Spaced repetition

Ebbinghaus also found a way to hold forgetting back: reviewing at intervals rather than all at once. To prepare for relearning a list on a given day, 68 repetitions crammed into the day before did no better than 38 repetitions spread over the three days before.

Studying something in one unbroken block is called massed practice. Spreading the same study over separate sessions is spaced practice, and its advantage is the spacing effect. It is one of the most dependable findings in the psychology of memory: a 2006 review gathered more than eight hundred comparisons from over three hundred experiments, and spaced study generally beat massed study once memory was tested after a delay.

Cramming can still get you through tomorrow's test. What it rarely gives you is a memory that lasts.

Why should spreading study out make such a difference? One leading explanation starts with forgetting. Straight after you study something, the answer is still fresh, so going over it again takes no effort and changes little. After a gap the memory has faded a little, so recall takes more effort, and that effort strengthens the memory more.

Psychologists describe this with two strengths that every memory has. Its retrieval strength, how easily it comes to mind right now, drops during the gap. When retrieval strength is low, a successful review adds more to how well the memory is stored. In this sense a gap is a desirable difficulty: it makes each review harder and more useful.

So the forgetting between sessions is not wasted time. It is part of what makes the next session work.

If spacing works so well, why does cramming stay so popular? Part of the answer is that massed study feels more effective while you are doing it. Each repetition comes quickly, the material stays fresh, and you finish feeling that you know it.

A study of people learning word pairs from flashcards shows how misleading that feeling is. Each learner studied some pairs spread out and others bunched together. Spacing produced better final scores for 90 per cent of the learners. Yet after their first session, 72 per cent said bunching them had worked better.

Learners, in other words, judge a method by how easy it feels rather than by how much it leaves behind. This is an illusion of competence, and it steers people toward the schedule that serves them less well.

If gaps help, how long should they be? It depends on how long the memory must last. In one study, more than 1,350 people learned facts, reviewed them after a gap of up to three and a half months, and were tested up to a year later.

At every test delay, recall first rose as the gap grew, then slowly fell once it grew too long. The best gap grew with the delay, but more slowly: a fifth to two-fifths of the wait for a test a week away, but only a twentieth to a tenth of a year. That span, from learning to when you need the memory, is the retention interval.

A family of four psychologists tested this on themselves for nine years with 300 foreign words. Relearning sessions 56 days apart let them use half the sessions that two-week gaps needed for the same result.

Each successful review makes forgetting slower than before, so the next review can safely wait longer. That suggests a schedule of expanding intervals, in which every gap is longer than the one before.

The idea appeared in a 1932 book on study by the British psychologist C. A. Mace: "Acts of revision should be spaced in gradually increasing intervals, roughly intervals of one day, two days, four days, eight days, and so on." Each gap there is double the last.

In 1967 the linguist Paul Pimsleur published a schedule for language courses that begins in seconds: five seconds, then 25 seconds, two minutes, ten minutes, and on to months and years, each gap roughly five times the one before. Both schedules rest on the same bet: that forgetting slows after each review.

Expanding schedules sound sensible, but do they beat uniform gaps, all the same length? A 1978 study of learning the names that go with faces found that they did. Later work was less kind.

In 2007 two psychologists compared expanding gaps with uniform gaps for learning word pairs. Ten minutes after practice the expanding schedule was ahead, but two days later the uniform gaps had won. The deciding factor seemed to be the first test. An expanding schedule tests you again very soon, while recall is still easy, and delaying that first test helped memory whichever schedule followed.

A 2021 review of the research found no reliable difference between expanding and uniform schedules. What matters most is spacing reviews out at all, and letting the first review wait long enough to take some effort.

Memorising the Qur'an has always gone together with revising it. A hadith recorded by al-Bukhārī and Muslim has the Prophet telling Muslims to keep reciting the Qur'an regularly, because it slips away faster than a camel breaks free of its rope.

Muslim scholars also wrote down schedules for revision. Al-Zarnūjī, a scholar of Central Asia in the twelfth or thirteenth century, gave one in his manual for students, Taʿlīm al-Mutaʿallim (Instruction of the Student), which is still taught in traditional Islamic schools. A student, he wrote, should repeat yesterday's lesson five times, the lesson of the day before four times, then three, two and finally one: one fewer each day.

That is not a modern expanding schedule, but it rests on a related idea. The newer the lesson, the more often it needs going over.

Keeping track of many different gaps by hand is hard, so in 1972 the German science writer Sebastian Leitner proposed a simple method with paper flashcards and a box divided into compartments. It became known as the Leitner system.

Every new card starts in the first compartment. When you recall a card correctly, it moves forward one compartment. When you miss it, it goes all the way back to the first. Later compartments are reviewed less often, so a card you keep getting right comes back at longer and longer gaps, while a card you keep missing stays in front of you.

In Leitner's own design each compartment was wider than the last, from one centimetre to fourteen. You reviewed a compartment only when it filled up, so the wide back compartments came round far less often.

A computer can keep a separate schedule for every card and adjust it after every answer. In 1987 the Polish researcher Piotr Woźniak wrote a rule for his SuperMemo program: review a new card after one day, then after six days, then multiply the gap each time by an ease factor that starts at 2.5. When you struggle with a card its ease factor drops, so the software shows it more often.

Newer schedulers go further. FSRS, an open-source scheduling algorithm available in the popular Anki app since 2023, predicts for each card the probability that you can still recall it. It schedules the next review for when your predicted recall reaches the target you set, 90 per cent unless you change it.

The program cannot remember for you, but it can choose the moment.

Spacing and testing work best together. The psychologists Katherine Rawson and John Dunlosky call the combination successive relearning. In each session you practise recalling every item, checking the answer after each attempt, until you have recalled each one correctly. Then, in later sessions spread over days or weeks, you do it again.

The rule for stopping matters. A session ends not when the time is up but when every item has been recalled correctly.

In classroom studies, students used successive relearning for part of a course. They scored higher on course exams for that material than for material they studied their own way, and the advantage held on a test weeks later.