Curriculum Prerequisite Map¶
Document — instantiates Dependency Ordering
A representation of learning dependencies among concepts, skills, modules, courses, or assessments.
A Curriculum Prerequisite Map applies dependency ordering to learning, where the prerequisite relation is not physical or temporal but cognitive: a learner cannot meaningfully take on a later concept until an earlier capability is genuinely in place. The map records which skills, concepts, modules, and courses depend on which others, and — this is its distinguishing feature — it treats the readiness signal as demonstrated capability rather than seat-time, completion of a prior course, or the calendar. Its unique claim among the siblings is that the "predecessor state" lives in a human head and can only be inferred, so the map must be paired with assessments that verify mastery and gates that hold advancement until that mastery is shown.
Example¶
A university mathematics department maps its lower-division sequence. The nodes are competencies, not just courses: "manipulate limits," "differentiate elementary functions," "set up a definite integral," "solve a first-order linear ODE." Edges encode true cognitive dependencies — differential equations depends on integration technique, which depends on differentiation, which depends on functions and limits. Drawing it reveals that a course everyone treats as an isolated elective, linear algebra, is actually a hidden prerequisite for the later proofs course, and that two topics long taught in sequence have no real dependency and could be split into parallel tracks.
Incoming students take a placement assessment mapped to the graph's early nodes. A student who tests strong on functions and differentiation but weak on limits is not simply "placed in Calculus I"; the map shows precisely which upstream competency is missing and routes them to shore up limits first. Each course then carries a mastery gate: advancement to the integral-calculus module is held until the differentiation competency is demonstrated on an assessment, not merely until the previous term ended. When a downstream instructor later reports that students arrive unable to handle a technique, the map makes the missing edge diagnosable rather than a mystery.
How it works¶
What is specific to the learning setting, beyond drawing the graph:
- Nodes are capabilities, edges are cognitive dependence. The map distinguishes hard prerequisites (you truly cannot do X without Y) from mere curricular convention, so false ordering can be removed and real ordering protected.
- Readiness is measured, not assumed. Placement and diagnostic assessments probe whether the upstream capability is actually present in a given learner — the same node can be "satisfied" for one student and not another.
- Gates hold on evidence of mastery. Advancement to a dependent node is contingent on demonstrated competence at its prerequisites, with the threshold set deliberately rather than defaulting to a passing grade.
Because readiness varies per learner, the map is less a single route than a personalized ordering constraint: many valid paths through it exist, and independent strands can be pursued in parallel.
Tuning parameters¶
- Granularity — whole courses, modules, or fine-grained competencies as nodes. Fine granularity enables precise placement and remediation but is expensive to build and maintain.
- Mastery threshold — how high a demonstrated-competence bar gates advancement. A high bar protects downstream learning but slows progression and can trap learners; a low bar preserves flow but lets shaky prerequisites through.
- Prerequisite strictness — which edges are enforced hard versus advisory. Over-strictness serializes learning that could run in parallel; under-strictness admits under-prepared learners.
- Assessment placement — whether readiness is checked at entry, at each gate, or continuously. More checkpoints catch gaps earlier but add testing load.
When it helps, and when it misleads¶
Its strength is that it converts vague complaints ("students aren't ready for this course") into an inspectable structure where the missing capability and its gate are named, and it enables both remediation targeted at the actual gap and safe parallelism across independent strands. It draws directly on the idea that a learner's knowledge is a state within a structured space of prerequisite-linked competencies.[n1]
Its failure mode is that cognitive prerequisites are contested and often wrong: an edge asserted by tradition may not reflect how anyone actually learns, and a map frozen into policy can enforce a false ordering for years, blocking learners for no real reason. The mirror failure is a stale map that omits a genuine dependency, so students advance and then fail downstream. A classic misuse is treating "passed the prior course" as proof of mastery when the two are only loosely correlated. The guarding discipline is to validate edges against actual downstream performance, revisit them as pedagogy and content change, and keep the readiness signal tied to demonstrated capability rather than course completion.
How it implements the components¶
dependency_map— the document is the map of learning dependencies: competencies and courses as nodes, cognitive prerequisite relations as directed edges.prerequisite_check— placement and diagnostic assessments verify, per learner, that an upstream capability is actually present before dependent study begins.stage_gate— mastery gates hold advancement to a dependent node until competence at its prerequisites is demonstrated to a set threshold.
It does not name the chain that controls total duration (critical_path_marker, Critical Path Method), compute an ordering algorithmically (sequencing_rule, Topological Sort), or define undo paths for work already done (rollback_or_return_path, Deployment Runbook); a learning map governs which capabilities gate which, not those concerns.
Related¶
- Instantiates: Dependency Ordering — the Curriculum Prerequisite Map applies it to cognitive prerequisites in learning design.
- Sibling mechanisms: Topological Sort · Critical Path Method · Prerequisite Matrix · Deployment Runbook · Manufacturing Process Plan · Treatment Sequencing Protocol · Dependency Graph
Editorial Notes¶
Form Classification¶
Form family: Representation, Specification & Plan
Rationale: Curriculum Prerequisite Map operates as a non-executable information artifact that externalizes static or prospective structure because it a representation of learning dependencies among concepts, skills, modules, courses, or assessments.
Independent corroboration: The frozen evidence defines Curriculum Prerequisite Map as 'A representation of learning dependencies among concepts, skills, modules, courses, or assessments', so its operative form is Representation, Specification & Plan.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Education & Pedagogy
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Learning-science and curriculum design cohered prerequisite maps that order concepts by demonstrated learner capability rather than calendar completion.
Related originating lineages:
- Cognitive Science — Knowledge-space theory formalized prerequisite-linked knowledge states and readiness inference.
Review resolution: Learning-science and curriculum design cohered prerequisite maps that order concepts by demonstrated learner capability rather than calendar completion.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] Knowledge space theory, developed by Jean-Paul Doignon and Jean-Claude Falmagne, models a learner's knowledge as a state within a structured space of prerequisite-linked items; it underlies adaptive assessment systems that infer what a learner is ready to learn next. ↩