标题： 三角函数导数理解中的全球盲点：一项跨国分析 显示英文标题

标题： Global Blind Spot in Understanding Trigonometric Derivatives: A Multinational Analysis

摘要： 三角函数导数在数学和物理学中都是基础性的，但它们的正确应用，尤其是弧度和角度之间的区别，对全球大学生来说都是一个重大挑战。 本研究发现了一种普遍的“盲点”，即对三角函数导数及其对物理系统影响的理解，突显了物理教育中的一个重要空白。 一项针对来自以色列、美国、中国和印度的769名大学生（主要是本科和研究生STEM专业）的跨国调查，评估了他们在数学和物理情境中区分弧度和角度的能力，重点在于简谐运动。 结果显示，只有26.3%的学生正确识别出三角函数导数的著名表达式仅在弧度下成立，而70.7%的学生错误地认为弧度和角度都有效。 值得注意的是，学生在物理情境中对弧度的识别能力（59.0%的正确回答）比在数学情境中有所提高，这表明当应用数学概念时，学生会依赖熟悉的物理方程作为认知参考点。 这些误解在全球范围内普遍存在，表明这是一个普遍的挑战。 研究结果突显了需要进行课程改革，以更好地将数学形式主义与物理应用联系起来。 显示英文摘要

摘要： Trigonometric derivatives are fundamental in both mathematics and physics, yet their proper application, particularly the distinction between radians and degrees, poses a significant challenge for college students globally. This study identifies a widespread "blind spot" in understanding trigonometric derivatives and their implications for physical systems, highlighting a critical gap in physics education. A multinational survey of 769 college students, primarily undergraduate and graduate STEM majors, from Israel, the United States, China, and India assessed their ability to differentiate between radians and degrees in mathematical and physical contexts, focusing on harmonic motion. Results reveal that only 26.3\% of students correctly identified that the well-known expressions for trigonometric derivatives hold exclusively in radians, while 70.7\% incorrectly assumed both radians and degrees are valid. Notably, students demonstrated improved recognition of radians in physical contexts (59.0\% correct responses) compared to mathematical ones, suggesting that students rely on familiar physical equations as cognitive reference points when applying mathematical concepts. These misunderstandings appear worldwide, suggesting a universal challenge. The findings highlight the need for curriculum reforms to better connect mathematical formalism with physical application.