Optimization of Mathematical Cognitive Structure and Improvement of Modeling Ability from the Perspective of Cultivating Higher-Order Thinking Ability
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Abstract
In competency-oriented mathematics education reform, higher-order thinking has become a central objective, while optimized cognitive structures and modeling ability serve as key carriers for solving complex engineering problems, including electromagnetic field modeling, wave propagation analysis, and the quantitative optimization of textile fiber morphology and yarn spatial distribution. Current mathematics teaching in primary and secondary schools still faces structural problems such as fragmented cognitive frameworks, formalistic higher-order thinking cultivation, and weak transfer from abstract knowledge to practical modeling. This study proposes an optimization framework for mathematical cognitive structure and modeling ability from the perspective of higher-order thinking cultivation. Through diagnostic surveys, teacher interviews, classroom observations, and ability tests involving students and teachers from urban, county, and rural schools, the study identifies current deficiencies in knowledge systematization, modeling process training, and deep thinking stimulation. On this basis, a teaching model of knowledge structuring, thinking visualization, and contextualized application is developed. The model emphasizes conceptual association, problem representation, model construction, solution verification, and transfer innovation. The findings suggest that the coordinated development of cognitive structure, modeling ability, and higher-order thinking can enhance students ’ capacity to analyze complex technical problems and provides practical guidance for mathematics instruction supporting advanced electromagnetic and engineering education.
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