Teaching Machine: Branching Frame Map (2D)

Learner

Aptitude 50

Avg. frame difficulty 50

Auto-run speed 1.0×

Current Frame

Frame 1 — main line

P(correct) = 50%P(wrong) = 50%

Readouts

Frames completed

0 / 12

Total attempts

Remedial detours

Accuracy

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How it works

This is a 2D dashboard version of Norman Crowder's "intrinsic" (branching) programmed instruction from the 1950s–60s teaching-machine era: instead of one fixed sequence of frames (Skinner's linear model), each frame's multiple-choice response routes the learner to a different next frame. The frame map on the left is a draggable, zoomable node graph; the two small panels on the right plot the exact equations driving it live.

P(correct) = 1 / (1 + e^(-k·(aptitude - difficulty + practice)))
practice(frame) = 9 · ln(1 + visits_to_frame),  k = 0.09

Aptitude vs. difficulty — the logistic response curve panel plots this exact sigmoid against (aptitude − difficulty + practice); the marker shows exactly where the current frame sits on that curve.
Practice term — the practice-curve panel plots the diminishing-returns bonus against visit count, with a dot per frame showing how many times it has been visited — the same power-law shape found in real skill-acquisition data.
Branching ON — a wrong answer detours the token down to that frame's remedial branch (a simpler restatement, difficulty −22) before looping back to retry the main frame. Branching OFF reproduces Skinner's linear machine: a wrong answer just repeats the same frame in place.
Auto-run — the machine answers itself by sampling from P(correct) each step, so you can watch trajectories accumulate at different aptitude/difficulty settings while both curve panels update live.

Real-world relevance: this branch-on-error idea is the direct ancestor of every modern adaptive tutoring and mastery-based e-learning system.

Main-line frame Remedial frame Learner token

drag to pan · scroll to zoom (frame map)