In the Space a Teacher Creates: Modeling Student Movement Across Psychological Landscapes

What kind of psychological space do teachers and schools create — and how do students move through it? This study presents a computational framework for modeling student identity shifts within an affective-educational space. Drawing on questionnaire data, we construct a latent four-dimensional space using Principal Component Analysis (PCA), then simulate the impact of changing environments using directional vectors (FIS) that reflect variation in teaching clarity, personal support, peer atmosphere, and academic ambition.Students are assigned soft cluster identities based on proximity to psychological archetypes — Math-Engaged Achievers (MEA), Positively Detached (PD), Strugg\-ling/\-Gaps-focused (SG), and Discouraged Learners (DL) — and their psychological alignment evolves as environmental conditions shift. Through stylized narratives of three students, we illustrate the model's explanatory power and developmental nuance.Using Monte Carlo optimization, we identify environments that promote academic engagement while reducing psychological disengagement. While applied here to mathematics, the structure generalizes to other domains where educational climates shape identity. The model combines formal simplicity with interpretive power, offering a new lens for exploring how students move through the spaces we build around them.