Active Learning vs Passive Lecture: Classroom Retention Simulator

Teaching Mode

Active Learning (spaced retrieval)

Lesson Parameters

Retrieval interval 18s

Retrieval gain per event 35%

Class engagement rate 75%

Material forgetting rate λ 0.60

Class Statistics

Avg. retention

At mastery (≥80%)

0 / 30

Retrieval events

Class time

0.0 min

How it works

Each of the 30 students carries a retention level K ∈ [0,1]. Between events it decays continuously, following the classic Ebbinghaus forgetting curve:

dK/dt = −λ·K
K(t) = K₀·e^(−λt)

In Active Learning mode, a retrieval-practice event (a quiz, cold-call or think-pair-share) fires every interval. Each engaged student gets a testing-effect boost toward full mastery:

on event: K ← K + g·(1 − K)   for the engaged fraction e

In Passive Lecture mode there are no retrieval events — only a small continuous exposure gain, so decay dominates and the class converges toward low retention, matching the empirical "testing effect" result (Roediger & Karpicke, 2006) that repeated retrieval beats repeated re-reading for long-term retention.

Retrieval interval — spacing between practice events; shorter spacing fights forgetting harder.
Retrieval gain — how much one correct-retrieval event moves a student toward mastery.
Engagement rate — the fraction of the class that actually participates in each event (distraction, fatigue).
Forgetting rate λ — how quickly the material decays from memory; higher for harder or less meaningful content.

Real-world relevance: this is the mechanism behind spaced-repetition apps, peer instruction and low-stakes quizzing strategies used in evidence-based classroom design.

Low retention Partial retention Mastery

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