The forgetting curve, in plain terms
In the 1880s, the German psychologist Hermann Ebbinghaus memorized lists of nonsense syllables and tested himself at intervals. The result — the forgetting curve — has been replicated for over a century: memory for new material falls off steeply at first, then more slowly. Most of what we learn on Monday is unavailable by Friday, not because it was learned badly, but because that is how memory behaves by default.
The fix is in the curve itself. Each time you successfully recall something just before it slips away, the next forgetting happens more slowly. So the efficient schedule reviews a word right at the edge of forgetting: after a day, then a few days, then weeks, then months. The intervals stretch as the memory strengthens.
That is all spaced repetition is — review timed to the forgetting curve instead of to the calendar. The spacing effect it exploits is one of the oldest and most consistently replicated results in learning research.
Why cramming feels good and fails
Cramming works — for about a week. Massed practice produces fast, visible fluency: by the end of an hour with flashcards, a child answers instantly, and everyone concludes the words are learned. Memory researchers call this an illusion of competence. The words are highly available because they were just used, not because they are stored. Skip the review and watch the quiz scores a month later.
Robert Bjork's work on "desirable difficulties" — research we cite on our about page — explains the paradox: practice that feels harder, because some forgetting happened first, produces stronger long-term retention than practice that feels smooth. The slight struggle to retrieve a word is not a failure of the method. It is the method.
The same research favors retrieval over re-reading. Looking at a word list does little; pulling the word out of memory — ideally out loud — is what builds durable knowledge. A good system is therefore a quiz, not a slideshow.
What changes when the learner is eight
The memory math is the same for children; the packaging cannot be. An adult will tolerate a 40-minute review backlog out of guilt. A child will not, and should not. So the intake of new words has to be paced to keep the future review load short — Bóyǎ defaults to 7 new words a day, parent-adjustable — and sessions have to fit inside a real attention span: 15 to 20 minutes, ending cleanly.
Grading has to change too. Classic flashcard apps ask "how hard was that?" on a four-button scale — a question kids answer with whatever button is biggest. Bóyǎ rates difficulty implicitly, from correctness and response time, and a failed word simply re-enters a short learning cycle rather than a visible pile of shame.
And because the goal is spoken Mandarin, not quiz performance, retrieval should regularly happen out loud — recalling the tone (声调) and saying the word, not just recognizing it. The full method, including how this pairs with output-first speaking practice, is on How we teach.
What FSRS adds
Early spaced-repetition systems used fixed interval rules — the same "1 day, 6 days, then multiply" schedule for every learner and every card. FSRS (Free Spaced Repetition Scheduler), the open-source algorithm by Jarrett Ye that Bóyǎ uses, replaces the fixed rule with a model fitted to the learner's actual recall history. A word your child finds easy stretches to long intervals quickly; a confusable tone pair comes back sooner. No two children see the same schedule.
For a parent, the practical consequence is efficiency you can verify. Time goes only to the words at the edge of forgetting, so a short daily session is genuinely enough — most kids clear HSK 1 in about six weeks at 15 minutes a day, and the full HSK word lists stay learnable at the same calm pace all the way up. The dashboard then reports what actually matters: words retrieved correctly after three weeks without review. Mastery, not minutes.