Interactive Prototype · Project P4
Curriculum Dependency Visualizer
A synthetic applied linear algebra curriculum represented as a typed-dependency graph: 22 learning objectives connected by four dependency types. Click a node to focus its neighborhood; the stats panel updates live. This is an illustrative prototype — the research question in P4 is whether real instructor-annotated graphs produce structural signatures that predict student outcomes.
What this is and isn't. The graph and edge types are synthetic. The dependency grammar is a working hypothesis grounded in Harel's necessity principle and existing prerequisite-chain research (Auvinen et al., Wang et al.). The tool demonstrates what a typed curriculum graph looks like and which structural statistics it admits — not that those statistics are validated predictors of student outcomes. Validation is the job of P4.
Dependency types
- Conceptual — requires understanding of
- Procedural — requires ability to perform
- Motivational — provides intellectual need for
- Social — invokes peer or community context
Click a node to focus · click empty space to clear
How the stats are computed
- Density — actual edges divided by the maximum possible directed edges,
|E| / (|V| · (|V|−1)). A denser curriculum has more interdependencies per concept. - Longest path — the greatest number of edges on any dependency chain. Topologically sorted DAG, so computed in linear time. Long chains signal fragile curricula: one missed link cascades.
- Fan-in / fan-out — maximum in-degree and out-degree across nodes. High-fan-in nodes are natural bottlenecks where many earlier concepts must land before progress continues.
- Motivational ratio — share of edges whose type is motivational. A curriculum with a low motivational ratio has many procedural and conceptual dependencies but few places where one concept answers the question another raises. This is where Harel's necessity principle would predict students experience "why are we doing this?"
- Bottleneck candidates — nodes with in-degree ≥ 3 and at least one outgoing motivational edge. The first condition identifies where many things converge; the second filters to places where that convergence matters for ongoing learning. This is a heuristic, not a validated measure — it exists to illustrate what P4 would try to make rigorous.
Why typed dependencies
Most prerequisite-chain research treats dependencies as homogeneous: A depends on B. But not every dependency has the same pedagogical consequence. A conceptual dependency (you can't understand eigenvectors without understanding vector spaces) is different from a procedural dependency (you can't compute an eigendecomposition without having practiced matrix multiplication), which is different from a motivational dependency (Google's PageRank algorithm is a reason to want to know what eigenvectors do), which is different from a social dependency (this concept was originally motivated by a problem in population biology that a classmate is already working on). The four-type grammar is a hypothesis: that distinguishing these produces graph features that predict student outcomes better than undifferentiated prerequisite graphs do. P4 is the project to test the hypothesis.
← Back to Tools · See Project P4 · Synthetic data. No student records involved.