高等数学的概念边缘化与认知重构路径

Conceptual Marginalization and Paths of Cognitive Reconstruction in Advanced Mathematics

摘要: 高等数学作为高等教育核心公共课，对学生的知识建构和思维培养至关重要。然而，观察发现该课程中存在着明显的概念边缘化现象，学生普遍重技巧轻概念，学习效果不佳。本文基于教学实践，从学生认知偏差、教师教学失衡、评价体系导向偏差三个维度剖析概念边缘化的成因，及其在知识结构断裂、思维能力表层化等方面的危害，并结合APOS理论和概念的双重性，提出情景化引入、结构化分析、强化例题示范性、构建知识体系及改革评价方式的重构路径，为改善高等数学教学提供新视角，帮助学生实现从“会做题”到“懂数学”的转变，推动高等数学教育回归思维培养的本质。

Abstract: Advanced Mathematics, as a core public course in higher education, is crucial for students’ knowledge construction and thinking development. However, observations show that there is a prominent phenomenon of conceptual marginalization in this course: students generally prioritize skills over concepts, leading to unsatisfactory learning outcomes. Based on teaching practice, this paper analyzes the causes of conceptual marginalization from three dimensions—students’ cognitive biases, teachers’ unbalanced teaching behaviors, and the guiding deviations of the evaluation system—as well as its harms such as the fragmentation of knowledge structure and the superficialization of thinking abilities. Combining the APOS Theory and the duality of concepts, the paper proposes reconstruction paths including contextualized introduction, structural analysis, strengthening the demonstration of example problems, knowledge system construction, and reforming evaluation methods. These paths provide a new perspective for improving Advanced Mathematics teaching, help students achieve the transformation from “being able to solve problems” to “understanding mathematics”, and promote the return of Advanced Mathematics education to the essence of thinking cultivation.