Readiness and Mastery Dashboard
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About This MicroSim
This is where the whole book converges. Personalized Sequencing takes three inputs — a learner model, a mastery threshold, and a dependency graph — and produces one output: what this learner should study next. This dashboard puts all three under your hands at once.
Eight knowledge components, one mastery slider each. Move a slider and three things recompute immediately: the node's color, the readiness frontier, and the recommended sequence.
The readiness frontier
A component is in the frontier when every prerequisite is mastered but it is not yet mastered itself — it is exactly what this learner is ready to learn right now. Frontier components get a pulsing blue ring.
Two consequences are worth predicting before you verify them:
- At 0% mastery the frontier is not empty.
GraphandDirected Edgehave no prerequisites, so their condition is satisfied vacuously. There is always somewhere to start. - Raising the threshold can take mastery away. Set both roots to 80%, then drag the threshold to 90%. They stop counting as mastered, and the frontier collapses back to the roots. Mastery is a claim relative to a threshold, not an absolute property of a learner.
The constraint
The unconstrained sequence is a plain topological order: Graph → Directed Edge → DAG →
Traversal → Prerequisite → …. Both DAG and Traversal become available at the same moment,
and the graph alone does not say which to teach first.
That is what a learning path constraint is for. Toggle Add constraint to apply
Traversal before DAG — a curriculum policy that gets learners writing working code before they
meet the formal definition. The sequence reorders to Graph → Directed Edge → Traversal → DAG →
…, with the moved components highlighted in purple.
Notice what does not happen: no prerequisite is ever violated. The constraint only decides among orderings the graph already permits. A constraint that contradicted a real prerequisite would be unsatisfiable, not merely inconvenient.
How to Use
- Predict first. Before touching a slider, say which components you expect to enter the
frontier when
Graphcrosses 70%. Then drag it and check. - Drag the mastery sliders (0–100%). Nodes shade gray → gold → green; the sequence updates live; frontier rings appear and disappear.
- Drag the mastery threshold (default 70%). This is the cutoff that decides what "mastered" means, and moving it can reclassify components in both directions.
- Toggle Add constraint and watch the recommended sequence reorder.
- Hover any node for its mastery, its status, and its prerequisite list.
In the sequence strip: green = already above threshold, blue outline = study this next, purple = moved by the active constraint.
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Lesson Plan
Audience
Instructional designers, curriculum developers, and educational technologists working with concept dependency graphs.
Duration
15–20 minutes
Prerequisites
Learners need Learner Model, Knowledge Component, Mastery Threshold, Readiness Estimation, Personalized Learning Path, and Personalized Sequencing from Chapter 27.
Activities
- Predict the frontier (5 min): Starting from reset, have learners write down which
components enter the frontier after mastering
Graphalone, then after masteringDirected Edgetoo. The answer changes from{Traversal}to{Traversal, DAG}— becauseDAGneeds both roots andTraversalneeds only one. Verify by dragging. - The threshold is a policy, not a fact (5 min): Set every component to 75% and note the sequence. Then drag the threshold from 70% to 80%. Every "mastered" component reverts. Ask what that implies about reporting a learner as having "mastered" something without also reporting the threshold.
- Constraints and freedom (7 min): Toggle the constraint and identify what moved. Then ask
the harder question: could a constraint ever reorder
PrerequisitebeforeDAG? No — that is a real prerequisite edge, not a free choice. Have learners articulate the difference between what the graph requires and what a curriculum merely prefers.
Assessment
Learners can:
- Predict which components enter the readiness frontier as mastery values cross the threshold.
- Explain why the frontier is non-empty at zero mastery.
- Explain why raising the threshold can remove a component from "mastered".
- Explain why a path constraint can reorder some pairs but never violate a prerequisite.
Related Concepts
- Learner Model — the eight mastery values on the left
- Knowledge Component — each of the eight nodes
- Mastery Threshold — the cutoff that turns a percentage into a claim
- Readiness Estimation — the frontier computation
- Learning Path Constraint — the toggle, and its limits
- Personalized Sequencing — the recommended sequence this all produces
References
- Chapter 27: Learner Modeling and Advanced Assessment - The chapter this MicroSim supports.
- Chapter 16: Personalization and Adaptive Learning Paths - Where personalized paths are first introduced.
- Knowledge Space Theory - The formal theory behind the readiness frontier, where it is called the "outer fringe".
- Topological Sorting - Kahn's algorithm, which produces the recommended sequence.
- Mastery Learning - Bloom's framework, and the origin of the mastery-threshold idea.