This is a simplified, pedagogically-motivated model of the contextual interference effect: practicing several skills in mixed (interleaved) order feels harder and produces worse in-session accuracy, yet produces better long-term retention than practicing one skill at a time in a block — a case of what Robert Bjork calls a "desirable difficulty."
Each of the three skills carries two numbers: a slow-moving long-term strength L (consolidated memory) and a fast-moving short-term priming P (the "warm" feeling of just having practiced it):
immediate success prob. p = clamp(L + P, 0.05, 0.97)
retrieval effort e = 1 − P (low priming ⇒ harder retrieval)
on success: ΔL = k_L · (1 − L) · e P → min(1, P + k_P)
on miss: ΔL = 0.35 · k_L · (1 − L) · e
skill not practiced this trial: P ← P · 0.55 (priming fades fast)
every trial: L ← L · (1 − forget) (slow background forgetting)
- Blocked — the same skill repeats, so P stays high, retrieval feels easy, immediate accuracy is high, but effort e is low so each trial's L-gain is small.
- Interleaved — the skill switches every trial, so P has just decayed when it is tested; retrieval is effortful (e is high), immediate accuracy dips, but each successful trial buys a larger, more durable L-gain.
- Random — a middle case: switches are frequent but occasionally repeat, landing between the two.
The retention test simulates the classic Ebbinghaus forgetting curve applied to the long-term store only (short-term priming is assumed to be gone after any real rest): Lrest = L · e−h/τ, with τ = τ₀·(1 + 3L) — better-consolidated skills decay slower. Move the rest slider and watch the predicted-retention readout separate from immediate accuracy: after a long enough rest, the order that looked worse during practice (interleaved) usually ends up ahead. This mirrors findings from motor-skill studies (Shea & Morgan, 1979) and interleaved mathematics practice (Rohrer & Taylor, 2007); the constants here are illustrative, not fitted to any single dataset.