高等代数中抽象思维能力的培养

Cultivation of Abstract Thinking Ability in Advanced Algebra

摘要: 抽象思维能力是数学素养的一个重要方面，它不仅是解决数学问题的核心能力，也是学生进行科学研究与创新的基础。《高等代数》作为高中《代数》的进阶，具有高度抽象性。因此，在《高等代数》课程中如何培养抽象思维能力，使学生实现高中到大学学习的顺利过渡是值得研究的课题。本文分析了《高等代数》中抽象性思维四个方面的体现，并从抽象概念的理解、逻辑推理的训练、推广与类比、可视化、解决问题、以及探索与创新等方面给出了抽象性思维培养的途径和方法。

Abstract: Abstract thinking ability is an important aspect of mathematical literacy. It is not only a core competence for solving mathematical problems but also the foundation for students’ scientific research and innovation. As a progression from high school Algebra, Advanced Algebra is highly abstract. Therefore, how to cultivate abstract thinking skills in the Advanced Algebra course to facilitate a smooth transition for students from high school to university learning is a worthy topic of research. This paper analyzes several aspects of abstract thinking in Advanced Algebra and provides approaches and methods for cultivating abstract thinking from the perspectives of understanding abstract concepts, training logical reasoning, generalization and analogy, visualization, problem-solving, and exploration and innovation.