If you want to learn more about spaced repetition, read that Gwern article. But for the most basic idea, here’s a simple variant of spaced repetition that even a child can learn. In fact, this is the system I plan on teaching my children, once they are old enough to benefit from it.

• Write down facts as question-and-answer pairs: the question can go on one side of a card, and the answer on the other.2² These cards are known as flashcards, an alternative name for the question is a prompt. Stick new cards in a box marked Daily.
• Every day, go through the box marked Daily and for each card, read the question and formulate an answer in your head. Flip the card. If your answer matched the real answer, put the card in a box marked Semiweekly. If your answer did not match the real answer, put the card back in the Daily box.
• Two times a week, go through the box marked Semiweekly and test yourself on each card in it. If you remembered the answer, move it to a box marked Biweekly. If you didn’t remember, move it back to the box Daily.
• Every other week, go through the box Semiweekly the same way: if you remember, keep the card in Semiweekly. If you forget, move the card back to Daily.

The general idea is to tap into the apparent geometric/exponential decay of memories: if we test ourselves3³ It is important that we honestly test ourselves. Active recall is the technical term. just as a memory is about to fade, it seems to last longer, which means we can increase the time between testing quite drastically every time we successfully remember something. The practical outcome of this is that we can invest very little time in each individual fact, and still remember it for a long time.

The system I presented above is a variation of what’s known as the Leitner system and it’s optimised for simple use with physical cards and boxes. The exact parameters aren’t that important; we can vary the practise intervals and the number of boxes4⁴ If the Semiweekly box grows too large, we can add a Quarterly box or whatever.. We don’t have to do all the Semiweekly cards in one sitting5⁵ It is probably more comfortable to do 7 % of them every day, so that after 14 days we have been through all of them.. However, the more we try to optimise the Leitner system, the more difficult it will be to keep track of everything using paper cards and boxes. This is where computers come in: spaced repetition software can keep track of everything for us and just present us with the most urgent recall tasks at any given time.

Since you and I are disciplined adults who are able to harness computers for good and not get distracted by the possibilities they offer for entertainment, we can skip the physical cards and use software instead.6⁶ I personally use org-drill, since I live in Emacs anyway and it’s nice to be able to convert notes into batches of flashcards with regexes and keyboard macros. But there are many other alternatives. For my children, I want to emphasise that this is not a computer technique, it is a human memory exploit.

One reason I didn’t continue with spaced repetition after university was that I sucked at writing flashcard prompts. That skill is vital to being successful with spaced repetition. How to do it well is a separate article, but here are some initial pointers:

If you ever find that, “Yeah, I remembered this answer…but not all of it”, that means you need to refine the flashcard and break it down into multiple flashcards. The danger of incomplete or inconsistent recollection is that (apparently – I haven’t dug into the original research) it can suppress some of the memories we are trying to form.

Example: I was reading a book on enumerative combinatorics7⁷ Mathematics of Choice; Niven; Mathematical Association of America; 1975. and encountered the concept of a derangement. Old me would have written one prompt asking something like “The number of derangements of a sequence length n is?…” which covers way too much ground for a single flashcard. Instead, I made 10 flashcards, starting from the basic “What is a derangement?” going through notation variants to derivation and then some consequences and examples of when the concept is relevant.

Good prompt-writing is a lot of work, and I believe (though I haven’t seen anyone else say it) that a significant chunk of the improved recall that comes from spaced repetition is due to spending time and effort on the prompts.

Writing good prompts forces one to circle around a concept, look at it from multiple angles, probe its properties, link it to other concepts through similarities and differences, reason about consequences and significance, derive parts of it from more fundamental pieces, and come up with a few concrete examples of it. These are the things that really build understanding.

Since I’ve only been doing this for three months now, there’s one thing I don’t yet know: will increased retention result in improved retrieval? In other words, I may memorise lots of useful things like what a derangement is and how many of them there are for a sequence of a given length, but will I be able to pick that knowledge up any time I have a problem that actually involves derangements?

One way to help this process is to also make flashcards based on situational cues, i.e. to try to imagine a situation in which the knowledge would be useful, and then write a prompt to force recollection of the knowledge in response to that cue. But what about situations that I didn’t think of ahead of time? They probably outnumbers the ones I did.

Will I know where to go in my brain to find the knowledge that would be useful in any given situation? Time will tell.

• Learning Some Logarithms
• Who Was On the Winning Team?
• Reading Slightly More Incrementally
• Huffman Codes – How Do They Work?