Spatial characteristics of physical education teacher allocation in basic education: a GIS-based case study of Xi’an, China

Background Achieving educational equity requires understanding how physical education (PE) teachers are spatially distributed. Methods Guided by a sports-geography lens on spatial allocation (center–periphery dynamics; clustering/dispersion), we operationalized the framework into a composite PE-teacher allocation index covering quantity, structure, quality, and professionalization. Indicator selection and interpretation follow the spatial framework, whereas data-driven weights are obtained via the entropy method, which uses between-school variation to avoid subjective expert weighting. We analyzed 1,504 schools in Xi’an (2024), cross-validating official statistics for accuracy and completeness. Spatial visualization (GIS) used Jenks natural breaks (k = 5) to reveal heterogeneity; ordinary Kriging interpolation depicted continuous gradients; and Global/Local Moran’s I (with permutation tests) quantified spatial autocorrelation patterns. Results Xi’an exhibits a pronounced center-strong/periphery-weak pattern. High–high clusters of well-resourced schools concentrate in the urban core, whereas low–low clusters in remote districts indicate pockets of persistent under-resourcing. The Global Moran’s I for the composite index is 0.268 (Z = 5.079, p < 0.01), confirming moderate positive spatial autocorrelation. Only 3.4% of schools fall into the top-tier category of the composite index, while medium-low and low tiers dominate peripheral counties. Student–teacher ratios are markedly higher in central urban areas, and teacher vacancies as well as limited training participation are more prevalent in outlying areas. Policy implications We propose time-bound, measurable targets (e.g., reducing vacancy rates, increasing the full-time teacher share and continuing professional development participation) and a GIS-enabled monitoring system to track progress toward equity goals. Limitations This single-city, cross-sectional study limits generalizability and cannot establish causality. Contribution By explicating how a sports geography theoretical framework structures the indicator system and how the entropy method assigns objective weights, the study offers a transparent, replicable template for diagnosing and managing spatial inequities in PE-teacher allocation.