The Forgetting Curve: Ebbinghaus's 140-year-old discovery
In 1885, Hermann Ebbinghaus published "Über das Gedächtnis" — and, in doing so, produced one of the most consequential findings in the history of cognitive science. Ebbinghaus memorised thousands of nonsense syllables, then tested his own recall at regular intervals. The result was what we now call the Forgetting Curve: a roughly exponential decay in retention that begins almost immediately after learning.
The numbers are sobering. Without review, learners typically forget:
- ~40% of new material within 20 minutes
- ~56% within one hour
- ~66% within one day
- ~75% within six days
The Forgetting Curve is not a sign of a poor learner or a weak memory. It is the default behaviour of the human memory system. Our brains are ruthlessly efficient — they discard information that is not used, freeing resources for what actually recurs in daily life.
Why cramming doesn't work
Cramming — compressing many hours of study into the 24–48 hours before an assessment — produces high short-term recall and catastrophic long-term retention. This has been reproduced in hundreds of experiments since Ebbinghaus. The mechanism is well-understood: cramming produces a single exposure per piece of information, which is not enough to consolidate the memory trace.
Performance on a test taken the day after cramming can look impressive. Performance on a test taken four weeks later, without any intermediate review, is typically not substantially better than chance for material that was not already highly familiar.
For homeschooling families, this matters because the compliance documents you generate — VRQA learning plans, NESA statements, NY IHIP quarterly reports — are supposed to reflect durable learning. A child who crammed their multiplication tables for two weeks and then stopped drilling them has not genuinely mastered multiplication in the sense that VRQA assessors mean by "mastery." The Forgetting Curve is eroding that knowledge every day.
What FSRS-23 is and why it matters
FSRS stands for Free Spaced Repetition Scheduler. Version 2023 (FSRS-23) is the algorithm adopted by Anki 23+ as its default scheduler, replacing the SM-2 algorithm that had been the industry standard since 1987.
FSRS-23 is based on the DSR model (Difficulty, Stability, Retrievability):
- Difficulty is a per-card parameter representing how hard a specific piece of knowledge is for a specific learner. Cards that the learner consistently struggles with acquire a higher difficulty score over time.
- Stability represents how long a successfully recalled memory will last before dropping below a target retrievability threshold (Anki's default is 90% — that is, FSRS tries to ensure you see a card just before your probability of recalling it falls below 90%).
- Retrievability is the current estimated probability of successfully recalling the information right now.
The key innovation over SM-2 is that FSRS-23 was trained on a dataset of tens of millions of real Anki reviews, making its predictions of forgetting much more accurate than the hand-tuned heuristics of SM-2. It also models individual learner parameters — someone who forgets quickly will get shorter intervals; someone with high retention gets longer ones.
In practical terms: after each review, FSRS-23 computes the next review date by finding the point in the future where your estimated retrievability will have decayed to 90%. Review it then, and you reinforce the memory at exactly the moment it is most beneficial. Review it too early, and the reinforcement is weak (the memory is still fully active — there is nothing to strengthen). Review it too late, and you are essentially relearning rather than reviewing.
The difference between FSRS and BKT mastery tracking
FSRS and BKT (Bayesian Knowledge Tracing) answer different questions, and a well-designed adaptive learning system uses both.
BKT asks: "Has this learner acquired this skill?" It maintains a probability (pMaster) that the learner has a stable internal representation of the knowledge, separate from the surface-level fluctuations of performance. pMaster accounts for slipping (getting a question wrong despite knowing) and guessing (getting it right without knowing). It is a diagnosis of whether learning has occurred.
FSRS asks: "Is this memory still accessible? When should we review it to prevent forgetting?" It does not diagnose whether you ever learned something — it assumes you have a memory trace and models how long that trace will remain retrievable.
The practical difference: BKT is what determines whether a student should move on to the next curriculum descriptor. FSRS determines when they should come back to descriptors they have already passed.
Think of it this way: BKT is the gating mechanism (did they learn it?), and FSRS is the maintenance mechanism (will they keep knowing it?). A system that uses only BKT risks the Forgetting Curve erasing hard-won mastery. A system that uses only FSRS lacks a principled way to decide when a student is ready to progress.
How Docent combines both
Docent runs BKT and FSRS in parallel for every curriculum descriptor a student has encountered.
When a student works on AC9M4N03 (Year 4 Maths — multiplication and division), the BKT model tracks their pMaster. Once pMaster exceeds the mastery threshold (default 0.85), the system marks the descriptor as mastered and lets the student progress to the next descriptor in the sequence.
At the same time, FSRS begins scheduling future review sessions for AC9M4N03. These reviews appear in the student's queue automatically — typically a short session of three to five questions — at intervals determined by the student's individual stability and difficulty parameters. The reviews are not graded or stressful; they are low-stakes retrieval practice designed to reset the Forgetting Curve.
If a review session reveals that the student has forgotten the material (pMaster falls significantly on the review questions), the descriptor is re-queued for instruction, not just review. The system distinguishes between "needs a quick reminder" and "needs re-teaching."
A practical example: Year 4 Maths
Imagine a Year 4 student working on multiplication. Over two weeks of daily sessions, she achieves pMaster 0.88 on AC9M4N03 — the BKT model is confident she has mastered it. She moves on to division.
FSRS-23 has been computing her stability score across those two weeks. Based on her response pattern — she answered confidently and quickly when she knew answers, but took longer on harder facts — her stability score is approximately 14 days. FSRS schedules her first review of AC9M4N03 fourteen days after mastery was declared.
On day 14, she completes a three-question review. She gets two correct immediately and one after a brief pause. FSRS updates her stability upward — the successful retrieval after 14 days has strengthened the memory trace. The next review is scheduled for 30 days later.
If she continues to recall successfully at each review, the intervals grow: 14 days → 30 days → 65 days → 4 months → 9 months. Eventually, multiplication facts are a permanent part of her long-term memory — not because she drilled them endlessly, but because FSRS timed the reviews to occur at exactly the moments that maximise the memory-strengthening effect.
What this means for your compliance documents
A mastery log that includes FSRS review history is substantially more credible to assessors than one that only shows initial mastery dates. When a VRQA assessor sees that AC9M4N03 was first mastered in February and has been successfully retrieved at regular intervals through June — with stability scores showing growing confidence — they are looking at evidence of durable learning, not a one-off performance. That is the difference between a plan that describes what your child did and one that demonstrates what your child knows.