Remember your Formulas

How do you remember your formulas for an upcoming test? How do you remember those theorems, those definitions, all that little things that seem so difficult to remember, you know, I think gives you stress when you are preparing for a test. And the reason why I wanted to make this video because one of the most popular ways that I've always caught students cheating has been to use formulas. And they'll just write down a formula on like a little sheet of paper and, you know, they put it in their waistband or they, you know, put it up their sleeve and they have it folded somewhere. Maybe they write it down on their calculator or whatever may be the case. But being as small and as meaningless as a formula, students want to risk grade and their integrity and cheat for a stupid formula. I think that's kind of crazy. And I do not advise you to cheat on your test, especially to try to memorize a formula. But I do understand that a lot of students have this question because they trying to memorize these little things that are very, very difficult sometimes to remember in the context like what they're learning or what their test is on. That it's one of the most common questions that I get on my last year was like, how do I remember all of this stuff? In this video, that's exactly what I want to do. I want to give you some tips and some tricks to you be able to do that. However, I do have to warn you, I'm not a big fan really of this kind of topic because one thing that I found, I'm like, why are students cheating on this? That makes me upset. And then I had to talk with them. I had to talk with their teacher. I had to talk with counselor, the principal. It brings in this whole ordeal. And I'm like, for what? A grade and because some stupid formula that you like are never really going to need to know in real life. But one thing that I decided that I wanted my class to be defined as is not for students if they could remember a formula or not. The one thing I always did was I gave my students a formula sheet for every test, for every exam, allowed them to write down anything they wanted front and back on a sheet of paper because I did not want that stress. I did not want them to fail my class for cheating. I did look at the review sheets. So there are certain things that you couldn't put on the review sheets. But in general, like I wanted them to put all those formulas and all those definitions and theorems and stuff like that because my test was going to test if they were going to measure how they could apply the information, not how well they could regurgitate the information. I think it's even more important now that we've seen like AI like ChatGPT and like we've had PhotoMath and MathWay and all these online apps that have come through in this time where students are still like in this mindset like they feel like they have to compete against one another by being able to memorize all the certain stuff over somebody else. And I don't want you to feel like this is the most important thing. I know not every teacher or every educational system is just like me. I know not everybody values the same things or values their education process the same way I did. So I'm not saying I'm superior or that's the way things should be done. It's pretty complex. The other thing I didn't want to mention is even though I did give students a cheat sheet, I said, write down whatever you want on this cheat sheet, right? Like there would always be things that students would forget. They probably didn't think like they needed to have memorized. And that's the kind of the difficult thing about memorizing some formulas. Yeah, there's some like direct formulas that are being taught inside of the current class. But then there's also pieces of information that I as a teacher, I'm just going to expect that you know throughout the whole course or throughout your history of getting up to that course, you should know that information. Even like for this, maybe you came from a different school. Maybe you didn't take a certain class. So maybe there is some piece of information if you are in my class that you would not remember or you would not know how to do that you would need to make sure that you went through this process to be able to remember and understand that stuff. Because again, even on a cheat sheet, there's no way you can put it everything on it. Before I get into my tips, let's go into just some what I like to call cheap tricks. The reason why I call them cheap tricks is because they work, but they're not going to have any long lasting effect. You're going to probably remember them hopefully if you do it well or you work hard enough on it. But it's not a long-term solution. It's not something that I'd really highly advise for you to have. Something that I think they do have some impact and it's something that I even used to do with my students. I even do it with my daughter right now is like just working through like flashcards. Just constantly going over seeing it multiple, multiple, multiple times. One thing I would recommend if you are going to go down the flashcard route and I think it's also a personality thing. I hated flashcards, but I remember like my sister loved flashcards. So I think there might be a little bit of personality kind of trait that goes into it. But you know, I think that if it's something that you can do repetitive and this is one thing I always like mentioned to students. I don't hate flashcards. It's something you can do consistently every single day. If you're staying up till midnight trying to do like 500 flashcards the night before, it's probably not going to be that useful. But if it's something that you do, like you do flashcards and then every single time you're learning something new, you add them to the stack and you just keep on reviewing them. Maybe you spend like five, 10 minutes every single day just like going back through the flashcards and maybe you have like the definitions or something else on the other side. I can see that, you know, that can be helpful. That can be beneficial. It's you're going to get that photo memory built up. More likely than not, it's something that you're going to be a member for the test. The next thing, which is also like another just cheap trick would be like writing it down, like writing down the formula, like multiple times, just constantly writing it over and over and over again. Not something that I would highly recommend, you know, the night before, but usually when it comes down to cramming techniques, this is something you can do, right? If you want to memorize, you know, I don't know, some weird formula, like write it down 10 times, write 20 times and I guarantee after that, you're probably going to have it ingrained in your memory for a couple of days. And therefore, then you can go ahead and apply it during your test. The number third thing is try to bring some analogy, right? We always say when you're introducing somebody or you're getting their name, people forget their names. You know, one thing you want to do is like kind of connect their name to something that you can remember, like, you know, about their short jeans or like what their hair looks like and give that a name, like, you know, I don't know, Benny the goat or something you can remember that you can relate, right? One thing I always remember with the sum and difference formulas for tangent, I just always remember like the plus or minus. That was one thing I just remembered. The tangent has the opposite signs on their sum and difference formulas because I didn't remember the formulas. I just remembered the plus or minus. And then that helped me kind of recreate things back when I needed to. Now, that's not really the best way how I remembered it, but that's like a little analogy. If you can kind of connect it to something easier for you to remember, that can be helpful. And so go through those formulas, go through those definitions, go through those theorems and try like, all right, what is something easy that I know I can remember that I can relate to this? Again, if you have your test tomorrow, if you have it this week, these are all valuable techniques that I think you can use. I don't want you to rely on them. I want to do something else because I want to remember the formulas, the definitions, the theorems for my next test. I don't want to be stressed out. Even though I wish I had Mr. McLogan because he would give me a formula sheet and my teacher doesn't. Sorry, teachers, don't want to throw you into the bus. What are some ways that I can remember and actually remember what exactly I am doing? The first way, which I think is the most important way, it just comes down to learning, guys, like doing enough problems with those techniques. And this kind of gets into like the writing the problem down, but like what's the point of writing a problem down like 20 times? Like that's just a complete waste of time. Like you're just doing it to trick your brain to remember it. So therefore you can take it on the test. I always tell students, I don't want you memorizing anything in my class. It's all about your reply. But there will be things that I will expect you to be able to bring back, like for you to recall in this class. But the only way that you should be able to recall this work is because you have done this over and over and over. So for instance, students would always be like, do we have to memorize the unit circle? Like how am I going to memorize this? There's so many points on the unit circle. I was like, no, no, no, we're not memorizing the unit circle. I mean, obviously if like you want to go through the last three tips and you want to memorize it, like you do you. I don't advise it at all. That is a complete waste of your time as well as your brain capacity to be able to do that. What I want you to do is to do every single problem that I ask you to do in this class on the unit circle. Because I guarantee you, if you do every problem that I'm asking you to do, you will know how to evaluate the unit circle and you will know all the values on the unit circle. Because I think a lot of times what students want to do, and this is what I did as a student, is they want to do shortcuts. They don't actually want to, you know, go through the process of doing each and every one of the works. It's like, you know, they know how to do it. They're like, okay, now let me go and finish my work quickly as possible, not have to like go through the same process. And that's the problem, guys. If you go through that process of evaluating your unit circle, finding the coordinate points over and over and over, one, you will get faster on it. And then two, there's no way that you're going to forget, oh crap, what was pi over three? Is that the same thing as pi over six? Like no, if you do enough problems, then you are going to be prepared. Now I know not every teacher maybe has like enough problems set up for you to be able to remember or have like a good confidence in being able to remember the material. Everybody's going to be a little bit different in that regard. So I would just challenge you to practice whatever formula that you are trying to remember. If you're trying to remember a formula, like do enough problems, it's kind of going through the same process. You're writing down the formula, but you are applying the formula. And that's where those connections are going to help you remember things. Another thing that I would go through is, you know, when I would teach every single year and I always forget most of the identities, like when you teach like six class periods, right? Or eight class periods a day, depending on what it was, like I'm constantly going through doing all of those problems. By the next day, once I've just refreshed my memory of that, like I've done so many problems already, I remembered everything. Like I never had to look at the book and reference anything like, nope, I remember it was from the brain because I had went through that many problems. And I always challenged students. I said, once you do as many problems as I do, you're not going to have to be worried. Like do I remember what the formula is or not? Like it's ingrained in you because you have put in the work. So a lot of times students say, hey, how do I memorize? Most common response I say, put in the work, put in the work. Do the problem enough times that you have it memorized, like do problems by applying it and you will not have to worry about trying to memorize the information. The next thing I would highly recommend you do is create a cheat sheet. Who cares if your teacher says you can't use this on your test, right? But one thing I told my students to do is I said, create a cheat sheet every test and then create a cheat sheet for your semester exam, then create a cheat sheet for your final exam. And if you think about that, one thing what you're doing is, you know, obviously let's just say there's like some really important formulas and stuff like that. But every single time that you write a formula down on your cheat sheet and then when you use your cheat sheet to study, so one, you're writing it down from like your notes, you're putting on the cheat sheet, right? That's like writing it down twice. And then usually we use our cheat sheet to study. So you're reviewing, you're doing that visual memory of your formula when you are studying. And then let's say you come into your semester exam. So then you're going to rewrite it. So again, that's the fourth time you're going to study again for it. That's the fifth time. And then obviously you're coming to your studying for your final exam, which would be like the sixth time or the seventh time. And obviously any other time that you need to reference that cheat sheet, it's going to be more and more time. Now, again, my biggest advice to students was if you create a quality cheat sheet, you don't need to use it on your test. And this is the one thing that a lot of students never really understood about the cheat sheet. They always thought like I was such a nice teacher for giving them a cheat sheet. And it was the farthest thing from the truth. I didn't give them a cheat sheet because I wanted them to cheat. I kind of liked calling it cheat sheet because it kind of gave them this false thought of like, oh, Mr. McLogan's letting me cheat on their test. But no, I wasn't letting them cheat on their test because if they put in the work, which when they created their cheat sheet, they are doing, they're not referencing that cheat sheet. And again, a lot of times my test would be, again, it's application based. So it's not just like recall, like what is this formula? And then like, oh, the answer is right here on my cheat sheet. Like, no, that's not that easy. But then the other thing is like it was like time-based. Like if they're spending their time trying to learn the stuff from the cheat sheet and apply it for on their test, they're not going to have time to finish their test. So it was kind of like this false prophecy of like, I'm going to be able to cheat. Like, no, no, no. I want you to put in your time creating that cheat sheet. And I can tell you time and time again, students will be like, Mr. McLogan, I spent hours and hours creating this cheat sheet. And I looked at it like once and I'm like, yes, that's just like music to my ears. I'm like, that's exactly what I wanted you to do. And that's what I think the power of having a cheat sheet is. It's like you are ready and prepared for that test. And it also like kind of removes that anxiety for you taking the test. And I never saw students that didn't want to prepare for my test did just as well as they would when I didn't give a cheat sheet. Students that were prepared for my test did just as well as they would with the cheat sheet. So I think it benefited students and it didn't benefit the other students. It wasn't one of those overall great things. But if like your teacher doesn't allow you to take the cheat sheet, like that's fine. I didn't do that for crap 10 out of my 14 years that I was a teacher. Now the last thing that I give to you, I remember when I was in college, this was the first time I had this. I was struggling with physics. I was about to fail, I think, actually I did drop the class before I officially failed the class. But one of the things I could not remember my physics formulas. I was taking calc two at the time and it was calc-based physics. I was just overwhelmed with all my studies. I think I was trying to do like the cheap tricks, just trying to memorize the formulas, you know, and didn't really understand how to apply them. And I remember I sat next to one of my friends like throughout the class and I asked him, how do you remember your formulas? How do you know which formula to use? And he's like, I don't remember the formulas. I just remember how to build them. I was just learning math, again, still to just regurgitate it. But he had a better understanding, like he was a better math student than I was. Like the connections in the formulas and what we were doing. When the professor would teach us, he took those and hung on to them. Because what was powerful and important is like he saw how the formulas were connected to one each other. He understood how we could build out those formulas. So then rather trying to, for instance, understand like, let's say four formulas, if he could remember one formula and then learn how to build out to create the other formulas, that's a great trick. So it's not going to be possible for every single formula or theorem or technique. Look for things that you can go and build out, combine with other formulas and theorems. Therefore, you can create them when you need them. Hopefully all these techniques that I've mentioned, even the cheap ones and the ones tried and true, you can use them for this exam or test that you have coming up or apply them for next year. So wish you guys all the best of luck on your test or exam. And let me know how you guys do down below.