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References: Concept Dependencies and Prerequisites

  1. Mastery learning - Wikipedia - Explains the instructional approach requiring prerequisite competence before advancing, the educational theory underlying this chapter's ready-to-learn and learned-concept vocabulary and its cascading-unlock model of progress.

  2. Topological sorting - Wikipedia - Covers the algorithm for ordering a DAG's nodes so every edge points forward, the formal technique behind computing a valid prerequisite chain and journey map from a learning graph's dependency structure.

  3. Shortest path problem - Wikipedia - Describes algorithms for finding the minimum-length path between two nodes, the graph-theory foundation for this chapter's hop count metric measuring distance along a prerequisite chain.

  4. Introduction to Algorithms (3rd Edition) - Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein - MIT Press - The standard algorithms reference covering topological sort and breadth-first search, the exact techniques this chapter's dependency-analysis and hop-count sections rely on.

  5. How Learning Works: Seven Research-Based Principles for Smart Teaching - Susan A. Ambrose, Michael W. Bridges, Michele DiPietro, Marsha C. Lovett, and Marie K. Norman - Jossey-Bass - A research-based teaching guide explaining how prior knowledge shapes readiness to learn, directly relevant to this chapter's ready-to-learn concept and skill gap vocabulary.

  6. Topological Sorting - GeeksforGeeks - A worked tutorial on topological sort algorithms for DAGs, with code examples illustrating the same ordering technique this chapter uses to derive a valid prerequisite chain.

  7. Breadth First Search (BFS) - GeeksforGeeks - Explains level-by-level graph traversal, the algorithm this chapter's Hop Count diagram uses to find the shortest path and measure distance between two concepts.

  8. Lecture 16: Dijkstra - MIT OpenCourseWare - A free lecture on finding shortest paths in DAGs via topological sort, the precise algorithmic technique behind this chapter's hop-count and transitive-dependency calculations.

  9. Connect Prior Knowledge to New Learning - CAST UDL Guidelines - Describes instructional strategies for activating prerequisite knowledge before new material, reinforcing this chapter's point that a concept becomes ready-to-learn only once its prerequisites are mastered.

  10. Skills Gap Analysis - MindTools - A step-by-step guide to identifying and quantifying gaps between current and required capabilities, the same analytical move this chapter formalizes as the skill gap between a learner and a goal concept.