Spaced Repetition Algorithm

The spaced repetition algorithm is one of the most important components of VocabularyShop.  It enables the users’ vocabulary building/improvement process to be automated and optimized according to each individual user’s brain characteristics.  Consequently, the users will achieve the highest possible learning productivity in their vocabulary building/improvement endeavor.

This spaced repetition algorithm is implemented in VocabularyShop’s core function, the Study function.


Human Memory and Spaced Repetition Algorithm

Human Memory Operation

According to modern cognitive psychology, when human brain receives information from the outside, the information will go into the brain’s short-term memory and that information will be forgotten quickly.  However, if the same information is rehearsed multiple times at different intervals, then that information can be encoded in the brain’s long-term memory.  Information stored in long-term memory will take long time to forget.  The method of rehearsing the information multiple times at different intervals is known as Spaced Repetition method.

When dealing with a limited amount of information, the arrangement of the rehearsals will not have a big impact on the result.  However, when the amount of information is large and diverse, managing the rehearsals will become critical.  You can quickly entangle the information you want to learn with the way you learn it, lose track of what you have done, and waste a lot of time fighting chaos.

An intelligent spaced repetition algorithm will organize your rehearsals in an orderly manner, optimize all aspects of the operation, like number of rehearsals, intervals of rehearsals, how the rehearsals are conducted, and other application specific elements to guarantee the best results.



User’s Word Selection

See User Guide for description.


User’s Database

See User Guide for description.


Study Round ( or Round of Study)

A study round or round of study of a word is a set of user’s learning-memorizing activities for a particular word under VocabularyShop’s Study function.  It involves a series of multiple choice questions and answers about that particular word.  A round of study begins when that word is presented to the user the first time after the user entered the Study function.  It ends when a defined condition is met or when the user exits the Study function.  In the former case, that word is said to have passed a round of study.

Word Study Status

When a word is being actively studied under the Study function, it will have the following status recorded or calculated to enable the spaced repetition algorithm to manage the study process for the user.

  • Total Answer: Total answers the user provided to the multiple choice question in the current round of study.
  • Correct Answer: Total correct answers the user provided in the current round of study.
  • Ratio of Correct Answers to Total Answers: The calculated result of (number of correct answers) / (number of total answers ).

The total answers and correct answers the Study function displayed with the multiple choice question are the sum of all rounds of studies so far, not just for the current round of study.

Word Review Status

The review status of a word is the overall progress a user has made on studying that word towards the final goal.  It allows the spaced repetition algorithm to manage the review scheduling for every word in the user’s word selection.  Below table lists all status a word can have.

Word Status

The following are more explanations of the above statuses

  • New: Studies on these words have not started, and the exact date to start is not decided yet.
  • First Review to Sixth Review: These words are called Learning Words.  Study on these words have started, and at least one round of study has passed on them.  They will be scheduled for review repeatedly until their status becomes Learned.
  • Learned: The designed study process has been completed on these words.  Reviews have been scheduled for them every 180 days.
  • Known:  Status for words in the Known List.  These words will not be scheduled for study.


Flow of the Spaced Repetition Algorithm

The overall flow of the spaced repetition algorithm includes picking up a new word from the user’s word selection, arranging the word to be studied, then reviewed for 6 times at different intervals.  The algorithm will monitor and record the progress the user made on learning this word, and manage the learning process base on the use’s progress information in real time.  There can be hundreds of flows for hundreds of words going on at the same time.

VocabularyShop Study function has 2 different implementations of the spaced repetition algorithm on 2 different levels.  One is on the word study round level and the other is on the review scheduling level.

In the following text the words Study and Review mean roughly the same thing in many places and will be used arbitrarily.

Spaced Repetition Algorithm in Study Round

When the study function started, a study list is created from the user’s word selection.  The total number of words and total number of new words in the list will not exceed the maximum values related to user configured study session length.  When adding words to the list, words scheduled to be reviewed on and before the current day will precede any new words.  Also, new words added to the user’s word selection earlier will precede those added later.

After the study list is created, words in the study list will be picked and presented as multiple choice questions to the user randomly and repeatedly.  Every word in the study list has the equal chance to be picked.  A word will not be picked for the second time before every word has been picked once.

The interval between 2 presentations of the same word depends on how many words were picked between the 2 presentations, and how much time the user spent on those words.  The length of the intervals is random,  but it will be a few minutes in general.  This means the user will focus his or her attention on a particular word for some time, then shift his or her attention away to other words, then come back a few minutes later to refresh his or her memory on that particular word.

After a word is presented to the user for at least 3 times, and after the number of correct answers to the multiple question reaches above two-thirds (>= 67%) of the total answers, that word is defined to have passed this round of study.  That word is then removed from the study list, its review status is upgraded to the next level, and its next review date is set according to the above review status table. Other word may be added to the study list to maintain the list at configured condition.

The spaced repetition algorithm at this level forces the brain to retrieve the information it just moved away a few minutes ago repeatedly.  These actions boost the information encoding in the long-term memory.  The requirement that the user must deal with a word at least 3 times ensures the user’s brain get enough exercise.  The criterion that a word passes a round of study when correct answers reached above two-thirds of total answers prevents the user from wasting time on already strengthened memory.


Spaced Repetition Algorithm in Review Scheduling

As mentioned above, when the Study function started, it will check the review date of all words in the user’s word selection.  All words set to be reviewed on and before the current day will be scheduled for review by the user.  The review date was set when a word passed a round of study.

From the “Days to the Next Review” column of the above review status table, the space or the time is doubled after each review for the learning words.  This increased space allows adequate time for the word information to fade away after being strengthened by a review.  However, such amount of space will not cause the information to fade away completely.  Thus the next review will not be too difficult. The goal at the scheduling level is to create a fade away and refresh back cycle in the user’s brain to help the encoding process while keeping the time and effort from the user as low as possible.

Below figure provides a rough description of how the memory strength of a word changes in a user’s memory following the scheduled review activities, and how the information is encoded gradually in the user’s long-term memory.  The actual situation varies depend on particular user, particular word and many other conditions.

Scheduled Review and Memory

The review process looks very long and time consuming because a word has to be studied 7 times in total 64 days to become learned.  In fact, if a particular word is easy for a user, then he or she will spend just a few seconds to finish reviewing that word each time.  He or she can also move that word from Study List to Known List after one or two review to save the time on reviewing that word.  Sixty-four days looks very long,  but the users spend only a few minutes or seconds each time for 7 times.  There are hundreds of words going through the same flow at the same time.  The actual time users spent on each individual word is very small.