Exam Readiness Index (ERI): A Theoretical Framework for a Composite, Explainable Index
This provides a theoretical foundation for an explainable index to assess exam readiness for learners, but it is incremental as it focuses on theory without empirical validation.
The authors tackled the problem of summarizing a learner's readiness for high-stakes exams by proposing a theoretical framework for an Exam Readiness Index (ERI), a composite score from 0 to 100 that aggregates six signals to remain interpretable and actionable, with results including proofs of properties like monotonicity and uniqueness under constraints.
We present a theoretical framework for an Exam Readiness Index (ERI): a composite, blueprint-aware score R in [0,100] that summarizes a learner's readiness for a high-stakes exam while remaining interpretable and actionable. The ERI aggregates six signals -- Mastery (M), Coverage (C), Retention (R), Pace (P), Volatility (V), and Endurance (E) -- each derived from a stream of practice and mock-test interactions. We formalize axioms for component maps and the composite, prove monotonicity, Lipschitz stability, and bounded drift under blueprint re-weighting, and show existence and uniqueness of the optimal linear composite under convex design constraints. We further characterize confidence bands via blueprint-weighted concentration and prove compatibility with prerequisite-admissible curricula (knowledge spaces / learning spaces). The paper focuses on theory; empirical study is left to future work.