Obstacles to Mathematization in Physics: The Case of the Differential
Obstacles to Mathematization in Physics: The Case of the Differential
复制标题
物理学数学化的障碍：微分的情况
作者：
R. Lopez;J. M. Sáez;J. M. Torregrosa
通过微积分将物理情况数学化的过程需要理解物理学背景下微分的合理性和意义。在这项工作中，四个不同的概念，在物理学中的微分确定和评估，根据他们的实用程序的实现过程。我们还提出了一个实证研究，以探讨有关微分的概念，是由学生在物理中使用，以及学生的看法，他们希望如何在物理中使用微分。结果支持的说法，学生有一个准排他性的概念的微分作为一个无穷小的增量，他们认为，他们的老师只希望他们使用微分的算法的方式，没有一个健全的理解他们在做什么，为什么。这些结果与传统物理教学对物化过程缺乏重视有关。最后，提出了一些行动建议。
The process of the mathematization of physical situations through differential calculus requires an understanding of the justification for and the meaning of the differential in the context of physics. In this work, four different conceptions about the differential in physics are identified and assessed according to their utility for the mathematization process. We also present an empirical study to probe the conceptions about the differential that are used by students in physics, as well students’ perceptions of how they are expected to use differential calculus in physics. The results support the claim that students have a quasi-exclusive conception of the differential as an infinitesimal increment and that they perceive that their teachers only expect them to use differential calculus in an algorithmic way, without a sound understanding of what are they doing and why. These results are related to the lack of attention paid by conventional physics teaching to the mathematization process. Finally, some proposals for action are put forward.