线性代数教学的反思与创新
Reflection and Innovation of Linear Algebra Teaching

本文主要讨论了线性代数教学的创新和改革。首先，强调了线性代数的基本目标是培养学生的理解力、应用能力、逻辑思维能力和创造性思维。然后，提出了教学方法的创新，包括互动式教学、案例分析、技术工具的应用、探究式学习和线上线下混合式教学，以提高学生的学习效果和兴趣，培养他们的创造性思维和问题解决能力。同时，也提出了将线性代数与课程思政、数学史、数学应用和爱国主义相结合，培养学生的思想道德素质、爱国情感和社会责任感。最后，对线性代数的评价方式进行了讨论，包括书面考试、解决问题的能力评估、实践项目评价和讨论及小组合作评估，以确保评价的有效性。
In this paper, we discuss the innovation and reform of linear algebra teaching. Firstly, it emphasizes the fundamental goal of linear algebra to cultivate students’ understanding, application, logical thinking, and creative thinking abilities. Next, innovative teaching methods are proposed, such as interactive teaching, case analysis, the utilization of technological tools, inquiry-based learning, and a blended approach of online and offline instruction. These methods aim to enhance students’ learning outcomes and interest, as well as nurture their creative thinking and problem-solving skills. Moreover, the integration of linear algebra with subjects like ideological and political education, the history of mathematics, mathematical applications, and patriotism is suggested in order to foster students’ ethical and ideological qualities, patriotic sentiments, and sense of social responsibility. Lastly, various evaluation approaches for linear algebra are discussed, including written exams, problem-solving assessments, practical projects evaluations, and discussions and group collaborations, which aim to ensure the effectiveness of assessment.