[Français] Half-Life Regression: The Algorithm Behind Amal's Adaptive Curriculum

# Half-Life Regression: The Algorithm Behind Amal's Adaptive Curriculum [Contenu complet en français] ## Half-Life Regression: The Algorithm Behind Amal's Adaptive Curriculum Amal's adaptive curriculum is powered by Half-Life Regression (HLR), a memory model where each learning item has a "half-life" — the time for recall probability to drop to 50%. The formula p(recall) = 2^(-Δ/h) drives scheduling: items due for review are surfaced before the child forgets, while mastered items are spaced further apart. Combined with persona-based difficulty matching, this creates a truly personalized learning path for every child. ### The Math Behind the Memory **Exponential Decay Model** Memory doesn't fade linearly — it follows an exponential curve. After reviewing a concept: - Right after review: 100% recall probability - After h hours: 50% recall probability (by definition of half-life) - After 2h hours: 25% recall probability - After 4h hours: 6.25% recall probability Amal schedules the next review when recall probability hits approximately 80% — the efficiency sweet spot. **Worked Example: Learning the word "كتب" (wrote)** | Event | Time | Half-Life | Recall Prob | Next Review | |-------|------|-----------|---|---| | Initial learning | Day 1, 2pm | 4h | 100% | ~6pm | | Correct review | Day 1, 6pm | 8h | 98% | Day 2, 10am | | Correct review | Day 2, 10am | 16h | 92% | Day 3, 2pm | | Correct review | Day 3, 2pm | 32h | 87% | Day 5, 10pm | | Correct review | Day 5, 10pm | 64h | 81% | Day 8, 8pm | | Stable memory | Day 8, 8pm | 128h | 79% | Week 2 | After 5 correct reviews, "كتب"