Pedagogical Classroom Culture Simulation

Teacher Actions

Praise nudges one random student up; correction knocks one down hard and briefly chills their neighbors; the community activity gives everyone a gentle boost.

Culture Parameters

Peer contagion strength 0.35

Culture decay rate 0.12

Ambient noise 0.05

Classroom State

Mean engagement

50%

Culture cohesion

100%

Disengaged students

0 / 30

Correction events

How it works

Each of 30 seated students carries an engagement value e_i ∈ [0,1]. Every simulated tick the room updates by a leaky-integrator + local-diffusion rule, the same class of model used for opinion dynamics and social contagion on a network:

e_i(t+dt) = e_i(t) + dt·[ decay·(0.5 − e_i)
                          + peer·mean(e_j − e_i for j in seat-neighbors)
                          + teacherInput_i + noise ]
clamped to [0,1]

Decay term — without any teacher input, engagement relaxes toward a neutral baseline (0.5). This is why a classroom culture is never "set and forget."
Peer contagion term — each student's engagement drifts toward the average of their four seat-neighbors (front/back/left/right), the standard nearest-neighbor diffusion coupling. Turn it up and pockets of enthusiasm or apathy spread across the room; turn it to zero and students never influence each other.
Praise — a direct +0.35 pulse to one random student, which then diffuses outward through the contagion term.
Public correction — a −0.45 pulse to one student and a smaller −0.12 pulse to their four neighbors, modeling how a public reprimand chills the students who witnessed it, not just the one corrected.
Community-building activity — a flat +0.15 pulse to every student at once, representing icebreakers or collaborative tasks that raise the room's floor rather than one individual.
Cohesion readout is 1 − 2·stdev(e), i.e. how uniform the culture is across the room (a class can have high average engagement but low cohesion if it's split into engaged and checked-out cliques).

Seat color encodes engagement live: red/orange = disengaged, yellow = neutral, green = highly engaged. This is a simplified but genuine agent-based diffusion model, not a scripted animation — every seat's color is driven by the differential equation above.

Highly engaged Neutral Disengaged

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