No Final Exam
Here’s a thought: what if the class you were in had no final exam?
I know, it seems preposterous. Whenever one thinks of a mathematics or science course, a final exam is a no-brainer. It’s never a surprise to the students that your class will have a final exam, because that’s the tradition. Mathematics classes have final exams as a rule. It’s the way that students show that they’ve understood the material throughout the semester.
But is it necessary?
Goals of a final exam
There are several goals of a final exam, both implicit and explicit ones. On the explicit side, the final exam is there to test a student on their knowledge of everything they learned in a semester. It serves the purpose of verifying that a student has a good general knowledge of the subject. Plus, the nature of the final exam ensures that students aren’t just copying answers online, and can do the work themselves.
On the implicit side, the exam’s format and time limit makes students answer the question, “Can they perform under pressure?” Also, the fact that students have multiple exams bunched up within a week or two only increases stress.
The result of this is that the final exam period is a stressful time for students. They have to perform their best on multiple tests (often concerning different subject matter) in a small time range. I think we can all agree that this isn’t the most conducive environment to student performance. Yet, this is the most important part of the semester for students! This assymmetry between the importance of the exams and the fact that everything is bunched up has never made sense to me. Shouldn’t we be promoting student performance, rather than having them go through such a stressful time?
To give a personal example, I had to write six final exams in the span of seven days. That’s already a lot of exams in a short period, but it gets worse. During that period, I had three days off. This meant that I wrote six exams in four (non-consecutive) days. I can assure you that it wasn’t the most enjoyable time in the world.
Each semester that passes makes me more and more convinced that final exams aren’t worth it. They create an artificial environment that wouldn’t ever be present elsewhere, and the stress on students is enormous. It’s not worth the burden to students’ mental health to give “one last go” at studying before the semester is over. This is without even mentioning the fact that there are other assignments and projects that are due during an exam period, creating more work for the students to manage. It creates what I call the “Big Squeeze”, a period in which students and teachers have a huge workload just before everything becomes calm again. I want to argue that we can do without such an end to the semester, without compromising the goals of a course.
It’s evident that we cannot just remove the final exam and be done with it. Classes will become too easy, due to the way they are structured at the moment. This is why I would like to see more instances of a much different philosophy to a class.
First, remove the final exam. It creates unneeded stress on the students, who have a lot on their plates already. Instead, I would like to see the emphasis of grades be put on the assignments.
Yes, you heard me right. If I had my way, I would create a class where almost the entire grade was based on assignments. Before, you shake your head and say that this is impossible, hear me out. The reason that most people who read this will think this is unreasonable is because solutions to problems are so easy to find online. Type in part of the question, and one can find the answer to any question. This is not good, since it means the student could get a great grade in the class without being able to do anything on their own. So what’s the solution?
You might know where I’m going with this. The answer is for teacher to create their own problems. If teachers want students to work through their assignments and not copy the solutions online, making up the problems is the best bet. There are two reasons why this is useful. For one, teachers can ensure that they’re getting students to practice the exact topics that think think is important. Second, since they created the problems, they know that the students had to work at solving these problems without only copying.
I know, it’s long and difficult work to create your own problems. It’s time-consuming, and isn’t a high priority compared to the million other things you have to do. Becoming a problem-designer isn’t what teachers want to do. But, I want to argue that this is the path forward if we want to eliminate final exams.
Also, keep in mind that teachers don’t have to design as many assignments. For example, they could give a few “regular” assignments whose purpose is to get students to practice applying the concepts that they learned in class. Then, they could create a few larger assignments that form the backbone of the course, where students have to dig deep and think about the concepts. You don’t need a lot of these in a course. A few will do the trick. Teachers can give these assignments more weight, and get rid of a final exam.
Furthermore, consider the material that teachers put on their final exams. Chances are, the material isn’t complicated. In fact, it deals with the more elementary concepts that were taught in class. Why? Because we know that students are stressed, and the time limit doesn’t help. As such, the questions are in general easier. But with assignments, teachers can create many more challenging questions that force students to pause and ponder. They won’t have to worry about a deadline, because they will have ample time to think about the questions and answer them. In this sense, it’s a win for both the students (who aren’t as stressed out) and the teacher (who gets to ask deeper questions).
Final exams are a sort of certification at this point. They declare that a student is good enough to pass a course. But the implementation of final exams isn’t so great. The fact that students have to deal with multiple final exams in a short period of time only increases stress. This isn’t conducive to performance. Instead, it encourages students to adopt habits that create exhaustion and that aren’t aligned with learning. The focus is all about getting “past” one exam in order to prepare for the next. I think we can all agree that we can do better. Moving from a final exam type of course to one that is based on assignments could be that different format which helps students learn more, without as much stress1.
Of course, student’s might get stressed out about more work in the semester, but I think that this would be an acceptable tradeoff for no final exam. ↩
Patting Yourself On The Back
As a student or an academic, chances are you have a lot of work to do. Whether that is homework, studying for exams, preparing a presentation, writing a paper, doing research, or teaching, there is a lot that is asked of you. Often, the weeks seem like undulating waves, with regular spikes in work followed by brief periods of respite. This can lead to an unhealthy lifestyle if you are not careful with how you tackle your work.
Here is a question: when you finish some work, do you move right on to the next item on your list, or do you take a break? My bet is on the former. It’s easy as an academic to think that the only way to combat that never-ending list is to take as many bites out of it as you can. After all, if you could just get a bit more time now, you will get to relax later. This is an enticing dream, and we tell ourselves this over and over again.
The issue is not the working itself. Rather, it’s the tendency to forget about all we have done and immediately move on to the next thing. As a student, the steady influx of homework and tests is enough to make you never take a break. If you stop, you quickly become inundated with work, so there is always pressure to keep on working and never stop to appreciate what you’ve done.
When is the last time you thought to yourself, “Wow, I’ve come a long way since I first started learning this topic/area”? On the other hand, when is the last time you thought to yourself, “Alright, I got this piece of homework done. What’s next?” The sad reality is that we do not appreciate our past work when we are on the steady treadmill of completing something new. When there is barely a break between tasks, it’s difficult to spend time appreciating what you accomplished when it can be spent getting through the next thing.
I often find myself slipping into this tendency. At first, it’s nothing major. I start doing back-to-back assignments without a break, or I work on homework throughout the whole weekend and ignore everything else. But if the work keeps piling on, I quickly become fatigued, and just start going through the motions. Instead of focusing on doing my best work, I am trying not to fall off the treadmill. It’s at this point that I try to take a step back and appreciate what I have done.
Related to this is the idea of feeling knowledgeable about a subject. As a student, I am learning a bunch of new concepts in physics and mathematics. Because they are new, there is an inherent tension and struggle in learning. I do not know everything beforehand, which means throughout the semester I feel more clueless than knowledgeable. Of course, this is not a bad thing, because it signals that you are growing and expanding your intellectual boundaries. However, the downside is that, well, you start feeling like you do not know much. This is only exacerbated by moving quickly from one topic to the next, which means you barely have time to appreciate your newly-acquired knowledge before you have to struggle again.
I am not blaming schools or the curriculum here. Rather, I am trying to point out that the environment in which we work as students is not designed for you to take stock of what you learned and how you have grown. It’s kind of like climbing a mountain while only being able to look right in front of you at your feet. You can get to the top, but when you are there you cannot take in the wonderful landscape. In the same way, moving on from one thing to the next can be just as frustrating as a student. The difficulty is that we often do not talk about this. Instead, we take it as a given that students should move on from one thing to the next, implicitly agreeing with a bad attitude towards work.
So how can we go about fixing this? Well, I don’t think there is something we do to “fix” it. The issue is baked deep within the bones of our educational system, which means it’s unlikely that we will change how the system works. However, that does not mean we cannot each take steps in our own lives to fight against this tendency to always work on the next thing.
My first suggestion is to institute breaks in your work. Have you just slogged through a long assignment? Then take a break and celebrate. I do not mean throw a party. Rather, go take a walk, meet with friends, play a sport, or go enjoy one of your hobbies. The point here is to force yourself to take breaks in which you can celebrate your work. This will not magically make you better at what you do, but what it will provide is a way to stop feeling like you are on a never-ending treadmill. I am warning you in advance that this is difficult. You will feel the pull to just get started on the next thing, and it will be up to you whether to follow through on it. The first (and best) step to appreciating what you have done is to institute breaks.
To address the tendency to forget all of your achievements and what you learned, my second suggestion is to teach what you know. When you are in class and are struggling to learn a new concept, it’s easy to think you do not know much. However, if you then turn around and start helping younger students (through teaching/tutoring, or just by giving presentations), you will realize that you know quite a bit. It’s just that you did not place yourself in a situation in which this was clear.
I cannot stress enough how this changes the game in terms of making you appreciate how far you have come. When your sights are always on the future and learning things that you do not know, it’s easy to think that you are not that great. But when you realize that you can actually help these younger students who are in a similar position to where you were a few years ago, it transforms your perspective. In essence, it forces you to pat yourself on the back.
This happened to me when I began tutoring students in physics and mathematics. By helping them out with their homework and answering their questions, I realized that I had indeed learned quite a lot from when I was their age. Before that, I never really stopped to think about how far I had come, but working with those students was an eye-opening experience. I now find myself appreciating the work I do when I have completed an assignment or when I get through a semester filled with a bunch of work. In essence, I have learned how to pat myself on the back.
If you are anything like myself, this is not an easy thing to do. You do not tend to give yourself compliments, and you are always trying to figure out ways to become better. Even if you did well in the past, you do not tend to value your past performances. It’s all about what you still need to do in the future.
This is a precarious situation to be in. It means you are rarely satisfied with what you have done, which implies you do not pat yourself on the back very often.
My goal with this essay is for you to change if you identify with the above description. As students, we are continually going through a mountain of work, which means it is not easy to stop and appreciate what you have done. This is why it’s important to take breaks specifically for this purpose. It’s a mindset thing. By forcing yourself to stop and appreciate what you have done, you are signalling to your mind that the work you are doing is not “just another thing”. Each one is important, and deserves celebration. Likewise, if you can get into a situation in which you are helping students learn what you have already learned, you will not be able to help but appreciate the intellectual mountain you have climbed.
Patting yourself on the back sounds like something funny, but it really is not. It’s a key way to value the work you’ve done, and to show that the time you invested was worthwhile. It helps put in perspective the work I am doing. When I am faced with a mountain of work that I have to get through, I know that it will be difficult in the moment, but the effort will be worth it. By taking breaks in between things and making sure that I put myself in situations in which I can use the knowledge I have gained to help others, I have found I am much happier and able to continue working without everything feeling like a slog.
Nudging Along Versus Waiting
The eternal question as a teacher or tutor is what to do when a student is struggling. Should you give them a hint, re-explain a key concept to them, or let them sit there and struggle? It’s not always clear which approach should be taken.
I’ve often felt the pull to take the first route. After all, they are struggling! Shouldn’t I help them out? This meant I would give them some sort of pointer in the right direction. The result is that the problem gets done faster, and they understand what to do.
Now that I’ve reflected a lot on this, I’m not sure this is the best route to take.
Yes, it addresses the confusion and gets them moving again. But, the problem is that they aren’t fixing the problem. Sometimes, a student needs help and isn’t going to figure things out on their own. However, I think those moments are a lot more rare than we want to admit.
I notice this all the time when I’m working with students. I can see them struggling, and my instinct is to help them. I know what they should be doing, so I want to give them that knowledge. Seeing them struggle doesn’t seem right. Each time this happens though, I mentally restrain myself and give them more time. It’s not that I’m trying to frustrate students. Instead, I’m trying to instill in them a sense of persistence. I want them to succeed, but I also know that success is only “real” if they understand on their own.
To further complicate things, it feels like I should be doing something more than just sitting there as they work. After all, students pay me for tutoring. It feels like I’m not doing my job if I just sit there and let them struggle.
What I’ve found is that it takes a certain amount of courage to sit with a student and not rush to help them as they struggle. I’m not talking about courage in the heroic sense, but more in the sense of doing the right thing even when it’s difficult and uncomfortable. Despite wanting to jump in and help a struggling student immediately, I know that doing so will only help in the moment, not the long term.
Do I sometimes feel useless when working with students? Absolutely. But I also recognize that this is just a feeling I have, and it isn’t indicative of what’s happening. We often have the tendency of linking being busy with doing useful work. The reality is that this isn’t the case in every scenario. Sometimes, you just need to sit tight and wait.
Of course, I don’t let students struggle without ever helping them. I’m there to step in if they are struggling and getting nowhere. However, I wait until they actually try something. Sitting and staring at the paper won’t get a problem solved. You have to attempt the problem before figuring out if you’re wrong. When I’m working with a student, I look to see if they are making any sort of progress. While they still have momentum, I won’t interfere. I’ll only step in when it seems like their progress has ground to a halt.
It’s scary to just sit back and not help a student when they are struggling. But, just like checking the back of the book for the answer doesn’t encourage perseverance, jumping in to help a student at the first sign of struggle isn’t helpful either. The goal shouldn’t be making each problem seem easy. It should be to improve the skill of problem-solving. As such, it doesn’t matter if one particular problem is too difficult to solve. It’s about developing the grit to see a problem through to the end.
This will only come if we, as tutors and teachers, don’t jump in at the first sign of confusion. It’s worth letting students struggle a bit, because that’s the reality of mathematics. It isn’t always clear, and students should recognize that. If we’re always there to ensure that students have a smooth ride, we are setting them up for a big shock when they are on their own with a mathematical problem.
Learning is Offloading
When I’m learning a new topic, all of the details matter. If I want to understand what is going on, I need to have a firm handle on each detail. If I cannot imagine how each part operates and connects with the others, “getting” the concept is difficult. I suspect this happens for others, too. After all, if you want to understand without needing to take a result on faith, you have to know the concept as a whole.
This means learning takes a lot of effort up-front. I need to read the textbook, work through problems, and figure out what exactly is going on. If you imagine learning as a process that begins with a blank slate, anything that is introduced has equal weight. In other words, I cannot tell what new information is important and which is is not. Deciphering this requires extra effort and time, which is why it takes long to become comfortable with a new topic.
I have experienced this myself as I learned general relativity (and the associated mathematics) throughout my undergraduate degree. When I began, everything was new, which meant I had difficulty splitting what I was learning into a “useful” category and a “not-so-useful” category. This made it difficult to understand the big picture, because I could not determine the core ideas. Should I focus on the Einstein field equations, or was it better to become comfortable with the mathematical formalism first? Since I was learning the topic on my own, I did not have a bunch of support like you would have from a dedicated class. The result is that I spent a lot of time spinning my wheels and getting nowhere.
At least, this is how I perceived it. In reality, I was slowly gaining knowledge, figuring out what worked and what did not. However, there is no escaping the fact that it took an enormous amount of effort to get myself to the point where I feel comfortable.
As I right this, I am still not fully comfortable with the ideas. That being said, I worked with the concepts long enough to have some idea of how everything works. It is not perfect knowledge, but when I read about the geodesic equation, my mind does not offer up an empty box with a question mark inside. Instead, I have an idea of what the geodesic equation is. This is just one example, but it is the common thread I have seen while learning.
Familiarity breeds knowledge. Things might not make sense at first, but if you persevere and keep going, you will start to see progress. It might be slow, and it might take a lot of effort, but it will come. Since I needed to learn these ideas for the summer research I did as an undergraduate, I was given an incentive to keep going. This definitely helped, because I know it can be difficult to conjure up motivation out of thin air.
The reason I bring this up is that I always wanted to have the “effortless” knowledge that my professors have. Sure, I did well in school, but what I thought was amazing was how they seemed to know a bit about any piece of physics. Even if they were not an expert in that domain, they could quickly come up with an argument as to why the concept should be like this or that. How did they do it? I wanted to find out.
I think a big reason is that they have “offloaded” a lot of what they learn to the back of their minds. Essentially, they understand what parts of a concept are important, and they focus on those. The rest is “stored away” for retrieval if necessary. The reality is that a lot can be said by simply using the important parts, which is a lot easier to remember than everything. As such, they can explain the key features of a concept without too much difficulty.
Thinking back to material that I am comfortable with, I see a lot of agreement with this idea. As a tutor for secondary-level mathematics, I work with students solving basic linear equations, working through algebra, and solving geometry problems. These are ideas that I have so much experience with that I know what the important details in a problem are. While the student might read a problem and not know what “weight” to assign to each piece of information, it takes me seconds to figure it out. This is not a nod to my “brilliance”. Instead, it is the result of working on a lot of similar problems and understanding the key components. This lets me get to the core of the problem, without worrying about the details.
That is what I think learning really means. When you are presented with a concept, a problem, or a question, can you get to the heart of the matter, or do you get stuck in the details? As you learn a topic, I think you end up offloading a lot of the details to the back of your mind, allowing you to focus on what matters. Learning is offloading the non-essential details to the back of your mind.
I try to keep this in mind when I work with other students. If they are having trouble, it might not be because they do not understand. Instead, it could be a simple issue of not knowing what is important and what is not. In the case of mathematics, this can get tricky, especially with questions that are designed to fool you (hello, almost every word problem!). Giving a student the tools to let them abstract away from a particular problem and let them see the bigger picture is my mission, which means I want them to start offloading as much as possible.
I would compare this process to trail running. If you never ran on trails before, the key difference from regular running is that the terrain is uneven. Roots, rocks, mud, and a thousand other obstacles can hinder your progress, and “real” trails are not smooth. As such, you need to be careful when you run. However, if you try to focus on every single detail of the trail, you will often trip up on something. Instead, the best strategy is to take short and quick steps without thinking too much of where you are landing. In essence, you are offloading the task of obstacle avoidance to your subconscious.
In much the same way, I think it is critical to be able to grasp the core of a concept without worrying about the details. I am not saying that you should never worry about the details, but that they are not often useful in the beginning. Instead, the goal should be to get to the core, and then add in the details.