A Novel Neutrosophic Integral Framework for Classroom Teaching Quality Analysis in Children's Dance Aesthetic Education

Evaluating classroom teaching quality in children’s dance aesthetic education is challenging due to uncertainty, subjective judgment, and multiple viewpoints. Traditional assessment tools fail to capture emotional variation, developmental differences, and the vague nature of movement expression. This paper proposes a complete neutrosophic integral framework to model and measure teaching quality under uncertainty. We introduce several new mathematical tools: the Generalized Neutrosophic Integral (GNI), Time-Weighted Neutrosophic Integral (NTWI), Game-Theoretic Neutrosophic Integral (GTNI), and Neutrosophic Tensor Representation (NTL). These tools allow precise modeling of dynamic, emotional, and conflicting classroom observations. A structured model is built to collect and process evaluations from children, teachers, and observers, using neutrosophic values for movement, emotional engagement, and response. The framework outputs a unified quality score using the Neutrosophic Aesthetic Teaching Index (NATI). An example application is presented with complete equations and analysis. The proposed method advances neutrosophic theory and provides a practical tool for realworld educational environments where uncertainty is the norm.