Jagged Edges

As a student, you’re responsible for a fair amount of material from the various classes you’re taking. Whether that’s a bunch of facts concerning a part of world history or the way to prove the equivalent capacitance of capacitors arranged in series and parallel, it can be difficult to keep all of it in one’s mind while tests loom ever closer.

Therefore, it comes as no surprise that there comes moments where a small piece of information is presented and simply makes little sense. When this happens, it’s certainly tempting to let the detail slip away into the ether of your mind. It’s easy to convince oneself that the piece of information is of little consequence, and that practically speaking, there is a small chance this detail will be on the test. One will then forget about this detail, deeming it unimportant.

However, this is not a wise decision to take. Personally, I’ve done this many times and have usually paid the price on my exams. Discarding a detail is usually not the best course of action to take. Instead, one needs to take the time to address the confusion.

If it’s a small detail, asking the teacher during the class is a good idea. This can clear up any issue immediately and allow you to mentally be back in sync with the class lecture. I recommend this course of action first.

I know that this isn’t always possible (perhaps you don’t want to interrupt the entire class for your question), so the next thing to do is to figure out a way to ask the teacher about it later. This can be after class or during office hours, but the important step in this option is to write your problem down. The reason I want you to write down your issue is that I want you to detail exactly what doesn’t make sense to you. By doing this, you’re ensuring that you can accurately describe your confusion to your teacher at a later time. Additionally, this list of ideas that don’t make sense or don’t quite jive can be used as study guides for exams. By looking at these, one can virtually guarantee that these issues won’t be present in a test.

The best way to avoid jagged edges in one’s knowledge is to embrace them, and then work to improve them. It can be difficult to understand a lot of the content in classes, but by keeping a running list of what doesn’t make sense in a class, you’re creating a systematic way to tackle those issues.

No more getting caught in a test by the one thing you didn’t look at for the test.

Not Just For The Test

I have a bad habit when receiving an exam that is graded: instead of looking at my errors and trying to figure out what I could have done better, I simply try to put the whole exam out of mind.

This happens whether I have a good or bad exam. Basically, I want to see my grade and that’s it. I think the underlying reason is that I won’t need that information for a long time (until the end of semester). Therefore, I can afford to push it out of my mind once I receive my exam back.

Obviously, this points to a problem with the way we structure our learning. At the moment, I’m encouraged to become proficient with certain content, and then I’m free to forget it until the final exam. What this means is that I’m familiar with the content for only a small sliver of time before forgetting it once again.

If I asked you if you were good at foul shots in basketball and you proved to me you were by draining ten shots in a row, I’d probably think of you from then on as a great foul shot shooter. However, what I don’t know is that you practiced this shot for the past two weeks and you never plan to do it again after showing me.

Would this be considered as being great at foul shots?

I’d venture to say “no”, but this is exactly what happens for a lot of classes in school. I’m familiar with mathematics and science, but I’m sure this is applicable to other classes (particularly where memorization is important). Spend a few weeks remembering important content, take the test, and then forget. Rinse and repeat.

The consequence of this is that we don’t learn concepts as fully as we could. Sure, it’s an efficient way to get good grades (and nobody knows that more than I), but it isn’t as useful in the long term. Years later, I wish I took the time to understand more material.

Of course, it’s difficult to take this long term approach in the moment. Not only because one does not think of the consequences, but simply because taking this approach with a heavy course load is inconceivable if one wants to get good grades. Therefore, the shortcuts ensue.

Unfortunately, I don’t know the solution to this. I know that taking a long look at the mistakes made on a test and making an effort to understand those mistakes is a good step towards long term learning, which is why I’m trying to do that now. Additionally, I think returning to old content every once in a while as a refresher can be very valuable.

If you want to learn (and remember what you’ve learned!), take the time to internalize content even after the test is done.


When I first began my CÉGEP mathematics courses, one of the things I noticed that was new was how my teacher would give “motivation” to what we’re doing. Basically, the idea was to give us a reason for why we were doing something, instead of just throwing it out in the blue.

This was a welcome change from what I originally did in secondary school. There was some motivation for what we were doing, but most of the motivation was left up to us to find. We simply went from one subject to another. With my teacher in college however, there was nearly always some sort of motivation embedded into the lecture. Some of it might have went over our heads, but my teacher always made sure to give us some reason for what we did.

I’m still a student, but I’m also a tutor, and so I can see how both sides of the relationship see motivation. As a student, I like to know why I’m doing something or what the end goal is supposed to be. As a tutor, I know that giving students direction while learning new concepts is key to keeping their attention (and the inverse means a lack of interest). Therefore, I try to look for ways to motivate the line of reasoning I pursue with them in mathematics. It turns the learning experience from just myself giving information to the student to an experience where the student can feel like they are along for the ride.

And from personal experience, it’s a lot more fun to learn when you feel like you are an active observer with the teacher, instead of merely listening and taking notes.

A Bunch Of Formulas

At the beginning of my physics classes in CÉGEP, I would receive the formula sheet for my entire semester. That meant I had all the formulas on one page, allowing me to scope out what I would be doing in the semester.

At the outset, this is a bit overwhelming. Having all the formulas in front of me tends to make the course seem super complex. Plus, since I’m only beginning my journey through the world of mathematics and physics, I’m not accustomed to a lot of the new equations I see on these pages. Therefore, it can be difficult to understand what these equations even mean when the semester begins.

However, as I go through the material during the semester, it becomes easier to understand the formulas. It’s not magic or because I’m “smart”. Instead, working with the formulas becomes easier with practice and seeing how the formula comes about.

This sounds obvious, but I mention it because there are many people who don’t do science and think it’s some sort of magic that’s happening when we work with these crazy complicated formulas. And sure, to the uninitiated, they are complicated. But that’s because they are looking at the formulas for the first time, with no explanation or context. This is a surefire way to be confused. Indeed, I get confused if I approach new formulas in this way.

That’s why I try to play down situations in which others tell me that mathematics and physics is just too complicated for them. When they tell me this, I say something along the lines of, “Anyone can understand the concepts if they put their mind to it.”

Learn the why behind the equations first, and you’ll be much more satisfied moving forward because you will know what you’re doing.