Explanation Sequencing: Cognitive Load in Teaching

Explain the Concept Graph

Click a node to explain it. Explaining out of prerequisite order — or explaining too fast — overloads working memory and concepts get forgotten before they consolidate.

Working-memory capacity 4.0 chunks

Pacing — cooldown per concept 2.0 s

Use analogies (½ load, 2× time cost)

Live State

Click Sunlight, Chlorophyll or CO₂ Fixation to begin — they have no prerequisites.

Load: 0.0Capacity: 4.0

Comprehension

Forgotten (re-explain)

Not yet explained Consolidating Consolidating (confused) Understood Forgotten

How it works

Twelve concepts needed to explain photosynthesis form a prerequisite DAG (directed acyclic graph) — e.g. Calvin Cycle needs ATP, NADPH and CO₂ Fixation all understood first. Each concept carries an intrinsic complexity c (1–3 "chunks").

explaining a node adds load:
  L_node = c × (1  if all prerequisites consolidated
               k  otherwise, k = 2  — confusion penalty)
  L_node = L_node / 2   if "use analogies" is on

total active load:  L = Σ L_node  (all concepts mid-explanation)
overload:           o = max(0, L − capacity) / capacity
consolidation rate: dprogress/dt = r₀ / (1 + o)
forgetting chance:  p(dt) = o × k_f × dt → evicts the least-
                     consolidated active concept back to "unexplained"

Capacity — Cowan's estimate of working-memory span (~4 chunks) that all simultaneously "in progress" concepts must fit inside.
Pacing — the cooldown between explaining concepts. A short cooldown pushes load onto the buffer faster than it can consolidate.
Analogies — a real scaffolding technique from Cognitive Load Theory (Sweller): mapping a new idea onto a familiar one roughly halves its effective load, at the cost of extra explanation time.
Prerequisite violations — explaining a concept before its prerequisites are understood doubles its load, because the listener is building on nothing (shown as an orange/confused node).

This is the same tradeoff a live teacher, technical writer or onboarding flow faces: sequencing, pacing and scaffolding jointly decide whether an explanation actually lands, independent of how "clear" any single sentence sounds in isolation.

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