## 1. Summary

Spaced Repetition is a learning technique that shows flashcards that are difficult for you more frequently than easier ones. For instance, the I Aced Calculus (IAC) app asks users to rank how well they understood a flashcard on a scale from 1 to 5. Then, it employs an algorithm to decide what questions to show the user the next time they go through the cards. The flashcards that are harder for the user will appear more frequently than the easier ones.

## 2. Algorithm

Spaced Repetition is based on two main principles: students forget what they learn, and they forget different materials at different rates. Specifically, the rate at which students forget information is similar to exponential decay – the process begins rapidly, but the rate of decay slows down over time. However, it has been shown that periodically reviewing information allows students to increase retention. In other words, the review helps to “reset” this exponential decay. It also decreases the rate at which information is lost, meaning that repetitive review over a long period of time significantly improves the ability to retain certain facts.

In general, spaced repetition capitalizes on computing the probability of recall. This concept is defined as the chance of remembering a certain fact, and is computed by the equation:

Here, the variable *t* represents time. I_{1} represents the difference in time between initially learning the information and its first review. This is also regarded as an interval, hence the variable “I” is used. Lastly, C_{i} represents the ratio between the length of the i’th interval and the i-1’th interval. This variable is important – it allows spaced repetition algorithms to calculate when the next time a card will be shown based on the length of the preceding interval. In the algorithm SM-2, this variable is referred to as the Ease Factor (EF), which changes according to the difficulty rating given to a card. For instance, if a student determines that a flashcard is difficult, then the EF will be decreased. Subsequently, the ratio of the i’th interval and the i-1’th interval will decrease; this implies that the next time the card will be shown is sooner. The same is true for the flashcards a student finds easier – the EF will increase, meaning that the ratio of the i’th and i-1’th interval will increase, so the cards will be shown less frequently.

Being able to calculate C_{i} lies at the heart of many algorithms. However, this is a complicated task due to multiple factors influencing its value. One such factor is difficulty: the more difficult a flashcard is, the lower the C_{i} value will be. Another factor is stability: this refers to the time it takes for the probability of recall to decline from 100% to 90%. As a result, a higher stability value implies a better ability to retain information for long periods of time. Notice that stability is closely linked with C_{i}, because both concepts are related to how often a student would need to review a certain flashcard. In general, higher stability implies a lower C_{i} because it implies that reviews of a flashcard don’t need to be as frequent. Lastly, a third factor affecting C_{i} is the probability of recall, which was defined before. A higher probability of recall will result in a lower C_{i}, since it’s not as productive to frequently show a card that the student already memorized.

Despite this, some algorithms use methods that try to calculate C_{i} as realistically as possible. One such algorithm called SuperMemo uses a multi-dimensional matrix to represent C_{i}. Then, it tweaks the values of the matrix to imitate the user’s learning experience over time. However, this is imperfect and requires various approximations. As such, it is important to consider the inaccuracies involved with spaced repetition when choosing this learning method over others.

## 3. Benefits

Spaced Repetition is useful because it offers a more tailored learning experience. Concepts that are not well-understood are revisited more frequently. Students will spend their time practicing the material that they don’t understand, rather than repeating the same flashcards that they already grasp. As a result, this helps to improve the quality of the time spent learning.

The default option for studying flashcards is “Study in order.” However, some students find that this can be more time-consuming than Spaced Repetition. They may find themselves repeatedly encountering the same material that they understand as they are going through the flashcards (which they can hide if they prefer). By using Spaced Repetition, the app helps the user to skip directly to the material that they need to focus on the most. This also makes the experience more exciting, since it forces the user to spend their time solving more difficult problems.

The alternative to studying in order is the option to “Study shuffled.” However, some users may find that this can be disorienting. Students who want to shuffle topics but not every flashcard may want to use Spaced Repetition instead. This method will ensure that only the difficult questions will be shown, but they will nevertheless be shown in order.

## 4. Conclusion

In summary, embracing the Spaced Repetition algorithm offers students an effective way to target areas of improvement within a given topic. By focusing on the flashcards that pose a challenge, rather than reviewing material already mastered, students can optimize their study time and master complex concepts faster. While it’s essential to acknowledge the benefits of this approach, it’s also worth noting that no learning technique is without its limitations. Despite its efficiency, the Spaced Repetition algorithm may not always perfectly align with individual learning preferences or priorities. As such, students might want to combine it with “Study in Order” or “Study Shuffled”, to supplement their learning experience and address any shortcomings of the Spaced Repetition approach. Your preferred combination of these study strategies will help you maximize your learning potential and achieve academic success.

Resources:

- https://github.com/open-spaced-repetition/fsrs4anki/wiki/Spaced-Repetition-Algorithm:-A-Three%E2%80%90Day-Journey-from-Novice-to-Expert
- https://www.supermemo.com/en/blog/application-of-a-computer-to-improve-the-results-obtained-in-working-with-the-supermemo-method
- https://faqs.ankiweb.net/what-spaced-repetition-algorithm.html
- https://www.reddit.com/r/Anki/comments/1atdp4d/comment/kqwyxx1/