Many physics learners take the specific mathematical representations they are using as part of their learning and doing physics for granted. The paper addresses this problem by highlighting two goals. The first is to show how a historical investigation from history of science can be transformed into a concrete lesson plan in physics, in a physics teacher education program. The second is to explore the role of mathematical representations in scientific inquiry and discuss the educational affordances of historical case studies in explicating this role in preservice and in-service physics teacher education. The historical artifact that formed the basis of the lesson is a page cataloged as “folio 116v” that contains Galileo’s authentic laboratory notes and calculations written at the time he made his revolutionary discoveries on freely falling objects and projectile motion. To understand and reproduce Galileo’s authentic notes, students must first become explicitly aware that the mathematical tools and representations available in his time were radically different from the tools and representations available to physics learners now. The activity thus sparked discussions and reflections on the meanings and implications of mathematical representations in learning and doing physics.

中文翻译：

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跟随伽利略的脚步指导物理教师

许多物理学习者将他们正在使用的特定数学表示作为他们学习和学习物理的一部分是理所当然的。本文通过强调两个目标来解决这个问题。第一个是展示如何在物理教师教育计划中将科学史的历史调查转化为具体的物理课程计划。第二是探索数学表示在科学探究中的作用，并讨论历史案例研究在解释这一作用在职前和在职物理教师教育中的教育意义。构成本课程基础的历史文物是一个编目为“folio 116v”的页面，其中包含伽利略在他对自由落体和弹丸运动做出革命性发现时所写的真实实验室笔记和计算。要理解和复制伽利略的真实笔记，学生必须首先明确意识到他那个时代可用的数学工具和表示与现在物理学习者可用的工具和表示完全不同。因此，该活动引发了对数学表示在学习和做物理中的意义和影响的讨论和反思。学生必须首先清楚地意识到，他那个时代可用的数学工具和表示与现在物理学习者可用的工具和表示完全不同。因此，该活动引发了对数学表示在学习和做物理中的意义和影响的讨论和反思。学生必须首先清楚地意识到，他那个时代可用的数学工具和表示与现在物理学习者可用的工具和表示完全不同。因此，该活动引发了对数学表示在学习和做物理中的意义和影响的讨论和反思。