利用数学模型促进学生理解数学概念的物理应用
Using Mathcasts to Facilitate Student Comprehension of Physical Applications of Math Concepts
摘要：
许多物理教育研究者已经讨论了学生的数学技能和物理课堂表现之间的正相关关系。因此，为了加强他们在物理课程中的表现，教授们努力提高学生的数学能力，但课堂时间的限制迫使教师将他们的课程计划集中在物理概念上，而不是更新数学材料。为了保留课堂时间，许多教师正在转向通过翻转教室和MOOC（大规模在线开放课程）的方式在课外授课。视频可以加强解决问题的技能，一些PER研究人员已经开始将解决问题和课堂讲座转移到YouTube上。YouTube视频甚至在课堂讨论中使用的历史也相对较长。我们的目标是为学生提供视频，直接连接从以前的类数学概念（如点/叉积，积分的限制，求解方程组等）。E&M的概念在其当前的类（如功/扭矩，连续对象的电场，基尔霍夫定律等）。
英文摘要：
Many Physics Education Researchers have discussed the positive correlation between students' incoming mathematics skills and performance in their physics classes. Thus, in order to strengthen their performance gains in their physics courses, professors strive to bolster students' mathematics abilities but in-class time constraints force instructors to focus their lesson plans on physics concepts rather than renewing mathematics material. For the sake of preserving in-class time, many instructors are turning to lecture delivery outside of class by way of flipped classrooms and MOOCs (Massive Online Open Courses). Videos can strengthen problem-solving skill sets and some PER researchers have begun moving worked problems and class lectures to YouTube. YouTube videos even have a relatively long history of being used for in-class discussions. We aimed to provide students with videos that directly connected mathematics concepts from previous classes (such as dot/cross products, limits of integration, solving systems of equations, etc.) to E&M concepts in their current class (such as work/torque, electric fields from continuous objects, Kirchoff's Laws, etc.).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
