Spaced repetition

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The secret to learning more while studying less.

What is spaced repetition?

Spaced repetition is the process by which new or difficult concepts are studied more frequently than easier known concepts —thereby perpetually challenging you on your weakest areas of knowledge.

Does spaced repetition work?

Cognitive science shows that spacing repetitions within the optimal time intervals has actually been shown to be the most important factor in your ability to retain knowledge. It is literally how our brains are wired to encode memories.

Most spaced repetition tools fall short.

It has historically been inconvenient to study in frequent, bite-sized sessions: Physical books are tough to transport; while most flashcard apps are either 'vocab-only', limited in their analytics, difficult to use, unrefined in their repetition algorithms, or inflexible in their content creation & study features.

Brainscape has optimized spaced repetition.

Our web & mobile app finally makes spaced repetition more accessible, by respecting or leveraging other key pillars of cognitive science such as motivation, hyperbolic discounting, active recall, self-assessment, motivation & metacognition.

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It works because we focus on your weaknesses.

Brainscape's spaced repetition algorithm places you into a virtuous cycle that builds upon your knowledge:

Fact: The more you use Brainscape the better you learn.

Research has shown that Brainscape's spaced repetition algorithm improves both knowledge retention and test scores when compared to other study methods, like books and traditional flashcards.

Traditional flashcards
* Percent correct on post-test after 30 mins of studying, in a controlled experiment at Columbia University


Brainscape is a web and mobile study application designed to improve the retention of declarative knowledge. It complements the well-known benefits of spaced repetition with additional features that improve learner motivation, reduce the burden of planning study sessions, and deepen the level of cognitive processing involved in each exposure.

This paper assesses Brainscape's application of the latest research into education and cognitive science. We conclude that using Brainscape is among the world's most scientifically valid ways to enhance both learning speed and retention for any subject matter that can be studied via text, imagery, and/or sound.

Keywords: spaced repetition, expanding effect, metacognition, proximal learning, judgment of learning, confidence-based repetition, scaffolding, feedback, motivation, Bloom's 2 Sigma Problem, active recall, retrieval practice, social learning

The complete cognitive science behind Brainscape.

Table of contents:

  • Abstract
  • Table on contents
  • Introduction
  • Improving motivation & planning
  • Deepening cognitive provessing
  • Mitigating forgetting with confidence-based repetition
  • Conclusions
  • References


Educators throughout history have intuitively understood that personalized instruction is among the most effective methods of imparting knowledge and skills to others. From ancient craft apprenticeships, through today's academic tutoring businesses, we've consistently found that personalized human instruction offers a level of adaptivity that cannot easily be attained with large class sizes.

Psychologist Benjamin Bloom famously illustrated the benefits of such personalized instruction in his influential 1984 study, where he showed that students receiving 1-on-1 tutoring were able to perform a whopping 2 standard deviations higher on achievement tests than students who did not receive personalized interventions, conveying an extreme advantage (Bloom, 1984). Social justice advocates have accordingly recognized these inequities and have lobbied for smaller class sizes and against the expensive tutors enjoyed only by the elites.

Yet there may be a more practical and affordably scalable solution to the so-called "2 Sigma Problem", with the answer hiding in Bloom's original 1984 paper itself.

The key is to examine the variables impacting student achievement other than tutorial instruction. It turns out that four of Bloom's other top success factors, when measured individually, still have an impressive 1-sigma impact on learning outcomes. The opportunity unforeseen by Bloom and his researchers is that these factors could eventually be combined by educational software to create a potentially greater aggregate benefit than human tutorial instruction. (See Figure 1.)

Figure 1: Effect of selected alterable variables on student achievement (Bloom, 1984)

Object of change process

Alterable variable

Effect size

Tutorial instruction
Tutorial instruction
Tutorial instruction
Tutorial instruction
Tutorial instruction
Tutorial instruction
Tutorial instruction
Tutorial instruction
Figure 1: Note that activities including reinforcement, corrective feedback, cues & explanations, and student time on task proved to have a significantly higher impact than other traditional darlings such as cooperative learning, written homework, classroom morale, or home environment intervention

"Student time on task", for example, could be enhanced by software features that both improve motivation, through the use of frequent feedback and variable rewards; and by features that help students with planning their study sessions, through the use of learning schedules and the provision of a mobile interface that a student could access easily on their smartphone.

Similarly, the benefits of breaking concepts into more digestible "cues & explanations" could be leveraged by a flashcard-like Q&A software that engages users' active recall and metacognitive self-assessment faculties, thereby deepening the cognitive processing involved with each exposure. The programs' spaced repetition algorithms can also automate the processes of "corrective feedback" and "reinforcement" and thus mitigate the forgetting that would otherwise occur with traditional study methods.

The confluence of these four major ideas is what has motivated the Brainscape team to create our learning software in the way that we have.

Brainscape is a web and mobile study application that advances upon the traditional flashcard concept by improving student motivation, alleviating the burdens of planning study sessions, and deepening the amount of cognitive processing involved in each exposure -- all in the service of crafting a personalized spaced repetition algorithm that mitigates forgetting and enhances retention.

Millions of students, teachers, tutors, corporate trainers, and independent learners of all ages have used Brainscape to find, create, organize, and share flashcards for thousands of subjects, ranging from science, to law, to foreign languages. These flashcards can be studied in a web browser or smartphone, and come equipped with an engaging user experience that repeats concepts within a specific personalized interval of time, based on the user's self-rated confidence of each flashcards.

Improving study motivation & planning.

Long-term motivation is a primary prerequisite to any deliberate learning endeavor. Whether that motivation is driven by intrinsic interest in the subject, by professional ambition, by the desire to learn to communicate in a foreign language, or simply by the fear of parental punishment in the event of poor test scores, the prospect of an eventual "endgame" is a necessary spark that catalyzes any sustained educational pursuit.

The problem is that humans are not inherently skilled at conjuring the required short-term motivation that allows us to make progress toward those long-term goals in smaller steps. We suffer from a phenomenon known as hyperbolic discounting (or delay discounting), in which our instinctive brains subconsciously prefer smaller but more immediate rewards, even as our conscious brains still want the longer-term prize (Ainslie & Haslam 1992).

Fitness and diet are often cited as typical examples of delay discounting. We may want to get into physical shape, but that motivation does not necessarily ensure that we will schedule adequate gym time today. We may want to lose weight, but that chocolate cake looks so delicious right now.

To address this well-known myopia, students with financial means have traditionally hired personal human tutors to enforce structured study sessions onto their calendars, in the same way that they might pay for a personal trainer to schedule them a series of workout appointments they can't afford to miss.

Such forced accountability confers an unfair advantage upon students who are able to hire a human study coach, versus those left to wrestle with their own hyperbolic discounting weaknesses. Brainscape aims to bridge these gaps by providing the rigor that is necessary for learners to maintain short-term motivation and to schedule appropriately spaced study sessions over time.

Reducing logistical barriers to studying.

The first way Brainscape improves motivation to study is actually by doing the inverse: removing the biggest short- term de-motivators.

As most of us painfully know, traditional studying tends to involve activities like (i) remembering which books and notes to pack into our bags, (ii) finding a table in a quiet place where we can "spread out" our papers, and (iii) navigating to the point in our study materials where we last "left off". The collective burden of such activities can entail several minutes of preparation time, thereby imposing a daunting level of cognitive effort just to get started.

Brainscape reduces the barriers to initiating a study session in three major ways:

1. By providing convenient access through any web browser, smart phone, or tablet (eliminating the need to remember which study materials to pack);

2. By allowing the user to resume studying with a single button upon launch of the app (which automatically chooses the optimal next concept to review -- See Figure 2); and

3. By limiting each study session to a manageable set of only 10 flashcards (which can be easily extended to 10 more cards with the click of a single button -- See Figure 3)

Figure 2: The arrow indicates the user's ability to easily resume studying with a single click, on exactly the flashcard that is at the boundary of the user's Zone of Proximal Development. Brainscape users no longer have to remember where they left off or decide what to study next.
Figure 3: Note that each Brainscape study "Round" is a short, predictable 10 cards, which maintains a low barrier to getting started and establishing good study habits.

Orbell and Verplanken (2010), show that people are significantly more likely to establish a positive new habit if they reduce the number of steps and the amount of time necessary to perform each repetition of the habit. Just as keeping your blender on your counter makes you more likely to make your daily smoothie, Brainscape's one-click Continue Studying button makes learners more likely to study by eliminating all possible barriers to initiating a short study session.

Forecasting required study time.

The second key ingredient to improving study motivation is to help the learner establish a plan.

Human tutors typically provide this service by assessing the student's existing rate of learning and the amount of material remaining to be mastered, and by generating an estimate of the net amount of study time remaining. Simply knowing this concrete number increases the student's likelihood of remembering to study as they work toward their long-term mastery goal.

Unfortunately, students without access to a personal tutor often neglect to estimate their current rate of learning and therefore overwhelmingly tend to underestimate the time required to invest in their studies. Without a persistent reminder of the size of the remaining study burden, students end up "cramming" at the last minute, which dramatically reduces their longer-term memory retention per unit of time spent studying (Pashler et al., 2007).

Brainscape alleviates this knowledge gap by providing students with a continually revised estimate of the amount of study time needed to reach 100% mastery of a given topic. After each 10-flashcard "Round" is completed, the "Checkpoint" screen gives the student an updated projection of study time remaining (in addition to summarizing the progress made during the Round).

Figure 4 shows an example of Brainscape's Checkpoint screen, which includes an estimate of the student's remaining time needed to master the subject. After each Round, this estimate is updated to reflect their mean cumulative increase in self-rated "confidence points", per minute of time spent studying the subject thus far.

Figure 4: After each Round is completed, the Checkpoint screen provides an updated estimate of Study Time Remaining.

This "Study Time Remaining" estimate is a vast improvement upon the uninformed guess students otherwise have to make about the study time required to master a given topic. It gives students a key tool to help them appropriately allocate their remaining study sessions over the ensuing days, weeks, or months studying the subject, which is made convenient through Brainscape’s availability on both the computer and mobile devices.

Presenting immediate feedback.

Once a student has finally overcome the logistical and planning demotivators and has initiated a study session, she then has to grapple with the next unfortunate reality: the process of studying itself can be a tedious and thankless task.

This is particularly true in modern times, where we have become so accustomed to frequent dopamine hits and self- validating reassurances. Not every student has a personal human tutor to selectively dole out positive affirmations or constructive criticisms at just the right adaptive cadence.

Brainscape mitigates study monotony by giving and requesting four types of constant feedback:

1. Correct answers are revealed immediately. Unlike certain quiz applications that present correct answers only at the end of the quiz, flashcards -- by definition -- reveal the correct answer as soon as the card is "flipped". Lally & Gardener (2013) show that instant feedback on correctness is more salient than summative feedback.

2. Users are required to rate their confidence in each flashcard. After each answer is revealed, the user must rate how well she had known the answer, on a scale of 1-5 (where 1 means that she had been clueless, and 5 means that she'd known it perfectly). See Figure 6. Not only does requiring the user to self-assess keep her attention more engaged, but it also deepens the strength of the memory trace, as we will explore later.

3. Confidence upgrades are celebrated via an animation. Whenever a flashcard's new confidence rating is higher than its previous rating, a satisfying animated "poof" appears in the margin, indicating the size of the upgrade. (e.g. An increase from 2 to 3 would be a "+1" animation.) See Figure 7. The use of animations is well known to enhance user engagement in a variety of software applications.

4. Cumulative feedback pushes users toward Round completion. As the user proceeds in her studying, she is able to see a colorful representation of all cards seen during the 10-card Round, with an indication of how many cards are remaining. Additionally, a "Confidence Gained" meter depicts the sum of all the "+X" animations accumulated during the Round. See Figure 7.

Figure 6: As each answer is displayed, Brainscape asks the user to rate her confidence on a 1-5 scale. This not only increases engagement and metacognitive effort, but it also provides key information that Brainscape uses to determine when to repeat the flashcard again.
Figure 7: Upon rating her confidence, the user sees a "+X" animation in the left panel, as well as two graphical representations of her cumulative confidence upgrades throughout the 10-card Round.

The confluence of these various forms of feedback conspire to maintain the user's attention and motivation for as long as possible, as she works toward the Checkpoint at the end of the 10-card Round.

Providing variable rewards.

A common limitation of positive habit formation is often the repetitiveness of the reward. At a certain point, another scoop of the same vanilla ice cream ceases to motivate good behavior in the same way it did at the beginning.

Software developers have long seized upon this truism by implementing more variable reward schedules that make their apps more addictive (Eyal, 2013). The so-called "Hooked Model" has been used from games to social networks to shape user behavior and our brains in general. When you don't know exactly what "likes", "retweets", or "achievements" you might unlock, you feel increasingly compelled to keep posting, scrolling, or playing in search of that next unexpected reward, thus resulting in higher levels of dopamine (Zald et al 2004).

Brainscape presents a modest manifestation of such variable reward on its Checkpoint screen. Even though the timing of this reward is fixed (every 10 flashcards), the content of the reward changes, in the form of newly presented information about the learner's progress:

1. Overall Mastery %. Recall from Figure 6 that the Study screen itself only shows the user's progress through the 10- card Round, not her progress through the entire subject area. The user's overall Mastery % is shown only when she hits the Checkpoint screen.

2. Study Time Remaining. The updated estimate of Study Time Remaining is recalculated after each Round, based on the Confidence Gained and Time Elapsed.

By withholding both of these key pieces of information until the completion of the Round, the Brainscape user experiences a knowledge gap that helps push her toward that 10-card goal. Many users report that they often even create a mental game for themselves, where they guess what that new estimate will be, before it is revealed on the Checkpoint screen.

The combination of convenient access, short sessions, ease of planning, frequent feedback, and variable rewards all contribute to a Brainscape Round being among the most motivating and painless ways to study. Students find it difficult to resist clicking the button to study "10 more cards."

Using social motivators.

As a final driver toward improving the desire to study, we consider the influence of peers on student behavior, through the powers of camaraderie and competition.

Case studies from Hogg & Abrams (1993) show that the mere knowledge that other people are engaging in a behavior increases a person's desire to engage in that behavior themselves. Brainscape's subject-specific Learners screen leverages this bandwagon effect to provide the user with reassurance that she is not alone, and that other smart students have chosen to study using the same method.

Similarly, the competitive nature of the Learners list motivates users to out-study their peers, due to fear, shame, or superiority. Even though Brainscape only shows leaderboards based on participation (e.g. Cards Studied or Days Streak) rather than mastery (which is self-reported), the drive to be exceptional can be among the most compelling motivators of all (Atkinson, 1964).