Pedagogically Asymmetric Elo Models for Multidimensional Adaptive Learning Systems

Abstract

Adaptive learning systems commonly use psychometric models to estimate learner ability and task difficulty. Among the most widely used approaches are Item Response Theory (Harvey & Hammer, 1999) and modifications of the Elo rating system (Pelánek, 2016). These models typically assume a symmetric learner–task interaction, with maximum diagnostic information occurring at approximately a 50% probability of success. While appropriate for testing, this equilibrium may not correspond to pedagogically desirable conditions for sustained learning. This article presents a pedagogically asymmetric parameterisation of a multidimensional Elo model for adaptive mathematics education. The model combines a multidimensional representation of mathematical competencies based on the Global Proficiency Framework for Mathematics (UNESCO et al., 2020), scaffold-aware partial-credit scoring, and separate equilibrium parameters for learner and task updates. This enables learner-profile development and task-difficulty dynamics to be controlled differently rather than being governed by the same symmetric equilibrium. The model was implemented in the Edu-AI system for preparing Czech elementary school learners for standardised mathematics entrance examinations (Jančařík et al., 2023). The pilot dataset comprised 63,020 learner–task interactions involving 628 learners and 233 tasks. A replay-based simulation preserved the chronological interaction histories, achieved scores, and scaffold use while recalculating learner and task parameters under iteratively adjusted equilibrium settings. The analysis focused on model stability, learner-profile dynamics, task-difficulty convergence, and the interaction between equilibrium settings and scaffold-aware scoring. The replay results showed that relatively small changes in equilibrium parameters substantially affect learner and task dynamics. A configuration with an equilibrium of 0.80 for learner updates and 0.85 for task updates produced stable and pedagogically interpretable behaviour under the scoring policy used in the pilot. These values are treated as promising initial settings rather than as optimal parameters for learning effectiveness. The study therefore demonstrates the feasibility of introducing pedagogical asymmetry into a multidimensional Elo model and provides a basis for prospective testing of the model’s educational effects.