The Moment of Understanding: Cognitive State Transitions in Learning

ABSTRACTA well-documented but undertheorised phenomenon in learning concerns the instability ofnewly acquired understanding: learners who demonstrate correct conceptual access underone set of conditions frequently fail to reproduce it shortly afterwards or in altered contexts. Existing competence-based models of learning, which treat understanding as a fixedinternal state that is either present or absent, cannot adequately account for this patternof sudden comprehension followed by fragile and context-sensitive accessibility. The present paper proposes a dynamical framework in which understanding corresponds to a representational organisation whose accessibility varies as a function of stochastic cognitive dynamicsand contextual parameters. Early understanding is modelled as a metastable configurationwithin a potential landscape, a shallow local minimum from which the system can be displaced by cognitive noise, rather than as a stable attractor corresponding to consolidated knowledge. The framework combines a Langevin stochastic differential equation governing representational state dynamics with a probabilistic measurement model that formally separates latent representational state from observable accessibility. This architecture generates testable predictions concerningre-closure, context-dependent accessibility failure, and the stabilising effects of retrieval practice and contextual variation, interpreting these as mechanisms of progressive attractor deepening. The framework provides a principled theoretical basis for understanding the fragile transition between initial comprehension and durable, transferable knowledge.Keywords: conceptual accessibility, metastability, dynamical systems, representational change,attractor dynamics, learning consolidation