One does not learn computing by using a hand calculator, but one can forget arithmetic. Perlis 1982↩

Listing other neuroprosthetics is hard. It’s an interesting idea, but as proponents of externalism like Andy Clark have found, it’s easier to feel that externalism is meaningful than to nail down a clear definition which separates a neuroprosthetic or part of one’s mind from a random tool you like or find useful. Consider whether a pencil and paper a neuroprosthetic: clearly it is not for a child learning to write, who must carefully compose the words in his mind and put them down one after another, but it is not so clear for an adult who has been writing all his life and can doodle or write down thoughts without thinking about them and may even be surprised at what they happened to write.

I like this definition: a neuroprosthetic is anything whose results you use without further thought. So in the classic example, when Otto needs to go somewhere, he never thinks I am an amnesiac who stores locations in my notepad, and I must look up the location - he just looks up the location. A good heuristic would be anything whose destruction leaves one feeling lost, slow, stupid, or ignorant.

By this standard, I can think of only a few tools I use without noticeable thought:

• keybindings such as window manager shortcuts, in particular shortcuts for Google searches; on occasion, XMonad’s Prompt gets inscrutably wedged, locking it. When this happens, I have to restart X because I Google everything and the keybinding is so engrained that not using it is unbearable. It would be like trying to write with your weak hand.
• Google Calendar and PredictionBook: it is incredible how many followups or reminders or regularly happening tasks I can put into Google Calendar or PB. I have outsourced many habits or thoughts to them, and I no longer think of it as anything special. If either were gone, I would feel frightened - what events were passing, what beliefs falsified, what opportunities opening up (or closing!) that I had suddenly become ignorant of?
• Evernote, for a similar reason; many of my memories have ceased to be things like octopuses see too fast to watch TV and so only HDTV or UHDTV works for them; I read this in Orion Magazine and become things like octopus TV Evernote, and if I want to know what it was about octopuses & TV, well, I’ll have to look it up in Evernote. Mnemosyne plays a similar role for me, but there the memories are much clearer on their own because of the spaced repetition.
• my website gwern.net; I’ve had to say many times that I don’t know what I think about something, but whatever that is, it’s on my website. (A more extreme form of the Evernote/Mnemosyne neuroprosthetic.) A commenter once wrote that reading gwern.net felt like he was crawling around in my head. He was more right than he realized.

Ulrich Neisser, as quoted in Retrieval practice and the maintenance of knowledge, Bjork 1988.↩

From Close the Book. Recall. Write It Down: That old study method still works, researchers say. So why don’t professors preach it?; The Chronicle of Higher Education

Two psychology journals have recently published papers showing that this strategy works, the latest findings from a decades-old body of research. When students study on their own, active recall - recitation, for instance, or flashcards and other self-quizzing - is the most effective way to inscribe something in long-term memory. Yet many college instructors are only dimly familiar with that research…

From The Spacing Effect: A Case Study in the Failure to Apply the Results of Psychological Research (Dempster 1988), whose title alone summarizes the situation (see also Kelley 2007, Making Minds: What’s Wrong with Education - and What Should We Do About It?):

Second, it [the spacing effect] is remarkably robust. In many cases, two spaced presentations are about twice as effective as two massed presentations (e.g., Hintzman, 1974; Melton, 1970), and the difference between them increases as the frequency of repetition increases (Underwood, 1970)…

The spacing effect was known as early as 1885 when Ebbinghaus published the results of his seminal work on memory. With himself as the subject, Ebbinghaus found that for a single 12-syllable series, 68 immediately successive repetitions had the effect of making possible an errorless recital after seven additional repetitions on the following day. However, the same effect was achieved by only 38 distributed repetitions spread over 3 days. On the basis of this and other related findings, Ebbinghaus concluded that with any considerable number of repetitions a suitable distribution of them over a space of time is decidedly more advantageous than the massing of them at a single time (Ebbinghaus, 1885/1913. p. 89)

Son & Simon 2012:

Furthermore, even after acknowledging the benefits of spacing, changing teaching practices proved to be enormously difficult. Delaney et al (2010) wrote: Anecdotally, high school teachers and college professors seem to teach in a linear fashion without repetition and give three or four noncumulative exams. (p. 130). Focusing on the math domain, where one might expect a very easy-to-review-and-to-space strategy, Rohrer (2009) points out that mathematics textbooks usually present topics in a non-spaced, non-mixed fashion. Even much earlier, Vash (1989) had written: Education policy setters know perfectly well that [spaced practice] works better [than massed practice]. They don’t care. It isn’t tidy. It doesn’t let teachers teach a unit and dust off their hands quickly with a nice sense of Well, that’s done. (p. 1547).

• Rohrer, D. (2009). The effects of spacing and mixing practice problems. Journal for Research in Mathematics Education, 40, 4-17
• Vash, C. L. (1989). The spacing effect: A case study in the failure to apply the results of psychological research. American Psychologist, 44, 1547 (a comment on Dempster’s article?)

From Psychology: An Introduction:

In one practical demonstration of the spacing effect, Bahrick, Bahrick, Bahrick, & Bahrick (1993) showed that retention of foreign language vocabulary was greatly enhanced if practice sessions were spaced far apart. For example, Thirteen retraining sessions spaced at 56 days yielded retention comparable to 26 sessions spaced at 14 days. In other words, subjects could use half as many study sessions, if the study sessions were spread over a time period four times as long.

Synaptic evidence for the efficacy of spaced learning, Kramar et al 2012 (Take your time: Neurobiology sheds light on the superiority of spaced vs. massed learning):

The superiority of spaced vs. massed training is a fundamental feature of learning. Here, we describe unanticipated timing rules for the production of long-term potentiation (LTP) in adult rat hippocampal slices that can account for one temporal segment of the spaced trials phenomenon. Successive bouts of naturalistic theta burst stimulation of field CA1 afferents markedly enhanced previously saturated LTP if spaced apart by 1 h or longer, but were without effect when shorter intervals were used. Analyses of F-actin-enriched spines to identify potentiated synapses indicated that the added LTP obtained with delayed theta trains involved recruitment of synapses that were missed by the first stimulation bout. Single spine glutamate-uncaging experiments confirmed that less than half of the spines in adult hippocampus are primed to undergo plasticity under baseline conditions, suggesting that intrinsic variability among individual synapses imposes a repetitive presentation requirement for maximizing the percentage of potentiated connections. We propose that a combination of local diffusion from initially modified spines coupled with much later membrane insertion events dictate that the repetitions be widely spaced. Thus, the synaptic mechanisms described here provide a neurobiological explanation for one component of a poorly understood, ubiquitous aspect of learning.

There are many studies to the effect that active recall is best. Here’s one recent study, Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping, Karpicke 2011 (covered in Science Daily and the NYT):

Educators rely heavily on learning activities that encourage elaborative studying, while activities that require students to practice retrieving and reconstructing knowledge are used less frequently. Here, we show that practicing retrieval produces greater gains in meaningful learning than elaborative studying with concept mapping. The advantage of retrieval practice generalized across texts identical to those commonly found in science education. The advantage of retrieval practice was observed with test questions that assessed comprehension and required students to make inferences. The advantage of retrieval practice occurred even when the criterial test involved creating concept maps. Our findings support the theory that retrieval practice enhances learning by retrieval-specific mechanisms rather than by elaborative study processes. Retrieval practice is an effective tool to promote conceptual learning about science.

From Forget What You Know About Good Study Habits. New York Times;

Cognitive scientists do not deny that honest-to-goodness cramming can lead to a better grade on a given exam. But hurriedly jam-packing a brain is akin to speed-packing a cheap suitcase, as most students quickly learn - it holds its new load for a while, then most everything falls out….When the neural suitcase is packed carefully and gradually, it holds its contents for far, far longer. An hour of study tonight, an hour on the weekend, another session a week from now: such so-called spacing improves later recall, without requiring students to put in more overall study effort or pay more attention, dozens of studies have found.

The idea is that forgetting is the friend of learning, said Dr. Kornell. When you forget something, it allows you to relearn, and do so effectively, the next time you see it.

That’s one reason cognitive scientists see testing itself - or practice tests and quizzes - as a powerful tool of learning, rather than merely assessment. The process of retrieving an idea is not like pulling a book from a shelf; it seems to fundamentally alter the way the information is subsequently stored, making it far more accessible in the future.

In one of his own experiments, Dr. Roediger and Jeffrey Karpicke, who is now at Purdue University, had college students study science passages from a reading comprehension test, in short study periods. When students studied the same material twice, in back-to-back sessions, they did very well on a test given immediately afterward, then began to forget the material. But if they studied the passage just once and did a practice test in the second session, they did very well on one test two days later, and another given a week later.

The Mathematics of Gambling, Thorp 1984, Section Two: The Wheels, Chapter 4, pg43-44:

It was the spring of 1955. I was finishing my second year of graduate physics at U.C.L.A…I changed my field of study from physics to mathematics…I attended classes and studied from 50 to 60 hours a week, generally including Saturdays and Sundays. I had read about the psychology of learning in order to be able to work longer and harder. I found that spaced learning worked well: study for an hour, then take a break of at least ten minutes (shower, meal, tea, errands, etc.). One Sunday afternoon about 3 p.m., I came to the co-op dining room for a tea break…My head was bubbling with physics equations, and several of my good friends were sitting around chatting.

From Final Jeopardy: Man Vs. Machine and the Quest to Know Everything, by Stephen Baker, pg 214:

The program he put together tested him on categories, gauged his strengths (sciences, NFL football) and weaknesses (fashion, Broadway shows), and then directed him toward the preparation most likely to pay off in his own match. To patch these holes in his knowledge, Craig used a free online tool called Anki, which provides electronic flash cards for hundreds of fields of study, from Japanese vocabulary to European monarchs. The program, in Craig’s words, is based on psychological research on the forgetting curve. It helps people find holes in their knowledge and determines how often they need those areas to be reviewed to keep them in mind. In going over world capitals, for example, the system learns quickly that a user like Craig knows London, Paris, and Rome, so it might spend more time reinforcing the capital of, say, Kazakhstan. (And what would be the Kazakh capital? Astana, Craig said in a flash. It used to be Almaty, but they moved it.)

Our Interview With Jeopardy! Champion Arthur Chu:

[Chu:] …Jeopardy! is aimed at the sort of average TV viewer, so they’re not going to ask things that are pointlessly obscure…So I used a program called Anki which uses a method called spaced repetition. It keeps track of where you’re doing well or poorly, and pushes you to study the flashcards you don’t know as well, until you develop an even knowledge base about a particular subject, and I just made flashcards for those specific things. I memorized all the world capitals, it wasn’t that hard once I had the flashcards and was using them every day. I memorized the US State Nicknames (they’re on Wikipedia), memorized the basic important facts about the 44 US Presidents. I really focused on those. But there’s a lot more stuff to know. I went on Jeopardy! knowing that there was stuff I didn’t know. For instance, everyone laughs about sports - but I also knew that [sports clues] were the least likely to come up in Double Jeopardy and Final Jeopardy and be very important. So I decided I shouldn’t sweat it too much, I should just recognize that I didn’t know them and let that go, as long as I can get the high value clues. So that was how I prepared.

This image is only evocative! I whipped this up in Inkscape one night; it certainly is not a representation of a real experimental dataset or anything like that. Here are two more.↩

Alan J. Perlis, Epigrams in Programming (1982)↩

Web developer Persol writes in August 2012:

I actually wrote a site that did this [spaced repetition] a few months ago. I had about 4000 users who had actually gone through a complete session…As guessed, the problem is that I couldn’t get people to start forming it as a habit. There is no immediate payback. Less than 20 people out of 4000 did more than one session….Additionally, there are at least 18 competitors. Here’s the list I made at the time. Very few seem to be successful. I shut the site down about a month ago. There are numerous free competitors which don’t have any great annoyances. I wouldn’t suggest starting another of these sites unless you figured out an effective way to gamify it.

…~4000 people finished a session. Many more tried than 4000… I just couldn’t determine which users were bots that registered randomly vs users that didn’t finish the first session.

• Tried: lots (but unknown)
• Finished 1 session: ~4000
• Finished >1 session: ~20 [0.5%]

Play it Again: The Master Psychopharmacology Program as an Example of Interval Learning in Bite-Sized Portions, Stahl et al 2010:

Since Ebbinghaus’ time, a voluminous amount of research has confirmed this simple but important fact: the retention of new information degrades rapidly unless it is reviewed in some manner. A modern example of this loss of knowledge without repetition is a study of cardiopulmonary resuscitation (CPR) skills that demonstrated rapid decay in the year following training. By 3 years post-training only 2.4% were able to perform CPR successfully.⁶ Another recent study of physicians taking a tutorial they rated as very good or excellent showed mean knowledge scores increasing from 50% before the tutorial to 76% immediately afterward.⁷ However, score gains were only half as great 3-8 days later and incredibly, there was no [statistically-]significant knowledge retention measurable at all at 55 days.⁷ Similar results have been reported by us in follow-up studies of knowledge retention from continuing medical education programs.¹ [Stahl SM, Davis RL. Best Practices for Medical Educators. Carlsbad, CA: NEI Press; 2009]

…This may be due to the fact that lectures with assigned reading are the easiest for teachers. Also, medical learning is rarely measured immediately after a lecture or after reading new material for the first time and then measured again a few days or weeks later, so that the low retention rates of this approach may not be widely appreciated.^1,4 No wonder formal medical education conferences without enabling or practice-reinforcing strategies appear to have relatively little impact on practice and healthcare outcomes.^8,9,10

One study looking at cramming is the 1993 Cramming: A barrier to student success, a way to beat the system or an effective learning strategy?, Vacha et al 1993, abstract:

Tested the hypothesis that cramming is an ineffective study strategy by examining the weekly study diaries of 166 undergraduates. All Ss also completed an end-of-semester questionnaire measuring study habits. Ss were classified in the following study patterns: ideal, confident, zealous, or crammer. Contrary to the hypothesis, results suggest that cramming is an effective approach, most widespread in courses using take-home essay examinations and major research papers. Crammers’ grades were as good as or better than those of Ss using other strategies; the longer Ss were in college, the more likely it was that they crammed. Crammers studied more hours than most students and were as interested in their courses as other students.

Note that there is no measure of long-term retention, suggesting that people who only care about grades are rationally choosing to cram.↩

Anki has its Cram Mode and Mnemosyne 2.0 has a cramming plugin. When a SRS doesn’t have explicit support, it’s always possible to game the algorithm by setting one’s scores artificially low, so the SR algorithm thinks you are stupid and need to do a lot of repetitions.↩

Examining the examiners: Why are we so bad at assessing students?, Newstead 2002:

Conway, Cohen and Stanhope (1992) looked at long term memory for the information presented on a psychology course. They found that some types of information, especially that relating to research methods, were remembered better than others. But in a follow up analysis, they found that the type of assessment used had an effect on memory. In essence, material assessed by continuous assessment was more likely to be remembered than information assessed by exams.

Stahl 2010:

For example, simple restudying allows the learner to reexperience all of the material but actually produces poor long-term retention.^25,26,35 Why do students keep studying the original materials? Certainly if this is their only choice, then restudying is a necessary tactic. Another answer may be that repeated studying falsely inflates students’ confidence in their ability to remember in the future because they sense that they understand it now, and they and their instructors may be unaware of the many studies that show poor retention on delayed testing after this form of repetition.^25,26,35

From Kornell et al 2010:

Contrary to the massing-aids-induction hypothesis, final test performance was consistently and considerably superior in the spaced condition. A large majority of participants, however, judged massing to be more effective than spacing, despite making the judgment after taking the test.

…Metacognitive judgments-that is, judgments about one’s own memory and cognition-are often based on feelings of fluency(e.g., see Benjamin, Bjork, & Schwartz, 1998; Rhodes & Castel, 2008). Because massing naturally leads to feelings of fluency and increases short-term task performance during learning, learners frequently rate spacing as less effective than massing, even when their performance shows the opposite pattern (Baddeley & Longman 1978; Kornell & Bjork, 2008; Simon & Bjork, 2001; Zechmeister & Shaughnessy, 1980). Averaged across Kornell and Bjork’s (2008) experiments, for example, more than 80% of participants rated massing as equally or more effective than spacing,whereas only 15% of participants actually performed better in the massed condition than in the spaced condition.

…Such an illusion was apparent in the induction condition. Contrary to previous research, however, participants gave higher ratings for spacing than massing during repetition learning (see, e.g., Simon & Bjork, 2001; Zechmeister & Shaughnessy, 1980). This outcome may have occurred because of a process of a habituation: Six presentations and a total of 30 s spent studying a single painting may have come to seem inefficient and pointless. Thus, there appears to be a turning point in metacognitive ratings based on fluency: As fluency increases, metacognitive ratings increase up to a point, but as fluency continues to increase and encoding or retrieval becomes too easy, metacognitive ratings may begin to decrease.

…In advance of their research, Kornell and Bjork (2008) were convinced that such inductive learning would benefit from massing, yet their results showed the opposite. Undaunted, we remained convinced that spacing would be more beneficial for repetition learning than for inductive learning- especially for older adults, given their overall declines in episodic memory. The current results disconfirmed our expectations once again. If our intuitions are erroneous, despite our years spent proving and praising the spacing effect-including roughly 40 years’ worth contributed by Robert A. Bjork-those of the average student are surely mistaken as well (as the inaccuracy of the participants’ metacognitive ratings suggests). We have, perhaps, fallen victim to the illusion that making learning easy makes learning effective, rather than recognizing that spacing is a desirable difficulty (Bjork 1994) that enhances inductive learning as well as repetition learning well into old age.

From Son & Simon 2012:

Thus, while spacing may boost learning, it may be thought to be relatively inefficient in terms of study time. As we discuss later, this feeling of inefficiency may be one of the reasons that spacing is not the more popular strategy. Interestingly, in that same study (Baddeley & Longman 1978; and see also Pirolli & Anderson 1985 and Woodworth & Schlosberg 1954 [Experimental Psychology]), there was evidence of such a thing as laboring in vain. That is, exceeding a certain number of hours of practice a day (more than approximately 2 h) led to no increases in learning, as might be expected. Related to the deficient-processing theory mentioned above, these results are crucial in understanding intuitively how the spacing effect works: We simply get burnt out. These data are also analogous to the cognitive literature on overlearning, which shows that while continuous study over long periods of time might seem beneficial (and even feel good) in the short-term, the benefits disappear soon afterwards (Rohrer et al. 2005; Rohrer and Taylor 2006)…In the above-described Baddeley and Longman’s (1978) study, for example, after postal workers practiced typing in either massed or spaced study sessions, they had to indicate how satisfied they were with the training. Results showed that while spacing led to the best learning, it was the least liked. Similarly, Simon & Bjork (2001) found that people preferred the massing strategy on a motor learning task.

• Baddeley, A. D., & Longman, D. J. A. (1978). The influence of length and frequency of training session on the rate of learning to type. Ergonomics, 21, 627-635
• Pirolli, P., & Anderson, J. R. (1985). The role of practice in fact retrieval

Study strategies of college students: Are self-testing and scheduling related to achievement?, Hartwig & Dunlosky 2012:

Previous studies, such as those by Kornell and Bjork (Psychonomic Bulletin & Review, 14:219-224, 2007) and Karpicke, Butler, and Roediger (Memory, 17:471-479, 2009), have surveyed college students’ use of various study strategies, including self-testing and rereading. These studies have documented that some students do use self-testing (but largely for monitoring memory) and rereading, but the researchers did not assess whether individual differences in strategy use were related to student achievement. Thus, we surveyed 324 undergraduates about their study habits as well as their college grade point average (GPA). Importantly, the survey included questions about self-testing, scheduling one’s study, and a checklist of strategies commonly used by students or recommended by cognitive research. Use of self-testing and rereading were both positively associated with GPA. Scheduling of study time was also an important factor: Low performers were more likely to engage in late-night studying than were high performers; massing (vs. spacing) of study was associated with the use of fewer study strategies overall; and all students-but especially low performers-were driven by impending deadlines. Thus, self-testing, rereading, and scheduling of study play important roles in real-world student achievement.

(See also Dunlosky et al 2013.) Note the self-testing correlation excludes flashcards, a result that both the authors and me found surprising. The sleep connection is interesting, given the hypothesized link between stronger memory formation & studying before a good night’s sleep - you can hardly get a good night’s sleep if you are cramming late into the night (correlated with lower grades) but you can if you do so at a reasonable time in the evening (in time to get a solid night).

See also Susser & McCabe 2012:

Laboratory studies have demonstrated the long-term memory benefits of studying material in multiple distributed sessions as opposed to one massed session, given an identical amount of overall study time (i.e., the spacing effect). The current study goes beyond the laboratory to investigate whether undergraduates know about the advantage of spaced study, to what extent they use it in their own studying, and what factors might influence its utilization. Results from a web-based survey indicated that participants (n = 285) were aware of the benefits of spaced study and would use a higher level of spacing under ideal compared to realistic circumstances. However, self-reported use of spacing was intermediate, similar to massing and several other study strategies, and ranked well below commonly used strategies such as rereading notes. Several factors were endorsed as important in the decision to distribute study time, including the perceived difficulty of an upcoming exam, the amount of material to learn, how heavily an exam is weighed in the course grade, and the value of the material. Further, level of metacognitive self-regulation and use of elaboration strategies were associated with higher rates of spaced study.

Analytic Culture in the US Intelligence Community: An Ethnographic Study, Johnson 2005, pg89:

To investigate the intensity of instructional interactions, Art Graesser and Natalie Person 1994 compared questioning and answering in classrooms with those in tutorial settings.⁵ They found that classroom groups of students ask about three questions an hour and that any single student in a classroom asks about 0.11 questions per hour. In contrast, they found that students in individual tutorial sessions asked 20-30 questions an hour and were required to answer 117-146 questions per hour. Reviews of the intensity of interaction that occurs in technology-based instruction have found even more active student response levels. [J. D. Fletcher, Technology, the Columbus Effect, and the Third Revolution in Learning.]

Although Graesser & Person 1994 also found that sheer number of questions was not necessarily important, suggesting diminishing marginal returns or perhaps bad question asking.↩

SuperMemo is based on the insight that there is an ideal moment to practice what you’ve learned. Practice too soon and you waste your time. Practice too late and you’ve forgotten the material and have to relearn it. The right time to practice is just at the moment you’re about to forget. Unfortunately, this moment is different for every person and each bit of information. Imagine a pile of thousands of flash cards. Somewhere in this pile are the ones you should be practicing right now. Which are they? Gary Wolf, Want to Remember Everything You’ll Ever Learn? Surrender to This Algorithm, Wired Magazine↩

Make no mistake about it: Computers process numbers - not symbols. We measure our understanding (and control) by the extent to which we can arithmetize an activity. Perlis, ibid.↩

this exponential expansion is how a SR program can handle continual input of cards: if cards were scheduled at fixed intervals, like every other day, review would soon become quite impossible - I have >18000 items in Mnemosyne, but I don’t have time to review 9000 questions a day!↩

See the 2008 meta-analysis, Learning Styles: Concepts and Evidence (APS press release); from the abstract:

…in order to demonstrate that optimal learning requires that students receive instruction tailored to their putative learning style, the experiment must reveal a specific type of interaction between learning style and instructional method: Students with one learning style achieve the best educational outcome when given an instructional method that differs from the instructional method producing the best outcome for students with a different learning style. In other words, the instructional method that proves most effective for students with one learning style is not the most effective method for students with a different learning style.

Our review of the literature disclosed ample evidence that children and adults will, if asked, express preferences about how they prefer information to be presented to them. There is also plentiful evidence arguing that people differ in the degree to which they have some fairly specific aptitudes for different kinds of thinking and for processing different types of information. However, we found virtually no evidence for the interaction pattern mentioned above, which was judged to be a precondition for validating the educational applications of learning styles. Although the literature on learning styles is enormous, very few studies have even used an experimental methodology capable of testing the validity of learning styles applied to education. Moreover, of those that did use an appropriate method, several found results that flatly contradict the popular meshing hypothesis.

We conclude therefore, that at present, there is no adequate evidence base to justify incorporating learning-styles assessments into general educational practice. Thus, limited education resources would better be devoted to adopting other educational practices that have a strong evidence base, of which there are an increasing number. However, given the lack of methodologically sound studies of learning styles, it would be an error to conclude that all possible versions of learning styles have been tested and found wanting; many have simply not been tested at all.

Fritz, C. O., Morris, P. E., Acton, M., Etkind, R., & Voelkel, A. R (2007). Comparing and combining expanding retrieval practice and the keyword mnemonic for foreign vocabulary learning. Applied Cognitive Psychology, 21, 499-526.↩

From Balota et al 2006, describing Spitzer 1939, Studies in retention:

Spitzer (1939) incorporated a form of expanded retrieval in a study designed to assess the ability of sixth graders to learn science facts. Impressively, Spitzer tested over 3600 students in Iowa-the entire sixth-grade population of 91 elementary schools at the time. The students read two articles, one on peanuts and the other on bamboo, and were given a 25-item multiple choice test to assess their knowledge (such as To which family of plants does bamboo belong?). Spitzer tested a total of nine groups, manipulating both the timing of the test (administered immediately or after various delays) and the number of identical tests students received (one to three). Spitzer did not incorporate massed or equal interval retrieval conditions, but he had at least two groups that were tested on an expanding schedule of retrieval, in which the intervals between tests were separated by the passage of time (in days) rather than by intervening to-be-learned information. For example, in one of the groups, the first test was given immediately, the second test was given seven days after the first test, and the third test was given 63 days after the second test. Thus, in essence, this group was tested on a 0-7-63 day expanding retrieval schedule. Spitzer compared performance of the expanded retrieval group to a group given a single test 63 days after reading the original article. On the first (immediate) test, the expanded retrieval group correctly answered 53% of the questions. After 63 days and two previous tests, their score was still an impressive 43%. The single test group correctly answered only 25% of the original items after 63 days, giving the expanded retrieval group an 18% retention advantage. This is quite impressive, given that this large benefit remained after a 63-day retention interval. Similar beneficial effects were found in a group tested on a 0-1-21 day expanded retrieval schedule compared to a group given a single test after 21 days. Of course, this study does not decouple the effects of testing from spacing or expansion, but the results do clearly indicate considerable learning and retention using the expanded repeated testing procedure. Spitzer concluded that …examinations are learning devices and should not be considered only as tools for measuring achievement of pupils (p. 656, italics added)

Distributing Learning Over Time: The Spacing Effect in Children’s Acquisition and Generalization of Science Concepts, Vlach & Sandhofer 2012:

The spacing effect describes the robust finding that long-term learning is promoted when learning events are spaced out in time, rather than presented in immediate succession. Studies of the spacing effect have focused on memory processes rather than for other types of learning, such as the acquisition and generalization of new concepts. In this study, early elementary school children (5-7 year-olds; N = 36) were presented with science lessons on one of three schedules: massed, clumped, and spaced. The results revealed that spacing lessons out in time resulted in higher generalization performance for both simple and complex concepts. Spaced learning schedules promote several types of learning, strengthening the implications of the spacing effect for educational practices and curriculum.

See also Balch 2006, who compared spacing & massed in an introductory psychology course as well.↩

Roediger & Karpicke 2006b again.↩

Balota et al 2006 review:

No feedback or correction was given to subjects if they made errors or omitted answers. Landauer & Bjork 1978 found that the expanding-interval schedule produced better recall than equal-interval testing on a final test at the end of the session, and equal-interval testing, in turn, produced better recall than did initial massed testing. Thus, despite the fact that massed testing produced nearly errorless performance during the acquisition phase, the other two schedules produced better retention on the final test given at the end of the session. However, the difference favoring the expanding retrieval schedule over the equal-interval schedule was fairly small at around 10%. In research following up Landauer and Bjork’s (1978) original experiments, practically all studies have found that spaced schedules of retrieval (whether equal-interval or expanding schedules) produce better retention on a final test given later than do massed retrieval tests given immediately after presentation (e.g., Cull, 2000; Cull, Shaughnessy, & Zechmeister, 1996), although exceptions do exist. For example, in Experiments 3 and 4 of Cull et al (1996), massed testing produced performance as good as equal-interval testing on a 5-5-5 schedule, but most other experiments have found that any spaced schedule of testing (either equal-interval or expanding) is better than a massed schedule for performance on a delayed test. However, whether expanding schedules are better than equal-interval schedules for long-term retention-the other part of Landauer and Bjork’s interesting findings-remains an open question. Balota, Duchek, and Logan (in press) have provided a thorough consideration of the relevant evidence and have shown that it is mixed at best, and that most researchers have found no difference between the two schedules of testing. That is, performance on a final test at the end of a session often shows no difference in performance between equal-interval and expanding retrieval schedules.

Cull, for those curious (Cull, W. L. (2000). Untangling the benefits of multiple study opportunities and repeated testing for cued recall. Applied Cognitive Psychology, 14, 215-235):

Cull (2000) compared expanded retrieval to equal interval spaced retrieval in a series of four experiments designed to mimic typical teaching or study strategies encountered by students. He examined the role of testing versus simply restudying the material, feedback, and various retention intervals on final test performance. Paired associates (an uncommon word paired with a common word, such as bairn-print) were presented in a manner similar to the flashcard techniques students often use to learn vocabulary words. The intervals between retrieval attempts of to-be-learned information ranged from minutes in some experiments to days in others. Interestingly, across four experiments, Cull did not find any evidence of an advantage of an expanded condition over a uniform spaced condition (i.e., no [substantial] expanded retrieval effect), although both conditions consistently produced large advantages over massed presentations. He concluded that distributed testing of any kind, expanded or equal interval, can be an effective learning aid for teachers to provide for their students.

The Balota et al 2006 review offers a synthesis of current theories on how massed and spaced differ, based on memory encoding:

According to encoding variability theory, performance on a memory test is dependent upon the overlap between the contextual information available at the time of test and the contextual information available during encoding. During massed study, there is relatively little time for contextual elements to fluctuate between presentations and so this condition produces the highest performance in an immediate memory test, when the test context strongly overlaps with the same contextual information encoded during both of the massed presentations. In contrast, when there is spacing between the items, there is time for fluctuation to take place between the presentations during study, and hence there is an increased likelihood of having multiple unique contexts encoded. Because a delayed test will also allow fluctuation of context, it is better to have multiple unique contexts encoded, as in the spaced presentation format, as opposed to a single encoded context, as in the massed presentation format.

Storm et al 2010 did 3 experiments on reading comprehension:

On a test 1 week later, recall was enhanced by the expanding schedule, but only when the task between successive retrievals was highly interfering with memory for the passage. These results suggest that the extent to which learners benefit from expanding retrieval practice depends on the degree to which the to-be-learned information is vulnerable to forgetting.

From Mnemosyne’s Principles page:

The Mnemosyne algorithm is very similar to SM2 used in one of the early versions of SuperMemo. There are some modifications that deal with early and late repetitions, and also to add a small, healthy dose of randomness to the intervals. Supermemo now uses SM11. However, we are a bit skeptical that the huge complexity of the newer SM algorithms provides for a statistically relevant benefit. But, that is one of the facts we hope to find out with our data collection. We will only make modifications to our algorithms based on common sense or if the data tells us that there is a statistically relevant reason to do so.

Balota et al 2006:

Carpenter and DeLosh (2005, Exp. 2) have recently investigated face-name learning under massed, expanded (1-3-5), and equal interval (3-3-3) conditions. This study also involved study and study and test procedures during the acquisition phase. Carpenter and DeLosh found a large effect of spacing, but no evidence of a benefit of expanded over equal interval practice. In fact, Carpenter and DeLosh reported a reliable benefit of the equal interval condition over the expanded retrieval condition.

Balota et al 2006 again:

Rea and Modigliani (1985) tested the effectiveness of expanded retrieval in a third-grade classroom setting. In separate conditions, students were given new multiplication problems or spelling words to learn. The problem or word was presented audiovisually once and then tested on either a massed retrieval schedule of 0-0-0-0 or an expanding schedule of 0-1-2-4, in which the intervals involved being tested on old items or learning new items. After each test trial for a given item, the item was re-presented in its entirety so students received feedback on what they were learning. Performance during the learning phase was at 100% for both spelling words and multiplication facts. On an immediate final retention test, Rea and Modigliani found a performance advantage for all items-math and spelling- practiced on an expanding schedule compared to the massed retrieval schedule. They suggested, as have others, that spacing combined with the high success rate inherent in the expanded retrieval schedule produced better retention than massed retrieval practice. However, as in Spitzer’s study, Rea and Modigliani did not test an appropriate equal interval spacing condition. Hence, their finding that expanded retrieval is superior to massed retrieval in third graders could simply reflect the superiority of spaced versus massed rehearsal-in other words, the spacing effect.

Balota et al 2006.↩

Balota et al 2006; >1 is rare in psychology, see One Hundred Years of Social Psychology Quantitatively Described, Bond et al 2003↩

Rohrer & Taylor 2006↩

Balota et al 2006:

…long-term retention of information has been demonstrated over several days in some cases (e.g., Camp et al, 1996). For example, in the latter study, Camp et al employed an expanding retrieval strategy to train 23 individuals with mild to moderate AD to refer to a daily calendar as a cue to remember to perform various personal activities (e.g., take medication). Following a baseline phase to determine whether subjects would spontaneously use the calendar, spaced retrieval training was implemented by repeatedly asking the subject the question, How are you going to remember what to do each day? at expanding time intervals. The results indicated that 20/23 subjects did learn the strategy (i.e., to look at the calendar) and retained it over a 1-week period.

Rohrer & Taylor 2006 warns us, though, about many of the other math studies:

In one meta-analysis by Donovan and Radosevich (1999), for instance, the size of the spacing effect declined sharply as conceptual difficulty of the task increased from low (e.g. rotary pursuit) to average (e.g. word list recall) to high (e.g. puzzle). By this finding, the benefits of spaced practise may be muted for many mathematics tasks.

What is especially nice about this study was that not only did it use high-quality (intelligent & motivated) college students (United States Air Force Academy), the conditions were relatively controlled - both groups had the same homework (so equal testing effect), but like Rohrer & Taylor 2006/2007, the distribution was what varied:

The course topics, textbook, handouts, reading assignments, and graded assignments (with the exception of quiz, homework, and participation points) were identical for the treatment and control groups. The listing of homework assignments in the syllabus differed between groups. The control group was assigned daily homework related to the topic(s) presented that day in class. Peterson (1971) calls this the vertical model for assigning mathematics homework. The treatment group was assigned homework in accordance with a distributed organizational pattern that combines practice on current topics and reinforcement of previously covered topics. Under the distributed model, approximately 40% of the problems on a given topic were assigned the day the topic was first introduced, with an additional 20% assigned on the next lesson and the remaining 40% of problems on the topic assigned on subsequent lessons (Hirsch et al, 1983). In Hirsch’s research and in this study, after the initial homework assignment, problem(s) representing a given topic resurfaced on the 2nd, 4th, 7th, 12th, and 21st lesson. Consequently, treatment group homework for lesson one consisted of only one topic; homework for lessons two and three consisted of two topics; and homework for lesson four through six consisted of three topics. This pattern continued as new topics were added and was applied to all non-exam, non-laboratory lessons. As shown by Tables 1 and 2, the same homework problems were assigned to both groups with only the pattern of assignment differing. Because of the nature of the distributed practice model, homework for the treatment group contained fewer problems (relative to the control group) early in the semester with the number of problems increasing as the semester progressed. Later in the semester, homework for the treatment group contained more problems (relative to the control group)….The USAFA routinely collects study time data. After each exam, a large sample of cadets (at least 60% of the course population) anonymously reported the amount of time (in minutes) spent studying for the exam. Time spent studying was approximately equal for both groups (see Table 5). Descriptive data revels that, for both the treatment and control group, study time for the third exam was at least 16% greater than study time for any other exam. Study time for the final exam was at least 68% greater than study time for any of the hourly exams (see Table 5)

…The treatment produced an effect size (f 2) of 0.013 on the first exam, 0.029 on the second exam, 0.035 on the fourth exam, and 0.040 on the final course percentage grade. Although the effect sizes appear to be small, the treatment group outscored the control group in every case. A mean difference of 5.13 percentage points on the first, second, and fourth exam translates to an advantage of about a third of a letter grade for students in the treatment group. In addition, higher minimum scores earned by the treatment group may indicate that the distributed practice treatment served to eliminate the extremely low scores (refer to Table 3)….Oddly, the distributed practice treatment did not produce a [statistically-]significant effect on final exam scores. One possible cause for the disparity was the USAFA policy exempting the top performers from the final exam. Of the 16 exempted students, 11 were from the treatment group with only 5 from the control group.

Balch 2006 abstract:

Two introductory psychology classes (N = 145) participated in a counterbalanced classroom experiment that demonstrated the spacing effect and, by analogy, the benefits of distributed study. After hearing words presented twice in either a massed or distributed manner, participants recalled the words and scored their recall protocols, reliably remembering more distributed than massed words. Posttest scores on a multiple-choice quiz covering points illustrated by the experiment averaged about twice the comparable pretest scores, indicating the effectiveness of the exercise in conveying content. Students’ subjective ratings suggested that the experiment helped convince them of the benefits of distributed study.

See Cepeda et al 2006↩

Commins, S., Cunningham, L., Harvey, D., and Walsh, D. (2003). Massed but not spaced training impairs spatial memory. Behavioural Brain Research 139, 215-223↩

Galluccio & Rovee-Collier 2006, Nonuniform effects of reinstatement within the time window. Learning and Motivation, 37, 1-17.↩

See the previous sections for many using children; one previously uncited is Toppino 1993, The spacing effect in preschool children’s free recall of pictures and words; but Toppino et al 2009 adds some interesting qualifiers to spaced repetition in the young:

Preschoolers, elementary school children, and college students exhibited a spacing effect in the free recall of pictures when learning was intentional. When learning was incidental and a shallow processing task requiring little semantic processing was used during list presentation, young adults still exhibited a spacing effect, but children consistently failed to do so. Children, however, did manifest a spacing effect in incidental learning when an elaborate semantic processing task was used.

Another previously uncited study: Glenberg, A. M. (1979), Component-levels theory of the effects of spacing of repetitions on recall and recognition. Memory & Cognition, 7, 95-112.↩

See Kornell et al 2010; Simone et al 2012 shows the spacing benefits but reduced in magnitude in its 56-74 year old subjects, similar to Jackson et al 2012 and Maddox 2013↩

Mammarella, N., Russo, R., & Avons, S. E. (2002). Spacing effects in cued-memory tasks for unfamiliar faces and nonwords. Memory & Cognition, 30, 1238-1251↩

Childers, J. B., & Tomasello, M. (2002). Two-year-olds learn novel nouns, verbs, and conventional actions from massed or distributed exposures. Developmental Psychology, 38, 967-978↩

eg. Fishman et al 1968↩

The famous 10,000 hours of practice figure may not be as true or important as Ericsson and publicizers like Malcolm Gladwell imply, given the high variance of expertise against time, and results from sports showing smaller time investments, and Ericsson absurdly deny the powerful role of genetics and the necessary condition of having talent but the insight of deliberate practice helping talented people probably is real. One may be able to get away with 3,000 hours rather than 10,000, but one isn’t going to do that with mindless repetition or no repetitions.↩

Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95, 393-40↩

From Kornell et al 2010:

The benefits of spacing seem to diminish or disappear when to-be-learned items are not repeated exactly (Appleton-Knapp, Bjork, & Wickens, 2005)…a number of studies have shown that massing, rather than spacing, promotes inductive learning. These studies have generally employed relatively simple perceptual stimuli that facilitate experimental control (Gagné, 1950; Goldstone, 1996; Kurtz & Hovland, 1956; [Whitman J. R., & Garner, W. R. (1963). Concept learning as a function of the form of internal structure. Journal of Verbal Learning & Verbal Behavior, 2, 195-202]).

High error rates - indicating one didn’t actually learn the card contents in the first place - seem to be connected to failures of the spacing effect; there’s some evidence that people naturally choose to mass study when they don’t yet know the material.↩

SuperMemo as a new tool increasing the productivity of a programmer. A case study: programming in Object Windows↩

The 20 years look like this (note the scientific notation): [0.742675, 0.27044575182838654, 0.15275979054767388, 0.10348750000000001, 7.751290630254386e-2, 6.187922936397532e-2, 5.161829250474865e-2, 4.445884397854832e-2, 3.923055555555555e-2, 3.5275438307530015e-2, 3.219809429218694e-2, 2.9748098818459235e-2, 2.7759942051635768e-2, 2.6120309801216147e-2, 2.474928593068675e-2, 2.35890625e-2, 2.2596898475825956e-2, 2.1740583401051353e-2, 2.0995431241707652e-2, 2.0342238287817983e-2]↩

modulo things where knowing it is useful even if you don’t need it often - it can be a brick in a pyramid of knowledge; cf. page 3 of Wolf:

The problem of forgetting might not torment us so much if we could only convince ourselves that remembering isn’t important. Perhaps the things we learn - words, dates, formulas, historical and biographical details - don’t really matter. Facts can be looked up. That’s what the Internet is for. When it comes to learning, what really matters is how things fit together. We master the stories, the schemas, the frameworks, the paradigms; we rehearse the lingo; we swim in the episteme.

The disadvantage of this comforting notion is that it’s false. The people who criticize memorization - how happy would they be to spell out every letter of every word they read? asks Robert Bjork, chair of UCLA’s psychology department and one of the most eminent memory researchers. After all, Bjork notes, children learn to read whole words through intense practice, and every time we enter a new field we become children again. You can’t escape memorization, he says. There is an initial process of learning the names of things. That’s a stage we all go through. It’s all the more important to go through it rapidly. The human brain is a marvel of associative processing, but in order to make associations, data must be loaded into memory.

See Stephen R. Schmidt’s webpage Theories of Forgetting, which cites Woodworth & Schlosbeg (1961) when presenting a log graph of various studies’ forgetting curves.↩

which neatly addresses the issue of such mailing lists being useless (who learns a word after just one exposure?).↩

Mnemosyne in this case constitutes both a way to learn the quotes so I can use them, and a waste book; just the other day I had 3 or 4 apposite quotes for an essay because I had entered them into Mnemosyne months or years ago.↩

It’s well known that any speaker of a language understands many more words than they will ever use or be able to explicitly generate, that their reading vocabulary exceeds their writing vocabulary; less well-known is that on many problems, one can guess at well above random rates even while feeling unsure & ignorant, necessitating psychologists to employ forced-choice paradigms. Even less known is the capacity of recognition memory or implicit memory; this memory can apply to things like recognizing images or text or music, typing, puzzle solving, etc. Andrew Drucker, in Multiplying 10-digit numbers using Flickr: The power of recognition memory, employs visual memory to calculate $9883603368 \times 4288997768 = 42390752785149282624$; he cites as precedent Standing 1973:

In one of the most widely-cited studies on recognition memory, Standing showed participants an epic 10,000 photographs over the course of 5 days, with 5 seconds’ exposure per image. He then tested their familiarity, essentially as described above. The participants showed an 83% success rate, suggesting that they had become familiar with about 6,600 images during their ordeal. Other volunteers, trained on a smaller collection of 1,000 images selected for vividness, had a 94% success rate.

One sometimes sees people argue that something is insecure or unguessable or free from possible placebo effect because it involves too many objects to explicitly memorize, but as these examples make clear, recognition memory can happen quickly and store surprisingly large amounts of information. This could be used for authentication (see for example Bojinov et al 2012; HN discussion) or message since recognition memory could be exploited as a sort of secure communication system. Two parties can share a set of 20,000 photographs (10,000 pairs); to send a message, have a messenger spend 5 days on 10,000 picked ones; and then to receive it, ask him to recognize which photograph he saw in each of the 10,000 pairs. The subject not only does not know what the binary message is or what means, he can’t even produce it since he cannot remember the photographs!

At an 80% accuracy rate, we can even calculate how many bits of information can be entrusted to the messenger using Shannon’s theorem; a calculation gives 5.8 kilobits as the upper limit: if p = 0.2 (based on the 80% success rate), then $\frac{10000}{1 - (p \times log_2 p + (1 - p)\times(log_2 (1 - p)))} = 5807.44$. So we see that Frank Herbert was right after all: the securest way to send a message is through a distrans messenger. (The downside is that the implicit recognition memory decays considerably; see Landauer 1986 for adjusted estimates.)↩

In this vein, I am reminded of what a former polyphasic sleeper told me:

I’ve been polyphasic for about a year. (Not anymore; kills my memory.)…Anki reps, mostly. I found that I could do proper review sessions for about 2-3 days and would hit an impenetrable wall. I couldn’t learn a single new card and had total brain fog until I got 3 hours more sleep. That, however, would reset my adaptation. The whole effect is a bit less pronounced on Everyman, but not much. It is however easier to add sleep when you already have a core. I didn’t notice any other major mental impairment after the initial sleep deprivation.

For a more recent review, see Philips et al 2013.↩

Presumably one would immediately give them all some high grade like 5 to avoid suddenly having a daily load of 500 cards for a while.↩

All numbers from 2 May 2011.↩

Smaller is better.↩

For Mnemosyne 2.x, Ullrich is working on an official Mnemosyne iPhone client which will have very easy syncing.↩

Wired↩

See Page 4, Wolf 2008:

The spacing effect was one of the proudest lab-derived discoveries, and it was interesting precisely because it was not obvious, even to professional teachers. The same year that Neisser revolted, Robert Bjork, working with Thomas Landauer of Bell Labs, published the results of two experiments involving nearly 700 undergraduate students. Landauer and Bjork were looking for the optimal moment to rehearse something so that it would later be remembered. Their results were impressive: The best time to study something is at the moment you are about to forget it. And yet - as Neisser might have predicted - that insight was useless in the real world.

When I first read of SuperMemo, I had already taken a class in cognitive psychology and was reasonably familiar with Ebbinghaus’s forgetting curve - so my reaction to its methodology was Huxley’s: How extremely stupid not to have thought of that!↩

See page 7, Wolf 2008

And yet now, as I grin broadly and wave to the gawkers, it occurs to me that the cold rationality of his approach may be only a surface feature and that, when linked to genuine rewards, even the chilliest of systems can have a certain visceral appeal. By projecting the achievement of extreme memory back along the forgetting curve, by provably linking the distant future - when we will know so much - to the few minutes we devote to studying today, Wozniak has found a way to condition his temperament along with his memory. He is making the future noticeable. He is trying not just to learn many things but to warm the process of learning itself with a draft of utopian ecstasy.