数学文化视域下《常微分方程》教学实践研究

Research on the Teaching Practice of “Ordinary Differential Equations” from the Perspective of Mathematical Culture

摘要: 首先，通过深入研读教材，凭借对数学知识体系和教育理念的深刻理解，在教材的第一章到第五章内容中精准找到了数学文化融入的切入点。其次，为了让数学文化融入教学的理念更具实操性，我们精心提供了具体的教学案例。最后，为了验证数学文化融入教学的实际效果，设计了严谨的实验。选取条件相近的两个班级，分别作为实验组和对照组。实验组采用融入数学文化的创新教学方法，对照组则沿用传统教学模式。在一个完整的教学周期结束后，对两组学生的总成绩进行全面且深入的分析。结果表明：实验组学生在学习过程中展现出更高的积极性和主动性，课堂参与度明显提升，课后主动探索知识的频率增加，这充分说明融入数学文化能够有效激发学生的学习兴趣；从成绩数据来看，实验组的平均成绩显著高于对照组，证明了数学文化的融入对提升教学效果有着不可忽视的促进作用。

Abstract: First of all, through in-depth study of the teaching materials and relying on a profound understanding of the mathematics knowledge system and educational concepts, we accurately found the entry points for integrating mathematical culture into the content of Chapters 1 to 5. Secondly, in order to make the concept of integrating mathematical culture into teaching more practical, we carefully provided specific teaching cases. Finally, in order to verify the actual effect of the teaching, we designed a rigorous experiment. Two classes with similar conditions were selected as the experimental group and the control group respectively. The experimental group adopted an innovative teaching method that integrates mathematical culture, while the control group continued to use the traditional teaching mode. After the completion of a complete teaching cycle, a comprehensive and in-depth analysis was conducted on the total scores of the students in the two groups. The results show that: the students in the experimental group showed higher enthusiasm and initiative in the learning process, with a significant increase in classroom participation and a higher frequency of actively exploring knowledge after class, which fully demonstrates that integrating mathematical culture can effectively stimulate students’ interest in learning. From the perspective of the score data, the average score of the experimental group was significantly higher than that of the control group, proving that the integration of mathematical culture has a non-negligible promoting effect on improving teaching effectiveness.