Defining the Scope of Learning Analytics: An Axiomatic Approach for Analytic Practice and Measurable Learning Phenomena

2025-12-10

AI Summary

Learning Analytics (LA) lacks a rigorous theoretical foundation, with no formal characterization of its structure, boundaries, or fundamental limitations. Method: We propose the first axiomatized theory of LA, grounded in the psychological nature of learning and methodological requirements of analysis. Five foundational axioms—formalizing LA as a “science of state-transition systems”—are introduced, from which key theorems derive core properties: learner state unobservability, temporal irreducibility, constrained state reachability, and predictive non-determinism. The framework integrates axiomatic modeling, formal logical deduction, and cognitive modeling principles, ensuring compatibility with diverse paradigms including Bayesian Knowledge Tracing and visualization dashboards. Contribution/Results: This work achieves the first strict formalization of LA’s theoretical basis; clarifies the mapping between analytical practice and observable learning phenomena; provides empirically verifiable guidance for method design and data interpretation; and mitigates risks of behaviorist misapplication and category errors.

Technology Category

• Machine Learning: Learning Theory
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

Learning Analytics (LA) has rapidly expanded through practical and technological innovation, yet its foundational identity has remained theoretically under-specified. This paper addresses this gap by proposing the first axiomatic theory that formally defines the essential structure, scope, and limitations of LA. Derived from the psychological definition of learning and the methodological requirements of LA, the framework consists of five axioms specifying discrete observation, experience construction, state transition, and inference. From these axioms, we derive a set of theorems and propositions that clarify the epistemological stance of LA, including the inherent unobservability of learner states, the irreducibility of temporal order, constraints on reachable states, and the impossibility of deterministically predicting future learning. We further define LA structure and LA practice as formal objects, demonstrating the sufficiency and necessity of the axioms and showing that diverse LA approaches -- such as Bayesian Knowledge Tracing and dashboards -- can be uniformly explained within this framework. The theory provides guiding principles for designing analytic methods and interpreting learning data while avoiding naive behaviorism and category errors by establishing an explicit theoretical inference layer between observations and states. This work positions LA as a rigorous science of state transition systems based on observability, establishing the theoretical foundation necessary for the field's maturation as a scholarly discipline.

Problem

• Defines essential structure and scope of Learning Analytics
• Establishes theoretical foundation to avoid naive behaviorism
• Provides guiding principles for designing analytic methods

Innovation

• Axiomatic theory defines learning analytics scope
• Five axioms specify observation, experience, state transition
• Framework unifies diverse methods like Bayesian Knowledge Tracing