MODELS AND METHODS FOR INTELLIGENT MANAGEMENT OF PERSONALIZED LEARNING TRAJECTORIES BASED ON AN INTEGRATED IRT-FORGETTING FRAMEWORK
DOI:
https://doi.org/10.20998/2079-0023.2026.01.17Keywords:
personalized learning trajectories, adaptive learning, item response theory, spaced repetition, zone of proximal development, Wilson confidence interval, learning personalizationAbstract
Despite the widespread adoption of modern learning management systems, most of them primarily focus on providing access to content and assessing outcomes, while overlooking the formalized modeling of individual learning trajectories and the dynamics of knowledge forgetting. This paper presents a comprehensive set of models and methods for adaptive learning, developed within the FAHRAI platform (Framework for Adaptive Hierarchical Review and Instruction). The following key components are proposed: (1) an integrated model that multiplicatively combines the two-parameter Item Response Theory model (IRT 2PL) with a memory retention function, enabling improved calibration compared to classical IRT; (2) a dynamic memory stability model incorporating a composite response quality indicator and a context-dependent multiplier; (3) a hierarchical task selection method based on a multi-level system of strategies and context-dependent weights of a composite prioritization score; (4) an approach based on the Wilson confidence interval for statistically reliable estimation of mastery level, significantly reducing the rate of false-positive decisions compared to naive accuracy; (5) a composite readiness metric integrating IRT parameters, memory retention, and the statistical reliability of the estimation. For each model, a formal description, theoretical justification, and numerical examples are provided. The proposed set of models and methods constitutes a unified theoretical framework for the development of adaptive learning systems, enabling improved accuracy in predicting learning outcomes, greater efficiency in repetition scheduling, and enhanced reliability in assessing individual learner progress.
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