Spaced Repitition and the Problem of Sets
Anki support user rjgoif
January 6, 2014
Introduction
Spaced repetition systems (SRSs) are a popular and effective collection of similar techniques to aid in rapid memorization and long-term retention. Many tools to aid in spaced repetition exist across various platforms, including in-browser applets, computer software for all three major modern operating systems, and mobile device/tablet applications. Anki is a popular service for SRS learning that free syncing of SRS cards and progress across PCs, iOS, and Android devices in addition to an in- browser study application. Anki, like most SRS platforms, does not have an explicit solution to the problem of memorizing lists. This document outlines my proposed solution.
1 Sets and SRS learning
According to the often-cited “Minimum Information Principle”,1 lists are not an efficient method of memorizing and retaining information. Instead, users are encouraged to break the set information into single associations that can be individually learned in an SRS review schedule. For example, if learning the first letters of the Greek alphabet, one might intuitively make a flash card like this: First 8 Greek letters:
α, β, γ, δ, ε, ζ, η, θ This violates the Minimum Information Principle; there is too much information on the card to rapidly integrate and reinforce to memory. There are different ways to reduce the information for SRS, such as cloze deletion: First 8 Greek letters:
α, β, , δ, ε, ζ, η, θ overlapping subset memorization via cloze deletion:
1 Greek letters: β, , ζ
γ, δ, ε
Greek letters: γ, , η
δ, ε, ζ and enumeration: Greek letter #3:
γ Each of these techniques has disadvantages. Although single-component cloze deletion is easy to implement in Anki and other SRS software without generating a large list of cards, it reinforces visual pattern recognition over comprehension with larger sets, making makes every-day recall more difficult.∗ Single-item enumeration does not share this problem, but reinforces the knowledge into discrete units which take extra mental time/effort to link together. This is not a natural way to memorize large sets of information.† Overlapping interval cloze deletion is a compromise between the above two methods, but requires a larger number of cards of varying cloze length, adding to the effort of creating the cards as well as the size of the stack to get through.
2 Full-set information utility
As mentioned above, an alphabet is an example of a set that is less useful as discrete information compared to as a whole unit; we do not teach children to associate a position to a letter (akin to the way multiplication tables are taught), but rather teach a rhyming song to emphasize the order in which the letters fall and their relationships to each other. Scripts are an even more extreme example of high-content, sequential information memorization.‡ An intuitive solution is sequentially revealed cards: the first item of a set is learned, which “unlocks” the card with the first two items, learning which will “unlock” the card with the first three, etc. However, as stated on the Anki user manual,2 “This might sound like a nice idea in theory, but in practice it is not practical . . . Entering new notes into Anki would become a complicated process, as you’d have to search through the rest of the deck and assign relationships between the old and new material.”
∗This is based on personal experience. †Try yourself: if the 12th letter of the English alphabet is L, is it easier to recite the 14th through 19th by associating each with a discrete number, or by mentally going through the childhood ABC song from L, skipping M, and recalling N–S? ‡Medicine also relies on rapid, sequential recall of dense (and vital) information. This is what prompted this document.
2 But, as demonstrated by the “one note→many cards” technique Anki uses to generate cloze and other flashcard formats, creating sequential cards for use in Anki’s SRS algorithm might not be difficult.
3 Proposed card method for sequential sets
Anki creates sequential cloze deletion cards from a single note containing multi- ple cloze designations, such as
first Greek letters: {{c1::α}}, {{c2::β}}, {{c3::γ}}, {{c4::δ}} creating four cards, each with a missing term contained by {{cn::}}: first Greek letters: , β, γ, δ
first Greek letters: α, , γ, δ
first Greek letters: α, β, , δ
first Greek letters: α, β, γ,
A possible variant would be a sequential deletion, in which the four cards generated by
first Greek letters: {{s1::α}}, {{s2::β}}, {{s3::γ}}, {{s4::δ}} would be sequentially harder: first Greek letters: , β, γ, δ
first Greek letters: , , γ, δ
first Greek letters: , , , δ
first Greek letters: , , ,
The only new rules required to be added to the Anki algorithm are: 1. cards s + 1, s + 2, . . . , smax remain buried until card s is learned. 2. card s + 1 is unburied when card s is learned. 3. card s is buried when card s + 1 is learned. 4. card s + 1 is buried when previously learned card s lapses. 5. card s − 1 is unburied and reset as “newly learned” when learned card s lapses. 6. card s − 1 is reburied when previously lapsed card s is relearned. 7. card s + 1 is unburied when previously lapsed card s is relearned.
3 This should∗ result a learned card and a new, unlearned card both in the SRS schedule. If the user lapses on card 3, Anki has no way of knowing if the lapse was from item 1, 2, or 3 in the cloze sequence. To count for this, Anki unburies card 2 while card 3 is being relearned. Should the user lapse on card 2 as well, Anki knows that the error was farther back and the user needs to either relearn position 2 or 1. Should the user forget all positions, this will “regress” the sequential cloze back to the first position, with all cards being marked as lapsed (but only the first card unburied).
new learned s1 lapsed s2 s3 s4 B D A C
Figure 1: example of a 4-card sequential cloze deletion SRS timeline
Figure 1 shows a hypothetical timeline following all fo the rules outlined above. Up to point A, the learner is progressing through the sequence with slight increasing difficulty. While having difficulty remembering the last deletion in the sequence (B), the user lapses on s3, which buries s4 and revives s2. Since s3 contains all of the information of s2, learning s3 is sufficient to move back to s4, which the user does by point C. However, the user has somehow forgotten all of the preceding information by point D, illustrating a regression back to the earliest card from the note.
4 Variation
Because the future sequential deletions (s + 1, s + 2 ... ) are revealed in card s, the user might be given too many “hints” to require enough active recall as new cards are unburied. In this case, varying the structure of the sequential cards may help:
first Greek letters: ,...
first Greek letters: , ,...
first Greek letters: , , ,...
first Greek letters: , , ,
I believe that more exposure is always better and that this will not be a problem in learning, especially considering that the “final” card is all blank: if the user
∗as I figure it, but I may have missed something important
4 doesn’t really know the ordered set, a regression with relearning is unavoidable. I haven’t had time to test this technique manually, but this variation could be attempted if the original procedure proves inefficient in long-term retention. Of course there could be myriad other problems I am not imagining. Is anyone interested and able to give this a try? I’d love to hear it.
References
1. Wozniak, P. Effective learning: Twenty rules of formulating knowledge.
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