Online Learning Engagement Decay Simulator

Lecture Design

Content difficulty 50%

Interactivity / novelty 40%

Quiz interval 6 min

Break interval 15 min

Cohort Status

t = 0.0 min — next quiz in 6.0 min

Avg engagement

75%

Engaged (≥50%)

40/40

Checked out (<20%)

0/40

How it works

Each of the 40 students has an engagement level E_i ∈ [0,1] that decays continuously during instruction and is boosted by two kinds of interventions, based on the attention-decay pattern measured in real online-lecture analytics (engagement drops fastest in unbroken, low-interactivity stretches):

dEi/dt = -λ(1 + d)(1 - 0.5n) · ri · Ei
Quiz boost:  Ei += 0.35(1 - Ei) · (0.5 + 0.5ri)
Break boost: Ei += 0.5(1 - Ei)

where d is content difficulty, n is interactivity/novelty (both 0–1), λ is a base fatigue rate, and r_i is each student's fixed individual resilience factor (0.7–1.3), so decay is proportional to current engagement — a student who is still highly engaged has more attention left to lose than one who is already checked out.

Difficulty — harder content raises the decay rate λ(1+d).
Interactivity — richer, more interactive material slows decay by up to 50%.
Quizzes — retrieval-practice checks jolt engagement back up, with the biggest gain for students who had drifted lowest (diminishing returns near 1.0).
Breaks — a scheduled pause restores half of the remaining attention gap for everyone at once, modelling the well-documented recovery effect of short breaks in long online sessions.

Spheres rise and turn green as a student's E_i climbs, sink and turn red as it falls; a student below 20% visibly drops toward the floor — a proxy for "checked out" (tab-switched, or watching passively without processing).

Engaged student Checked out

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