Teaching Philosophy Learning-Curve Lab

Teaching Philosophy

Classroom Parameters

Feedback frequency 1.0×

Differentiation / scaffolding 20%

Practice pace 1.5 trials/s

Class Outcomes

Trial #

Class avg mastery

Achievement gap (σ)

0.00

At mastery (≥80%)

0 / 24

How it works

Each of the 24 students has a skill level s ∈ [0,1] that evolves one simulated practice trial at a time, following a diminishing-returns learning-curve model (the mechanism behind the classic power-law-of-practice finding that error rate falls as a power function of trials, Newell & Rosenbloom 1981):

Δs = k·(C − s) − f·s + e·max(0, s̄ − s) + noise
s ← clamp(s + Δs, 0, 1)

k — learning rate toward the ceiling; set by the chosen philosophy and scaled by the feedback-frequency slider (frequent, immediate feedback speeds acquisition).
C — skill ceiling for that philosophy: explicit/behaviorist methods plateau lower, discovery-based and mastery-gated methods reach a higher ceiling but more slowly.
f — forgetting/extinction rate without continued practice; highest for pure reinforcement schedules (Skinner), near zero for methods that build durable conceptual structure.
e·max(0, s̄ − s) — the differentiation/scaffolding term: pulls below-average students toward the class mean, modelling Bloom's (1968) mastery-learning remediation loops that shrink the achievement gap.
noise — individual variance in how a lesson lands, drawn per student per trial; inquiry-based learning has the widest spread, direct instruction the narrowest.

Direct Instruction (Rosenshine) — explicit, teacher-led, highly structured: fast, uniform early gains, moderate ceiling. Inquiry-Based (constructivist, Vygotsky's zone of proximal development) — slower start with high variance, but the highest long-run ceiling. Mastery Learning (Bloom) — gated remediation keeps the whole class moving together, the smallest achievement gap. Behaviorist Reinforcement (Skinner, operant conditioning) — the fastest early gains from immediate reward/correction, but the lowest ceiling and the most forgetting once reinforcement lapses.

avg. mastery vs. trial

Struggling Progressing Mastery

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