Last summer, I found out that MIT offers advanced standing exams (ASEs), which are a way to test out of introductory STEM classes. Since MIT has a pretty large set of STEM graduation requirements (two semesters each of physics and calculus, one semester each of chemistry and biology), it can be very helpful to pass some exams because it means that you can take major-relevant classes sooner.
I was excited that I’d the opportunity to take these exams. Unfortunately for me, however, I’d taken many of the corresponding classes more than two years ago and had forgotten most of the material. For example, I’d taken biology in 9th grade, and my class didn’t even cover all of the material that MIT did! Still, I wanted to see if I could pass as many of the exams as possible.
I started studying the usual way. I found a few textbooks online for biology, multivariable calculus, and linear algebra, and read the first few chapters. However, this didn’t feel very efficient. I would wake up the next day and forget everything I’d learned the previous day. Also, I still remembered some things from all of the subjects, which meant that some parts of the books felt way to slow, while others were too fast.
Discovering spaced repetition
Frustrated, I started looking into better ways to study and came across spaced repetition. This method minimizes the total amount of study time needed while maintaining a set retention threshold, which is typically around 90%. Every day, you learn 10-30 flashcards (unless you’re a masochist or in medical school and need to study more), while reviewing some of your flashcards from previous days. The scheduling algorithm is based on the human forgetting curve: the more times you review something, the longer it takes to forget it. Using this curve, it schedules reviews just before you’re likely to fall below that retention threshold.
Since biology is such a memorization-intensive subject, this was the first subject I started using spaced repetition for. This was huge. Instead of spending nearly an hour each day reading a chapter of the textbook, I could review flashcards for half an hour and actually retain the material. The specific app I used was called Anki. It’s free and implements the FSRS algorithm, which is currently the gold standard along with the SuperMemo algorithm.
At first, though, I wasn’t very disciplined. In the first few days, I was excited about Anki and had only a handful of reviews, so I always finished. But after about a week, the reviews started to pile up, and I lost motivation. As the ASE drew closer, however, I realized I needed to get back on track. With limited time left, I raised my new cards per day from 20 to 30. It was tough, but manageable.
People often use the “carrot and stick” metaphor when talking about motivation. Most productivity apps give the carrot. Anki gives you the stick. The more days you skip, the more reviews accumulate. Since I had to do 30 new cards daily just to stay on pace, I became diligent about keeping up with reviews. Otherwise, there was no way I’d finish in time. It actually got a bit addictive, and I began to enjoy the fact that I had a streak. Even now when I don’t have as many cards to do, I feel very motivated to continue my streak.
Meanwhile, I was also working through the multivariable calculus textbook and realized just how much there was to memorize. Sure, I could rederive the parameterization of a sphere on the exam, but that would waste a lot of time. My math teacher had mentioned last year that memorization is actually quite important in math. You can’t solve problems if you don’t even know the objects you’re working with.
Memorizing math
Unlike biology, you can’t simply learn math by memorizing. However, I realized it was a great tool to accompany reading the textbook. Whenever I came across an important formula, I would make a flashcard for the formula. I would also make a card for the derivation if it was relatively simple.
Looking back, I realized that I’d already memorized a lot of math I use regularly. For example, I know the quadratic formula and how to shift or scale functions entirely from memory. I could rederive and explain them if needed, but in practice, I recall them automatically. This saves me an enormous amounts of time and mental energy when problem-solving.
After passing the biology and multivariable calculus ASEs, I began studying for linear algebra. It is less memorization-heavy than multivariable calculus, since most of the results can be derived from first principles. However, there was still a lot of vocabulary to remember.
Math eventually became one of my largest Anki decks. Unlike other subjects, where I kept separate decks, I built a “mega-deck” for math because I wanted everything in one place. That way, I could see how different ideas were connected and interweave different fields of math in my studying. I realized that as long as I had flashcards, I wouldn’t have to worry about forgetting material I’d learned years ago. And it wasn’t particularly overwhelming. There really aren’t that many things to memorize in math, so I didn’t need to add too many new cards each day. This kept the number of reviews very manageable.
I also set this deck to a higher retention threshold (95%), because I wanted to be confident that I truly remembered all of the math I knew. This was incredibly useful, especially when reading papers. I could follow the arguments more easily because I always recognized the definitions, theorems, and notation being used.
Using Anki in college
During orientation, I took my final ASE, linear algebra, and passed! Since spaced repetition had been so effective, I decided to continue using it in my classes. Unlike the summer, when I was cramming entire courses into a month or two, the pace during the semester was much more manageable. I typically studied 10–15 new cards a day, finishing in about 15 minutes, yet I was able to retain material across all of my classes.
Unsurprisingly, having a tool for memorization was especially helpful in chemistry. I was also taking two definition-heavy math courses: Real Analysis and Fundamentals of Probability. Over the course of a month, I created 72 cards for probability and 40 for real analysis. This made it much easier to do the problem sets and understand the lectures in real time. I no longer had to expend any effort on recalling definitions and theorems.
It was also useful for economics. I hadn’t taken microeconomics in high school but chose to skip the introductory course after hearing the more advanced one was particularly well taught. Since economics uses many formulas over and over again, it was super helpful to have them ready at my fingertips when working out problems.
Importantly, using Anki didn’t replace my ability to reason. By removing the burden of recalling facts, I could devote more energy to problem solving. The way that I like to think of it is that knowledge can be thought of as a graph with millions of nodes and edges. Spaced repetition can help you build up the number of nodes you have, but it’s still up to you to make the connections between them. However, if you don’t have any nodes, you can’t possibly link ideas together.
I haven’t had any exams yet, so I can’t say anything about my scores. However, I do think that spaced repetition has made college significantly easier than I think it would have been otherwise. I’ve also taken some practice midterms, and I scored relatively without any preparation because I’d already spent the past month internalizing everything.
I will conclude this blog post with some statistics.
Statistics
- Total time spent on Anki: 1.16 days
- Total reviews: 10,449
- Biology cards: 801
- Chemistry cards: 108
- Economics cards: 95
- Math cards: 271
