Curriculum Content Sequencing Simulation

Teaching Order

Forgetting Between Topics

Gap decay rate 0.08 / step

Playback

Pace 1.0×

Outcome

Learning outcome score

Prereq violations

Topics taught

0 / 10

How it works

Ten curriculum topics form a fixed prerequisite DAG (gray arrows). You choose the teaching order (the blue path) independently of that graph. At the moment topic t is taught at sequence position i, each prerequisite p contributes an effective mastery that decays with the gap since p was taught:

effMastery(p) = mastery(p) · e^(−k · gap),  gap = i − posOf(p)
readiness(t)  = mean of effMastery(p) over all prereqs of t
                (an untaught prereq counts as 0 and is a violation)
mastery(t)    = clamp( 0.15 + 0.85 · readiness(t), 0, 1 )
Outcome score = mean of mastery(t) over all 10 topics

Optimal order — a real topological sort of the DAG: every prerequisite taught before its dependents, zero violations.
Randomize / Reverse — scramble the order to create violations and long gaps, then watch the score drop.
Gap decay rate k — how fast a prerequisite's benefit fades the longer ago it was taught relative to when it's needed; models forgetting between related lessons, distinct from spaced-repetition review scheduling.
Play — a learner walks the chosen path node by node; each node fills red→amber→green as its mastery is computed live.

This is the core claim behind sequencing-aware instructional design: presenting prerequisite ideas immediately before the topics that build on them measurably raises retention versus an arbitrary or reversed order, even though every topic still gets "covered".

Prerequisite (fixed) Chosen teaching order Learner

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