Teacher Technological Pedagogical Content Knowledge and Skills (TPCK-S) and Student Cognitive Agency: Determinants of Deep Learning Outcomes in Immersive Geometry Instruction

This study aims to investigates the determinants of student success in hologram-enhanced geometry classrooms by examining the mediating role of teachers' Technological Pedagogical Content Knowledge and Skills (TPCK-S). Employing a Sequential Explanatory Mixed-Methods Design, this research analyzed data from 12 secondary mathematics teachers (purposively sampled) and 248 Grade 8 students from four public schools implementing the national 'Kurikulum Merdeka' in a provincial capital city in Indonesia. Quantitative analysis utilizing Spearman’s rank-order correlation revealed a robust positive revealed a robust positive relationship (r = 0.78, p = 0.002) between teacher performative skills and student deep learning achievement. To explain this statistical link, a qualitative phase involving classroom observations and semi-structured interviews was conducted with four teachers selected through extreme case sampling. The findings illuminate a "Flywheel Mechanism," demonstrating that high-TPCK-S teachers act as "Pedagogical Orchestrators" who effectively transfer "Cognitive Agency" to students. This agency characterized by student-led hypothesis testing and spatial reasoning is identified as the primary driver of deep conceptual understanding. Conversely, low TPCK-S results in passive student observation. These results suggest that educational development must shift focus from mere technology procurement to the cultivation of teachers' orchestration skills.