Skill Decay Modeler (Ebbinghaus Personalized)

Ebbinghaus Forgetting Curve + individual adjustment: Predict EXACTLY when child will drop from 80% → 50% retention

Formula: R(t) = e^(-t/S) where R = retention, t = days, S = decay rate constant

Child A (Slow Decay)
Decay Rate: 0.85
50% in 18 days
013714210255075100

📅 Recommended Schedule:

Review every 14 days

⏱️ Trigger review when retention drops to ~80%

Child B (Fast Decay)
Decay Rate: 0.5
50% in 7 days
0123570255075100

📅 Recommended Schedule:

Review every 5 days

⏱️ Trigger review when retention drops to ~80%

Child C (Medium Decay)
Decay Rate: 0.68
50% in 11 days
01258110255075100

📅 Recommended Schedule:

Review every 8-9 days

⏱️ Trigger review when retention drops to ~80%

Individual Factors Affecting Decay Rate

Skill Complexity

Complex skills decay faster (higher β)

💡 Multi-step task: faster decay than single skill

Interest Level

High interest → slower decay

💡 Favorite game skill: 2-3x longer retention

Executive Function Level

Low EF → faster decay (working memory limitation)

💡 ADHD child: decay ~2x faster

Practice Spacing Quality

Distributed > massed practice

💡 5 spreads = 2x longer retention vs daily bunches

Sleep Quality

Poor sleep → significantly faster decay

💡 Sleep deprivation: ~2x decay rate increase

Optimization Protocol
1.

Identify individual decay rate from 3-5 practice sessions

Plot retention vs days; fit curve

2.

Calculate days-to-50% threshold

Use formula; trigger review before that day

3.

Schedule reviews at 80% retention point (sweet spot)

Not too early (wasted review) or too late (forgotten)

4.

Re-calibrate decay rate every 2 weeks

Child improves; decay rate might change

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