抽象函数的性质与赋值法策略的实践研究

Practical Research on the Properties of Abstract Functions and Assignment Method Strategies

摘要: 本文总结了抽象函数的性质，基于维果茨基“最近发展区”理论及Dubinsky的APOS认知发展理论，聚焦赋值法在解题中的核心作用，通过三类典型错误模型揭示认知机制，设计针对性教学干预方案。干预后学生错误率显著下降，证明通过搭建认知支架可有效提升学生抽象函数解题能力，为高中数学教学提供可复制的实践路径。

Abstract: This paper summarizes the properties of abstract functions, drawing on Vygotsky’s “zone of proximal development” theory and Dubinsky’s APOS cognitive development theory. It focuses on the central role of the assignment method in problem-solving, reveals cognitive mechanisms through three typical error models, and designs targeted instructional intervention strategies. Following the intervention, students’ error rates decreased significantly, demonstrating that constructing cognitive scaffolding can effectively enhance students’ ability to solve abstract function problems, providing a replicable practical approach for high school mathematics education.