高等代数多项式章节教学难点分析与优化教学策略

Analysis of Teaching Difficulties and Optimized Teaching Strategies for the Polynomial Chapter in Advanced Algebra

摘要: 多项式教学的核心障碍是学生从“算术思维”向“代数思维”转换困难，集中体现在整除形式化、辗转相除、不可约多项式、形式微商四方面认知问题。基于认知负荷与结构主义理论，提出“概念锚定–算法熟练–结构升华”三阶段模型，结合类比迁移、问题链、可视化策略，为课程建设提供参考。

Abstract: The core obstacle in polynomial teaching lies in students’ difficulty transitioning from arithmetical thinking to algebraic thinking, which manifests as cognitive obstacles in four dimensions: formalization of divisibility, the Euclidean algorithm, irreducible polynomials, and formal derivatives. Based on cognitive load theory and structuralism, this study proposes a three-stage model: concept anchoring-algorithm proficiency-structural sublimation. Combined with analogy transfer, problem chains and visualization strategies, the research offers references for curriculum development.