PRACTICAL APPLICATION OF THE STATIONARY DISTRIBUTION OF MARKOV CHAINS IN TEACHING-EFFECT EVALUATION

Abstract

To explore the application of Markov-chain models in process-oriented teaching evaluation, this study analyzes grade transitions among students in two Advanced Mathematics classes. A total of 80 students were included, and their scores from two stage assessments were classified into five levels: excellent, good, medium, pass, and fail. Based on the paired assessment records, transition-frequency tables and transition-probability matrices were constructed for the two classes. The short-term grade distributions and stationary distributions were subsequently calculated to examine the dynamic characteristics and potential evolution of students’ learning states. The results show that the two classes exhibited different grade-transition patterns. Class A demonstrated a relatively concentrated and stable transition structure, with most students tending toward the good and medium levels and a comparatively low proportion remaining at the failing level. Class B maintained a relatively prominent excellent group, but its lower-performing students showed greater dispersion and a stronger tendency to remain in or move toward the lower grade levels. The Markov-chain model integrates individual grade transitions with class-level score distributions, enabling a quantitative and visual description of changes in students’ learning states. This approach provides a methodological reference for stage-based learning assessment, differentiated instructional intervention, and data-informed optimization of Advanced Mathematics teaching.