Alright, let’s say you are at a physics lecture watching the professor write notes on the board. He writes an equation down and says: “memorize this.” So, you write it down in your notebook and make sure to review it until you have it committed to memory. Now, you do some practice problems for the class, and you learn which types of problems you need to use the equation for. You take the test, and you just repeat the same process you did on homework. Eventually the class is over, and you forget the equation because you will not need it again. This is the standard way that most people go about memorizing all their equations, and I think it is incredibly terrible!
When you just memorize an equation, you do not understand the equation. All you know is when it is needed. When you do this, you are solving problems on a superficial level, so you never develop a deep and fundamental mastery of the material. If you are looking to be as knowledgeable and familiar with material as you can, this is a terrible strategy. So, what do you do?
Back in math class in eighth grade, I just memorized equations. My teacher wrote down the quadratic formula on the board, and then I committed it to memory. My teacher wrote down the Pythagorean theorem, and I did the same without understanding it. Then he told us that we should use these theorems in specific cases. To be honest, I was completely lost in that class. I had no idea what I was learning, and I felt like I was going through the motions on homework. I was confused and frustrated. Fast forward, two months, and I was at the top of my class, teaching myself next years material in my free time. So what changed? Well, in between I had read a book called Fermat’s Last Theorem by Simon Singh. This was a math book about how a centuries old problem was solved by a mathematician. The book showed me all sorts of math that was used to create the solution, and it also showed me how this math was discovered. It showed me various popular equations and how they were derived. I had never heard the word “derived” before, but once I started looking at these equations, math took on a whole new meaning for me.
I started looking up how to derive all the theorems in my class. I learned how the Pythagorean theorem was discovered, I learned how pi was calculated, and I learned much more. Once I did all of this, something clicked in my head. Now all of the sudden, I was excelling at my math classes. By the end of the year, I had somehow aced the final and secured the highest grade in the class. The year before, I had no idea how someone could even manage to remember all the math that was going to be on the final. It seemed impossible to me. That summer, I taught myself calculus, and freshman year, I took the Calculus AB Exam and got the best score possible. By Junior year, I had finished the math curriculum at my highschool and had started taking classes at Villanova University.
All of this occurred because something clicked. I went from memorizing equations to understanding equations.
How You Can Do It
In you classes, stop mindlessly writing down the equations your professor puts on the board. Instead, pay attention to how they derive them. If your professor does not derive them (or does a terrible job explaining the derivations), then read your textbooks derivations until you understand them fully. If you are unsure what full understanding is, go ahead and read my post on the various stages of knowledge. As you read the theorems, they are not going to click right away. This is especially true if you are new to this. You are going to have to follow them line by line, and stop if you are missing something to go back. Once you can go through every line in a theorem, you are ready to use it.
You also need to be positive you understand exactly what the theorem is saying. In higher level classes, you may know a derivation is right, but you may forget what the various functions and variables mean in it. If this happens, just go over all the variables and functions until you understand exactly what the equation means.
Next, make sure you are good at applying the theorem to problems. This should come very naturally if you use this method. However, you still want to make sure that you can solve less straightforward problems. So, do a couple to make sure you have the method down. This is the best way to ensure you have a full understanding of the material as well. If you are unsure of the what the theorem means, then you will not be able to apply it. Also, you do not want to be solving a problem for the first time on a test. Certain parts may confuse you that you do not realize.
I guarantee that if you start doing this, you will be a lot better at solving problems and understanding the material in your classes. As you begin to do this, it is not going to be easy. You will struggle with a lot of simple derivations, but as you get better, you will get a feel for these. You start to understand the logic behind each derivations more, and the derivations that seemed impossible will feel trivial. All you need is hard work.
If you are interested in learning more about my technique for learning STEM subjects, I have a more expansive post coming this week. This post is a small part of the whole technique I use to master STEM material rapidly and permanently. Really, the trick is to know the material inside and out, and this is the first step!
Thank you for reading! If you have any questions at all, just comment below.