sort of battle cry for many who want to encourage people to learn about science and mathematics. The problem-solving skills you develop during these degrees allows you to be valuable in a wide range of careers later on.
While this is true, I would argue that it’s not one of the main skills you learn as a student. Instead, the skill you develop is persistence.
Let me tell you a story. When I was taking a quantum mechanics class, the professor assigned homework from a textbook. A few of the problems were marked as “very difficult”. When I began working on them, I knew I was in for a long calculation. It’s not that the problem was difficult so much as it was time-consuming. I even knew what I needed to do, but it just took forever (and it wasn’t clear where to start).
Multiple times, I felt like giving up. I wanted to find a shortcut, some way to make this less painful to do. If I was being rational, I could have decided that my time was being wasted on such a problem. I would only lose a few points, so it wouldn’t be the end of the world.
Of course, I have the “lovely” problem that I can’t hand in work that isn’t completed to the best of my ability, so skipping the question because it was too tedious wasn’t an option. Even with the hours ticking by, I gritted my teeth and finished the question.
Was it worth the extra time to get a few more points? Not really. The tedious part was a bunch of algebra, which also meant that the problem wasn’t any more illuminating when I finished. In the moment, it felt like a thankless task. However, the benefit came later. What I learned from doing a problem like this is that I can get through it with perseverance. If I set my mind to it, I can get a problem done. This is what I believe to be one of the best skills I’ve acquired through my science and mathematics degrees. Being unreasonable and pushing through the tedium and difficult parts of a problem to see it to the end is important. If not, you will tend to give up when you should push through.
Having the grit to push through is a skill that’s much more applicable than to just mathematics and science. Grit is an essential part of doing work that is important to us. Whether it’s writing, drawing, dancing, practicing a sport, making music, working on a business, or doing science and mathematics, grit is what helps us make breakthroughs when everyone else has given up. Plus, while it can be argued that others have more skill or talents from genetics or the environment, you control your decision to continue working when it seems useless.
This idea of developing grit during a science or mathematics degree is also why I don’t like having tests with time limits. Think about it. If you establish a time limit, you’re telling students to give up after this point. But isn’t it more impressive if the student keeps on working until they succeed? Sure, it might mean they have more trouble than others, but I would want to have that person on my team before the person that gives up after a few minutes.
One might object and say that people would all just stay until they get everything right, so the class average would be 100 (barring any mistakes). I don’t think this would be true, since my experience is that most students tend to give up quickly when they don’t know what to do. They don’t want to sit and think when they are stuck.
The point I want to emphasize here is that problem-solving skills are great, but I think developing grit is a skill that isn’t recognized as much as it should be. Of course, I’m not saying that we should persevere to the point of delusion, but being able to push past the initial point of discomfort is something we should all want to do. That’s why I think it’s one of the most important benefits of doing a science or mathematics degree, since you’re frequently put in the position of struggle. You learn that being stuck isn’t a bad thing, and is often temporary. You learn that giving up shouldn’t be your initial instinct, but one that is only considered after all other options are exhausted.
I know that this will be something I carry with me throughout my life, even if I don’t stay within the areas of science and mathematics forever. I’m thankful for learning this skill no matter where life takes me.