Spatial computing and mixed reality (MR) headsets represent the next frontier in educational technology, fundamentally altering how students interact with abstract mathematical concepts. This empirical study investigates the pedagogical efficacy of utilizing advanced spatial computing environments to teach high school geometry, specifically focusing on multi-dimensional proofs and volumetric calculations. Over an entire academic semester, 850 secondary students were divided into a control group utilizing traditional 2D textbooks and digital graphing software, and an experimental group provided with lightweight MR headsets that allowed them to physically manipulate and walk around holographic polyhedrons. The quantitative data revealed a remarkable 45% increase in the experimental group's ability to successfully solve complex, multi-step spatial reasoning problems, alongside a 32% reduction in time taken to grasp cross-sectional theorems. Furthermore, psychometric anxiety scales administered before and after the unit demonstrated a 50% decrease in math-related anxiety among students utilizing MR, who reported that physically interacting with the shapes demystified previously intimidating abstract concepts. Qualitative feedback from educators corroborated these findings, noting that spatial computing virtually eliminated the "visualization gap" that typically hinders students lacking innate spatial intelligence. However, the study meticulously documents significant logistical hurdles, including the cognitive fatigue associated with prolonged headset usage (often termed "cybersickness") and the acute need for specialized professional development for mathematics teachers to seamlessly integrate these dynamic 3D environments into standardized lesson plans. The authors conclude that spatial computing, while requiring substantial initial capital investment, provides a revolutionary, highly equitable bridge to mastering advanced mathematics.