Individual Spacing Algorithm Explainer

What This Skill Does

Generates a personalised spaced repetition schedule for a specific set of knowledge items based on student performance data, and explains the algorithm logic in teacher-friendly terms. This skill does NOT execute the spacing algorithm — execution requires a system like Anki, Quizlet, SuperMemo, or Kaku's own retention engine. What this skill does is DESIGN and EXPLAIN: given what students know and what they're forgetting, it produces a concrete review schedule with clear rationale for why each interval was chosen. The core insight from spacing research is that the optimal review interval depends on the desired retention period and the item's current memory strength. Ebbinghaus (1885) established that forgetting follows a predictable curve — steep initially, then gradually flattening. Cepeda et al. (2006) demonstrated in a comprehensive meta-analysis that spacing review across time produces substantially better long-term retention than massing the same amount of practice into a single session. The practical challenge is that the optimal interval is different for every student and every item — which is where personalisation becomes essential. AI is specifically valuable here because calculating optimal intervals across dozens of items for individual students is computationally trivial for a machine but practically impossible for a teacher doing it manually.

Evidence Foundation

Ebbinghaus (1885/1913) conducted the foundational experiments on forgetting, demonstrating that memory for newly learned material decays exponentially but that each subsequent review strengthens the memory trace and slows the rate of forgetting. This "forgetting curve" is the theoretical foundation for all spacing algorithms. Cepeda et al. (2006) conducted a meta-analysis of 254 studies on distributed practice, finding a robust spacing effect across a wide range of materials and age groups. They found that the optimal inter-study interval (ISI) depends on the retention interval (RI) — the time until the knowledge is needed. A rough guideline from their analysis: the optimal ISI is approximately 10-20% of the RI. So if you need knowledge for an exam in 30 days, optimal spacing is roughly every 3-6 days. Lindsey et al. (2014) moved spacing research into real classrooms, testing a personalised spacing algorithm with middle school students learning social studies. Their algorithm adjusted review intervals based on individual student performance, and they found significant improvements in long-term retention compared to massed review schedules chosen by teachers. Critically, the personalised algorithm outperformed a one-size-fits-all spacing schedule, demonstrating the value of individual calibration. Settles & Meeder (2016) developed the "half-life regression" model used in Duolingo, which predicts the probability that a student will recall a specific item at a specific time based on their individual history with that item. The model combines three variables: the number of times the item has been seen, the time since last review, and the student's accuracy on similar items. This represents the state of the art in practical, large-scale spacing algorithms. Pashler et al. (2007) translated spacing research into practical recommendations in an IES practice guide, noting that teachers rarely use spacing despite its robust evidence base — partly because it requires advance planning and partly because it feels counterintuitive (students feel more confident after massed practice, even though spaced practice produces better retention).

Input Schema

The teacher must provide:

• Content to space: What students need to retain. e.g. "Year 8 biology: cell organelles and their functions — mitochondria, nucleus, cell membrane, ribosomes, chloroplasts, vacuole, cell wall" / "Key dates and causes of WWI" / "French irregular verb conjugations — être, avoir, aller, faire" / "Times tables 6-12"
• Performance data: What is known about current retention. e.g. "End-of-topic quiz last Friday: class average 72%. Most students got mitochondria and nucleus correct but confused ribosomes with rough ER. Three students scored below 50%" / "Informal questioning suggests most students remember causes but not dates" / "Duolingo-style accuracy: être 95%, avoir 88%, aller 71%, faire 62%"

Optional (injected by context engine if available):

• Student level: Year group and proficiency
• Subject area: The curriculum subject