Empirical Study on the Correlation Between Mathematical Cognitive Structure, Higher-Order Thinking Ability, and Mathematical Modeling Ability
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Abstract
In core-literacy-oriented mathematics education, mathematical cognitive structure, higher-order thinking ability, and mathematical modeling ability have become key indicators for evaluating comprehensive mathematical literacy. These abilities are also fundamental to solving engineering problems such as electromagnetic field modeling, wave propagation analysis, fiber morphology optimization, and spatial distribution modeling of industrial materials. Existing studies mostly examine single abilities or pairwise relationships, lacking systematic empirical evidence on the intrinsic correlation among the three. This study constructs a theoretical model linking mathematical cognitive structure, higher-order thinking ability, and modeling ability, and verifies it through a multidimensional empirical design. Using stratified sampling, 826 valid samples were collected from five schools. Data were obtained through mathematical cognitive structure scales, higher-order-thinking scales, modeling ability tests, and classroom observation. SPSS and AMOS were used for descriptive statistics, correlation analysis, regression analysis, and structural equation modeling. The results show significant positive correlations among the three variables. Mathematical cognitive structure positively predicts higher-order thinking and modeling ability, while higher-order thinking partially mediates the relationship between cognitive structure and modeling ability. Group analysis further reveals differences by grade and mathematical foundation. The findings provide empirical support for integrated mathematics teaching aimed at engineering modeling and advanced electromagnetic problem solving.
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