Mathematical modelling of linguistic processes in professional vocabulary acquisition among engineering students

Abstract

This article examines the potential of mathematical modelling to describe and predict the acquisition of professional English vocabulary among engineering students. The study is grounded in the assumption that lexical development in English for Specific Purposes is not a strictly linear process, but a dynamic and probabilistic one shaped by repeated exposure, cognitive interference, contextual reinforcement, and partial forgetting. Against this background, the paper aims to develop and validate a stochastic model that captures the dynamics of specialised vocabulary acquisition in technical higher education. The research is based on a discrete-time Markov chain framework, in which the mastery of a professional term is represented as a sequence of transitions between several states, including an unknown term, passive recognition, partial understanding, and active professional use. Transition probabilities are estimated on the basis of empirical observations obtained engineering students, which makes it possible to model both progression and regression in lexical competence. In addition, such variables as exposure frequency and cognitive interference are treated as stochastic factors influencing the learning trajectory. The findings indicate that the proposed model provides a more accurate representation of vocabulary development than traditional deterministic approaches. In particular, it allows the identification of critical transition points and lexical bottlenecks that hinder the movement passive familiarity to confident professional use. The comparison between predicted and observed learning outcomes demonstrates a high degree of correspondence, which confirms the explanatory and predictive value of the model. The study argues that integrating stochastic modelling into ESP research offers a stronger methodological basis for analysing lexical learning in engineering education. The proposed framework may be used to support adaptive teaching strategies, improve assessment, and enhance the design of specialised language instruction for future engineers.