An Empirical Study on the Collaborative Application of Mathematical Visualization Software in Mathematical Modeling Teaching: A Quantitative Analysis Based on Multi-Competition Results

Aiming at the core pain points in traditional mathematical modeling teaching, such as difficulties in understanding abstract models and the disconnection between theory and application, this paper constructs a closed-loop teaching model of "software precise selection - animation layered design - real-time classroom interaction - competition application". It integrates four types of mainstream visualization tools, namely Manim, GeoGebra, Matlab, and Origin, and transforms core models such as Analytic Hierarchy Process (AHP) and Back Propagation (BP) Neural Network into dynamic demonstration and interactive operation processes. Taking 126 to 145 students of various majors from Hainan University of Science and Technology in grades 2021 to 2023 as the research objects, the teaching effect was verified through the comparison of competition results in four national/regional modeling competitions, combined with statistical methods such as independent samples t-test, multiple linear regression, and analysis of variance (ANOVA). The results show that after the implementation of visualization teaching, the number of valid awards won by students increased from 36 to 89, with an average annual growth rate of 42.3%, and the award-winning rate increased from 28.7% to 61.5%. All three statistical tests show that the differences are significant (P<0.05), and the proportion of high-level awards increased from 27.8% to 43.8%. The study confirms that the collaborative application of visualization software and refined teaching design can significantly lower the cognitive threshold of models and improve the ability of problem transformation, providing a replicable practical paradigm for the reform of mathematical modeling teaching.